WebSVN – wimsdev – /trunk/wims/public_html/scripts/js/jsxgraph/jsxgraphcore.js

/* Version 0.96 */
/*
Copyright 2008-2012
Matthias Ehmann,
Michael Gerhaeuser,
Carsten Miller,
Bianca Valentin,
Alfred Wassermann,
Peter Wilfahrt
This file is part of JSXGraph.
JSXGraph is free software dual licensed under the GNU LGPL or MIT License.
You can redistribute it and/or modify it under the terms of the
* GNU Lesser General Public License as published by
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version
OR
* MIT License: https://github.com/jsxgraph/jsxgraph/blob/master/LICENSE.MIT
JSXGraph is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU Lesser General Public License for more details.
You should have received a copy of the GNU Lesser General Public License and
the MIT License along with JSXGraph. If not, see <http://www.gnu.org/licenses/>
and <http://opensource.org/licenses/MIT/>.
*/
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u=[],a=[],f=(i[1]-i[0])/s,l=i[0],c,h,p,d,v,m=r.length,g,y=[],b=0;e.isString(t)&&(t=n[t]||n.euler),g=t.s;for(c=0;c<m;c++)u[c]=r[c];for(h=0;h<s;h++){y[b]=[];for(c=0;c<m;c++)y[b][c]=u[c];b++,d=[];for(p=0;p<g;p++){for(c=0;c<m;c++)a[c]=0;for(v=0;v<p;v++)for(c=0;c<m;c++)a[c]+=t.A[p][v]*f*d[v][c];for(c=0;c<m;c++)a[c]+=u[c];d.push(o(l+t.c[p]*f,a))}for(c=0;c<m;c++)a[c]=0;for(v=0;v<g;v++)for(c=0;c<m;c++)a[c]+=t.b[v]*d[v][c];for(c=0;c<m;c++)u[c]=u[c]+f*a[c];l+=f}return y},maxIterationsRoot:80,maxIterationsMinimize:500,fzero:function(n,r,i){var s=e.Math.eps,o=this.maxIterationsRoot,u=0,a=0,f=s,l,c,h,p,d,v,m,g,y,b,w,E,S,x,T,N,C,k,L,A;if(e.isArray(r)){if(r.length<2)throw new Error("JXG.Math.Numerics.fzero: length of array x0 has to be at least 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s=f(e,t,n);s[0]>r?(a(e,t,s[1],r,i),a(e,s[1],n,r,i)):i.push(e[n])},f=function(n,r,i){var s=0,o=r,u,a,f,l,c,h,p,d,v,m,g;if(i-r<2)return[-1,0];f=n[r].scrCoords,l=n[i].scrCoords;if(isNaN(f[1]+f[2]+l[1]+l[2]))return[NaN,i];for(a=r+1;a<i;a++)c=n[a].scrCoords,h=c[1]-f[1],p=c[2]-f[2],d=l[1]-f[1],v=l[2]-f[2],m=d*d+v*v,m>=e.Math.eps?(g=(h*d+p*v)/m,g<0?g=0:g>1&&(g=1),h-=g*d,p-=g*v,u=h*h+p*p):(g=0,u=h*h+p*p),u>s&&(s=u,o=a);return[t.sqrt(s),o]};u=n.length,s=0;while(s<u&&isNaN(n[s].scrCoords[1]+n[s].scrCoords[2]))s++;o=u-1;while(o>s&&isNaN(n[o].scrCoords[1]+n[o].scrCoords[2]))o--;return s>o||s==u||(i[0]=n[s],a(n,s,o,r,i)),i}}}(JXG,Math),JXG.Math.Statistics={sum:function(e){var t,n=e.length,r=0;for(t=0;t<n;t++)r+=e[t];return r},prod:function(e){var t,n=e.length,r=1;for(t=0;t<n;t++)r*=e[t];return r},mean:function(e){return e.length>0?this.sum(e)/e.length:0},median:function(e){var t,n;return e.length>0?(t=e.slice(0),t.sort(function(e,t){return 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e.Coords(e.COORDS_BY_USR,[0,0],n),l=new e.Coords(e.COORDS_BY_USR,[n.canvasWidth,n.canvasHeight],n),c,h,p,d=1,v=0,m=0,g=0,y,b,w,E,S,x,T,N=function(e,t){var n;for(n=0;n<t.length;n++)if(t[n].id===e)return!0;return!1},C=n.options.locus;e.Server.modules.geoloci===t&&e.Server.loadModule("geoloci");if(e.Server.modules.geoloci===t)throw new Error("JSXGraph: Unable to load JXG.Server module 'geoloci.py'.");E=f.usrCoords[1],S=l.usrCoords[1],x=l.usrCoords[2],T=f.usrCoords[2];if(C.translateToOrigin&&n.listOfFreePoints.length>0){C.toOrigin!==t&&C.toOrigin!=null&&N(C.toOrigin.id,n.listOfFreePoints)?c=C.toOrigin:c=n.listOfFreePoints[0],v=c.symbolic.x,m=c.symbolic.y;for(p=0;p<n.listOfFreePoints.length;p++)n.listOfFreePoints[p].symbolic.x-=v,n.listOfFreePoints[p].symbolic.y-=m;E-=v,S-=v,x-=m,T-=m;if(C.translateTo10&&n.listOfFreePoints.length>1){C.to10!==t&&C.to10!=null&&C.to10.id!=C.toOrigin.id&&N(C.to10.id,n.listOfFreePoints)?h=C.to10:n.listOfFreePoints[0].id==c.id?h=n.listOfFreePoints[1]:h=n.listOfFreePoints[0],g=e.Math.Geometry.rad([1,0],[0,0],[h.symbolic.x,h.symbolic.y]),y=Math.cos(-g),b=Math.sin(-g);for(p=0;p<n.listOfFreePoints.length;p++)w=n.listOfFreePoints[p].symbolic.x,n.listOfFreePoints[p].symbolic.x=y*n.listOfFreePoints[p].symbolic.x-b*n.listOfFreePoints[p].symbolic.y,n.listOfFreePoints[p].symbolic.y=b*w+y*n.listOfFreePoints[p].symbolic.y;h.symbolic.y=0,w=E,E=y*E-b*x,x=b*w+y*x,w=S,S=y*S-b*T,T=b*w+y*T;if(C.stretch&&Math.abs(h.symbolic.x)>e.Math.eps){d=h.symbolic.x;for(p=0;p<n.listOfFreePoints.length;p++)n.listOfFreePoints[p].symbolic.x/=d,n.listOfFreePoints[p].symbolic.y/=d;for(p in n.objects)n.objects[p].elementClass==e.OBJECT_CLASS_CIRCLE&&n.objects[p].method=="pointRadius"&&(a[p]=n.objects[p].radius,n.objects[p].radius/=d);E/=d,S/=d,x/=d,T/=d,h.symbolic.x=1}}for(p=0;p<n.listOfFreePoints.length;p++)w=n.listOfFreePoints[p].symbolic.x,Math.abs(w)<e.Math.eps&&(n.listOfFreePoints[p].symbolic.x=0),Math.abs(w-Math.round(w))<e.Math.eps&&(n.listOfFreePoints[p].symbolic.x=Math.round(w)),w=n.listOfFreePoints[p].symbolic.y,Math.abs(w)<e.Math.eps&&(n.listOfFreePoints[p].symbolic.y=0),Math.abs(w-Math.round(w))<e.Math.eps&&(n.listOfFreePoints[p].symbolic.y=Math.round(w))}s=this.generatePolynomials(n,r),o=s.join(","),this.cbp=function(e){u=e},this.cb=e.bind(this.cbp,this),e.Server.modules.geoloci.lociCoCoA(E,S,x,T,i,o,d,g,v,m,this.cb,!0),this.clearSymbolicCoordinates(n);for(p in a)n.objects[p].radius=a[p];return u}}}(JXG),JXG.Math.Geometry={},JXG.extend(JXG.Math.Geometry,{angle:function(e,t,n){var r=[],i=[],s=[],o,u,a,f;return e.coords==null?(r[0]=e[0],r[1]=e[1]):(r[0]=e.coords.usrCoords[1],r[1]=e.coords.usrCoords[2]),t.coords==null?(i[0]=t[0],i[1]=t[1]):(i[0]=t.coords.usrCoords[1],i[1]=t.coords.usrCoords[2]),n.coords==null?(s[0]=n[0],s[1]=n[1]):(s[0]=n.coords.usrCoords[1],s[1]=n.coords.usrCoords[2]),o=r[0]-i[0],u=r[1]-i[1],a=s[0]-i[0],f=s[1]-i[1],Math.atan2(o*f-u*a,o*a+u*f)},trueAngle:function(e,t,n){return this.rad(e,t,n)*57.29577951308232},rad:function(e,t,n){var r,i,s,o,u,a,f;return e.coords==null?(r=e[0],i=e[1]):(r=e.coords.usrCoords[1],i=e.coords.usrCoords[2]),t.coords==null?(s=t[0],o=t[1]):(s=t.coords.usrCoords[1],o=t.coords.usrCoords[2]),n.coords==null?(u=n[0],a=n[1]):(u=n.coords.usrCoords[1],a=n.coords.usrCoords[2]),f=Math.atan2(a-o,u-s)-Math.atan2(i-o,r-s),f<0&&(f+=6.283185307179586),f},angleBisector:function(e,t,n,r){var i=e.coords.usrCoords,s=t.coords.usrCoords,o=n.coords.usrCoords,u=i[1]-s[1],a=i[2]-s[2],f=Math.sqrt(u*u+a*a),l,c,h;return JXG.exists(r)||(r=e.board),u/=f,a/=f,l=Math.acos(u),a<0&&(l*=-1),l<0&&(l+=2*Math.PI),u=o[1]-s[1],a=o[2]-s[2],f=Math.sqrt(u*u+a*a),u/=f,a/=f,c=Math.acos(u),a<0&&(c*=-1),c<0&&(c+=2*Math.PI),h=(l+c)*.5,l>c&&(h+=Math.PI),u=Math.cos(h)+s[1],a=Math.sin(h)+s[2],new JXG.Coords(JXG.COORDS_BY_USER,[u,a],r)},reflection:function(e,t,n){var r=t.coords.usrCoords,i=e.point1.coords.usrCoords,s=e.point2.coords.usrCoords,o,u,a,f,l,c,h;return JXG.exists(n)||(n=t.board),l=s[1]-i[1],c=s[2]-i[2],o=r[1]-i[1],u=r[2]-i[2],h=(l*u-c*o)/(l*l+c*c),a=r[1]+2*h*c,f=r[2]-2*h*l,new JXG.Coords(JXG.COORDS_BY_USER,[a,f],n)},rotation:function(e,t,n,r){var i=t.coords.usrCoords,s=e.coords.usrCoords,o,u,a,f,l,c;return JXG.exists(r)||(r=t.board),o=i[1]-s[1],u=i[2]-s[2],a=Math.cos(n),f=Math.sin(n),l=o*a-u*f+s[1],c=o*f+u*a+s[2],new JXG.Coords(JXG.COORDS_BY_USER,[l,c],r)},perpendicular:function(e,t,n){var r=e.point1.coords.usrCoords,i=e.point2.coords.usrCoords,s=t.coords.usrCoords,o,u,a,f,l,c,h,p;return JXG.exists(n)||(n=t.board),t==e.point1?(o=r[1]+i[2]-r[2],u=r[2]-i[1]+r[1],a=!0):t==e.point2?(o=i[1]+r[2]-i[2],u=i[2]-r[1]+i[1],a=!1):Math.abs(r[1]-i[1])>JXG.Math.eps&&Math.abs(s[2]-(r[2]-i[2])*(s[1]-r[1])/(r[1]-i[1])-r[2])<JXG.Math.eps||Math.abs(r[1]-i[1])<=JXG.Math.eps&&Math.abs(r[1]-s[1])<JXG.Math.eps?(o=s[1]+i[2]-s[2],u=s[2]-i[1]+s[1],a=!0,Math.abs(o-s[1])<JXG.Math.eps&&Math.abs(u-s[2])<JXG.Math.eps&&(o=s[1]+r[2]-s[2],u=s[2]-r[1]+s[1],a=!1)):(f=r[2]-i[2],l=r[1]-i[1],c=i[1]*f-i[2]*l,h=s[1]*l+s[2]*f,p=f*f+l*l,Math.abs(p)<JXG.Math.eps&&(p=JXG.Math.eps),o=(c*f+h*l)/p,u=(h*f-c*l)/p,a=!0),[new JXG.Coords(JXG.COORDS_BY_USER,[o,u],n),a]},circumcenterMidpoint:JXG.shortcut(JXG.Math.Geometry,"circumcenter"),circumcenter:function(e,t,n,r){var i=e.coords.usrCoords,s=t.coords.usrCoords,o=n.coords.usrCoords,u,a,f,l;return JXG.exists(r)||(r=e.board),u=[s[0]-i[0],-s[2]+i[2],s[1]-i[1]],a=[(i[0]+s[0])*.5,(i[1]+s[1])*.5,(i[2]+s[2])*.5],f=JXG.Math.crossProduct(u,a),u=[o[0]-s[0],-o[2]+s[2],o[1]-s[1]],a=[(s[0]+o[0])*.5,(s[1]+o[1])*.5,(s[2]+o[2])*.5],l=JXG.Math.crossProduct(u,a),new JXG.Coords(JXG.COORDS_BY_USER,JXG.Math.crossProduct(f,l),r)},distance:function(e,t){var n=0,r,i;if(e.length!=t.length)return NaN;i=e.length;for(r=0;r<i;r++)n+=(e[r]-t[r])*(e[r]-t[r]);return Math.sqrt(n)},affineDistance:function(e,t){var n;return e.length!=t.length?NaN:(n=this.distance(e,t),n>JXG.Math.eps&&(Math.abs(e[0])<JXG.Math.eps||Math.abs(t[0])<JXG.Math.eps)?Infinity:n)},calcStraight:function(e,t,n,r){var i,s,o,u,a,f,l,c,h,p,d,v;r==null&&(r=10),a=e.visProp.straightfirst,f=e.visProp.straightlast,Math.abs(t.scrCoords[0])<JXG.Math.eps&&(a=!0),Math.abs(n.scrCoords[0])<JXG.Math.eps&&(f=!0);if(!a&&!f)return;l=[],l[0]=e.stdform[0]-e.stdform[1]*e.board.origin.scrCoords[1]/e.board.unitX+e.stdform[2]*e.board.origin.scrCoords[2]/e.board.unitY,l[1]=e.stdform[1]/e.board.unitX,l[2]=e.stdform[2]/-e.board.unitY;if(isNaN(l[0]+l[1]+l[2]))return;c=[],c[0]=JXG.Math.crossProduct(l,[r,0,1]),c[1]=JXG.Math.crossProduct(l,[r,1,0]),c[2]=JXG.Math.crossProduct(l,[-r-e.board.canvasHeight,0,1]),c[3]=JXG.Math.crossProduct(l,[-r-e.board.canvasWidth,1,0]);for(h=0;h<4;h++)if(Math.abs(c[h][0])>JXG.Math.eps){for(p=2;p>0;p--)c[h][p]/=c[h][0];c[h][0]=1}i=!1,s=!1,!a&&Math.abs(t.usrCoords[0])>=JXG.Math.eps&&t.scrCoords[1]>=0&&t.scrCoords[1]<=e.board.canvasWidth&&t.scrCoords[2]>=0&&t.scrCoords[2]<=e.board.canvasHeight&&(i=!0),!f&&Math.abs(n.usrCoords[0])>=JXG.Math.eps&&n.scrCoords[1]>=0&&n.scrCoords[1]<=e.board.canvasWidth&&n.scrCoords[2]>=0&&n.scrCoords[2]<=e.board.canvasHeight&&(s=!0),Math.abs(c[1][0])<JXG.Math.eps?(o=c[0],u=c[2]):Math.abs(c[0][0])<JXG.Math.eps?(o=c[1],u=c[3]):c[1][2]<0?(o=c[0],c[3][2]>e.board.canvasHeight?u=c[2]:u=c[3]):c[1][2]>e.board.canvasHeight?(o=c[2],c[3][2]<0?u=c[0]:u=c[3]):(o=c[1],c[3][2]<0?u=c[0]:c[3][2]>e.board.canvasHeight?u=c[2]:u=c[3]),o=new JXG.Coords(JXG.COORDS_BY_SCREEN,o.slice(1),e.board),u=new JXG.Coords(JXG.COORDS_BY_SCREEN,u.slice(1),e.board);if(!i&&!s){if(!a&&f&&!this.isSameDirection(t,n,o)&&!this.isSameDirection(t,n,u))return;if(a&&!f&&!this.isSameDirection(n,t,o)&&!this.isSameDirection(n,t,u))return}i?s||(this.isSameDir(t,n,o,u)?v=u:v=o):s?this.isSameDir(t,n,o,u)?d=o:d=u:this.isSameDir(t,n,o,u)?(d=o,v=u):(v=o,d=u),d&&t.setCoordinates(JXG.COORDS_BY_USER,d.usrCoords.slice(1)),v&&n.setCoordinates(JXG.COORDS_BY_USER,v.usrCoords.slice(1))},isSameDir:function(e,t,n,r){var i=t.usrCoords[1]-e.usrCoords[1],s=t.usrCoords[2]-e.usrCoords[2],o=r.usrCoords[1]-n.usrCoords[1],u=r.usrCoords[2]-n.usrCoords[2];return Math.abs(t.usrCoords[0])<JXG.Math.eps&&(i=t.usrCoords[1],s=t.usrCoords[2]),Math.abs(e.usrCoords[0])<JXG.Math.eps&&(i=-e.usrCoords[1],s=-e.usrCoords[2]),i*o+s*u>=0},isSameDirection:function(e,t,n){var r,i,s,o,u=!1;r=t.usrCoords[1]-e.usrCoords[1],i=t.usrCoords[2]-e.usrCoords[2],s=n.usrCoords[1]-e.usrCoords[1],o=n.usrCoords[2]-e.usrCoords[2],Math.abs(r)<JXG.Math.eps&&(r=0),Math.abs(i)<JXG.Math.eps&&(i=0),Math.abs(s)<JXG.Math.eps&&(s=0),Math.abs(o)<JXG.Math.eps&&(o=0);if(r>=0&&s>=0){if(i>=0&&o>=0||i<=0&&o<=0)u=!0}else r<=0&&s<=0&&(i>=0&&o>=0||i<=0&&o<=0)&&(u=!0);return u},intersectLineLine:function(e,t,n){var r=e.point1.coords.usrCoords,i=e.point2.coords.usrCoords,s=t.point1.coords.usrCoords,o=t.point2.coords.usrCoords,u,a,f,l,c;return JXG.exists(n)||(n=e.board),u=r[1]*i[2]-r[2]*i[1],a=s[1]*o[2]-s[2]*o[1],f=(i[2]-r[2])*(s[1]-o[1])-(r[1]-i[1])*(o[2]-s[2]),Math.abs(f)<JXG.Math.eps&&(f=JXG.Math.eps),l=(u*(s[1]-o[1])-a*(r[1]-i[1]))/f,c=(a*(i[2]-r[2])-u*(o[2]-s[2]))/f,new JXG.Coords(JXG.COORDS_BY_USER,[l,c],n)},intersectCircleLine:function(e,t,n){var r=t.point1.coords.usrCoords,i=t.point2.coords.usrCoords,s=e.center.coords.usrCoords,o,u,a,f,l,c,h,p,d,v,m,g,y,b,w,E,S,x,T;return JXG.exists(n)||(n=t.board),o=t.point1.Dist(t.point2),o>0?(u=e.center.Dist(t.point1),a=e.center.Dist(t.point2),f=(u*u+o*o-a*a)/(2*o),l=u*u-f*f,l=l<0?0:l,c=Math.sqrt(l),h=e.Radius(),p=Math.sqrt(h*h-c*c),d=i[1]-r[1],v=i[2]-r[2],m=s[1]+c/o*v,g=s[2]-c/o*d,u=i[1]*v-i[2]*d,a=m*d+g*v,y=v*v+d*d,Math.abs(y)<JXG.Math.eps&&(y=JXG.Math.eps),b=(u*v+a*d)/y,w=(a*v-u*d)/y,E=p/o,S=new JXG.Coords(JXG.COORDS_BY_USER,[b+E*d,w+E*v],n),x=new JXG.Coords(JXG.COORDS_BY_USER,[b-E*d,w-E*v],n),T=e.center.coords.distance(JXG.COORDS_BY_USER,S),h<T-1||isNaN(T)?[0]:[2,S,x]):[0]},intersectCircleCircle:function(e,t,n){var r={},i=e.Radius(),s=t.Radius(),o=e.center.coords.usrCoords,u=t.center.coords.usrCoords,a,f,l,c,h,p,d;return JXG.exists(n)||(n=e.board),a=i+s,f=Math.abs(i-s),l=e.center.coords.distance(JXG.COORDS_BY_USER,t.center.coords),l>a?[0]:l<f?[0]:l==0?[0]:(r[0]=1,c=u[1]-o[1],h=u[2]-o[2],p=(l*l-s*s+i*i)/(2*l),d=Math.sqrt(i*i-p*p),r[1]=new JXG.Coords(JXG.COORDS_BY_USER,[o[1]+p/l*c+d/l*h,o[2]+p/l*h-d/l*c],n),r[2]=new JXG.Coords(JXG.COORDS_BY_USER,[o[1]+p/l*c-d/l*h,o[2]+p/l*h+d/l*c],n),r)},meet:function(e,t,n,r){var i=JXG.Math.eps;return Math.abs(e[3])<i&&Math.abs(t[3])<i?this.meetLineLine(e,t,n,r):Math.abs(e[3])>=i&&Math.abs(t[3])<i?this.meetLineCircle(t,e,n,r):Math.abs(e[3])<i&&Math.abs(t[3])>=i?this.meetLineCircle(e,t,n,r):this.meetCircleCircle(e,t,n,r)},meetLineLine:function(e,t,n,r){var i=JXG.Math.crossProduct(e,t);return Math.abs(i[0])>JXG.Math.eps&&(i[1]/=i[0],i[2]/=i[0],i[0]=1),new JXG.Coords(JXG.COORDS_BY_USER,i,r)},meetLineCircle:function(e,t,n,r){var i,s,o,u,a,f,l,c,h,p;return t[4]<JXG.Math.eps?Math.abs(JXG.Math.innerProduct([1,t[6],t[7]],e,3))<JXG.Math.eps?new JXG.Coords(JXG.COORDS_BY_USER,t.slice(6,8),r):new JXG.Coords(JXG.COORDS_BY_USER,[NaN,NaN],r):(o=t[0],s=t.slice(1,3),i=t[3],u=e[0],a=e.slice(1,3),f=i,l=s[0]*a[1]-s[1]*a[0],c=i*u*u-(s[0]*a[0]+s[1]*a[1])*u+o,h=l*l-4*f*c,h>=0?(h=Math.sqrt(h),p=[(-l+h)/(2*f),(-l-h)/(2*f)],n==0?new JXG.Coords(JXG.COORDS_BY_USER,[-p[0]*-a[1]-u*a[0],-p[0]*a[0]-u*a[1]],r):new JXG.Coords(JXG.COORDS_BY_USER,[-p[1]*-a[1]-u*a[0],-p[1]*a[0]-u*a[1]],r)):new JXG.Coords(JXG.COORDS_BY_USER,[0,0,0],r))},meetCircleCircle:function(e,t,n,r){var i;return e[4]<JXG.Math.eps?Math.abs(this.distance(e.slice(6,2),t.slice(6,8))-t[4])<JXG.Math.eps?new JXG.Coords(JXG.COORDS_BY_USER,e.slice(6,8),r):new JXG.Coords(JXG.COORDS_BY_USER,[0,0,0],r):t[4]<JXG.Math.eps?Math.abs(this.distance(t.slice(6,2),e.slice(6,8))-e[4])<JXG.Math.eps?new JXG.Coords(JXG.COORDS_BY_USER,t.slice(6,8),r):new JXG.Coords(JXG.COORDS_BY_USER,[0,0,0],r):(i=[t[3]*e[0]-e[3]*t[0],t[3]*e[1]-e[3]*t[1],t[3]*e[2]-e[3]*t[2],0,1,Infinity,Infinity,Infinity],i=JXG.Math.normalize(i),this.meetLineCircle(i,e,n,r))},meetCurveCurve:function(e,t,n,r,i){var s=0,o,u,a,f,l,c,h,p,d,v,m,g,y,b;JXG.exists(i)||(i=e.board),arguments.callee.t1memo?(o=arguments.callee.t1memo,u=arguments.callee.t2memo):(o=n,u=r),c1X=function(t){return e.X.apply(e,[t])},c1Y=function(t){return e.Y.apply(e,[t])},c2X=function(e){return t.X.apply(t,[e])},c2Y=function(e){return t.Y.apply(t,[e])},p=e.X(o)-t.X(u),d=e.Y(o)-t.Y(u),v=p*p+d*d,m=i.D(e.X,e),g=i.D(t.X,t),y=i.D(e.Y,e),b=i.D(t.Y,t);while(v>JXG.Math.eps&&s<10)a=m(o),f=-g(u),l=y(o),c=-b(u),h=a*c-f*l,o-=(c*p-f*d)/h,u-=(a*d-l*p)/h,p=e.X(o)-t.X(u),d=e.Y(o)-t.Y(u),v=p*p+d*d,s++;return arguments.callee.t1memo=o,arguments.callee.t2memo=u,Math.abs(o)<Math.abs(u)?new JXG.Coords(JXG.COORDS_BY_USER,[e.X(o),e.Y(o)],i):new JXG.Coords(JXG.COORDS_BY_USER,[t.X(u),t.Y(u)],i)},meetCurveLine:function(e,t,n,r,i){var s=[0,NaN,NaN],o,u,a;JXG.exists(r)||(r=e.board);for(o=0;o<=1;o++)if(arguments[o].elementClass==JXG.OBJECT_CLASS_CURVE)u=arguments[o];else{if(arguments[o].elementClass!=JXG.OBJECT_CLASS_LINE)throw new Error("JSXGraph: Can't call meetCurveLine with parent class "+arguments[o].elementClass+".");a=arguments[o]}return u.visProp.curvetype==="plot"?s=this.meetCurveLineDiscrete(u,a,n,r,i):s=this.meetCurveLineContinuous(u,a,n,r),s},meetCurveLineContinuous:function(e,t,n,r){var i,s,o,e,t,u,a,f,l,c,h,p,d,v;u=function(n){return t.stdform[0]+t.stdform[1]*e.X(n)+t.stdform[2]*e.Y(n)},arguments.callee.t1memo?(h=arguments.callee.t1memo,i=JXG.Math.Numerics.root(u,h)):(h=e.minX(),p=e.maxX(),i=JXG.Math.Numerics.root(u,[h,p])),arguments.callee.t1memo=i,d=e.X(i),v=e.Y(i);if(n==1){arguments.callee.t2memo&&(h=arguments.callee.t2memo,s=JXG.Math.Numerics.root(u,h));if(!(Math.abs(s-i)>.1&&Math.abs(d-e.X(s))>.1&&Math.abs(v-e.Y(s))>.1)){l=20,c=(e.maxX()-e.minX())/l,f=e.minX();for(o=0;o<l;o++){s=JXG.Math.Numerics.root(u,[f,f+c]);if(Math.abs(s-i)>.1&&Math.abs(d-e.X(s))>.1&&Math.abs(v-e.Y(s))>.1)break;f+=c}}i=s,arguments.callee.t2memo=i}return Math.abs(u(i))>JXG.Math.eps?a=NaN:a=1,new JXG.Coords(JXG.COORDS_BY_USER,[a,e.X(i),e.Y(i)],r)},meetCurveLineDiscrete:function(e,t,n,r,i){var s,o,u,a,f,l,c=0,h,p,d=!1;s=e.numberPoints,i!=null&&(p=i.point,JXG.exists(p)&&!p.visProp.alwaysintersect&&(d=!0)),f=new JXG.Coords(JXG.COORDS_BY_USER,[0,NaN,NaN],r),a=[1,e.X(0),e.Y(0)];for(o=1;o<s;o++){u=a.slice(0),a=[1,e.X(o),e.Y(o)],l=this.distance(u,a);if(l<JXG.Math.eps)continue;h=this.meetSegmentSegment(u,a,t.point1.coords.usrCoords,t.point2.coords.usrCoords,r);if(0<=h[1]&&h[1]<=1){if(c==n){if(d&&(t.visProp.straightfirst==0&&h[2]<0||t.visProp.straightlast==0&&h[2]>1))break;f=new JXG.Coords(JXG.COORDS_BY_USER,h[0],r);break}c++}}return f},meetSegmentSegment:function(e,t,n,r,i){var s=JXG.Math.crossProduct(e,t),o=JXG.Math.crossProduct(n,r),u=JXG.Math.crossProduct(s,o),a=u[0],f,l,c;return Math.abs(a)<Math.eps?[u,Number.Infinity,Number.Infinity]:(c=[n[1]-e[1],n[2]-e[2]],f=(c[0]*(r[2]-n[2])-c[1]*(r[1]-n[1]))/a,l=(c[0]*(t[2]-e[2])-c[1]*(t[1]-e[1]))/a,[u,f,l])},projectPointToCircle:function(e,t,n){var r,i,s=t.center.coords.usrCoords,o,u,a;return JXG.exists(n)||(n=e.board),JXG.isPoint(e)?(r=e.coords.distance(JXG.COORDS_BY_USER,t.center.coords),i=e.coords.usrCoords):(r=e.distance(JXG.COORDS_BY_USER,t.center.coords),i=e.usrCoords),Math.abs(r)<JXG.Math.eps&&(r=JXG.Math.eps),a=t.Radius()/r,o=s[1]+a*(i[1]-s[1]),u=s[2]+a*(i[2]-s[2]),new JXG.Coords(JXG.COORDS_BY_USER,[o,u],n)},projectPointToLine:function(e,t,n){var r=[0,t.stdform[1],t.stdform[2]];return JXG.exists(n)||(n=e.board),r=JXG.Math.crossProduct(r,e.coords.usrCoords),this.meetLineLine(r,t.stdform,0,n)},projectCoordsToSegment:function(e,t,n){var r=[n[1]-t[1],n[2]-t[2]],i=[e[1]-t[1],e[2]-t[2]],s,o,u;return Math.abs(r[0])<JXG.Math.eps&&Math.abs(r[1])<JXG.Math.eps?t:(s=JXG.Math.innerProduct(i,r),o=JXG.Math.innerProduct(r,r),s/=o,[[1,s*r[0]+t[1],s*r[1]+t[2]],s])},projectPointToCurve:function(e,t,n){JXG.exists(n)||(n=e.board);var r=e.X(),i=e.Y(),s=e.position||0,o=this.projectCoordsToCurve(r,i,s,t,n);return e.position=o[1],o[0]},projectCoordsToCurve:function(e,t,n,r,i){var s,o,u,a,f,l,c,h,p,d,v,m,g,y,b,w,E,S,x=Number.POSITIVE_INFINITY,T,n,N,C,k,L,A;JXG.exists(i)||(i=r.board);if(r.visProp.curvetype=="parameter"||r.visProp.curvetype=="polar"){T=function(n){var i=e-r.X(n),s=t-r.Y(n);return i*i+s*s},k=T(n),A=20,L=(r.maxX()-r.minX())/A,N=r.minX();for(o=0;o<A;o++)C=T(N),C<k&&(n=N,k=C),N+=L;n=JXG.Math.Numerics.root(JXG.Math.Numerics.D(T),n),n<r.minX()&&(n=r.maxX()+n-r.minX()),n>r.maxX()&&(n=r.minX()+n-r.maxX()),s=new JXG.Coords(JXG.COORDS_BY_USER,[r.X(n),r.Y(n)],i)}else if(r.visProp.curvetype=="plot"){n=0,c=x,r.numberPoints==0?s=[0,1,1]:s=[r.Z(0),r.X(0),r.Y(0)];if(r.numberPoints>1){y=[r.Z(0),r.X(0),r.Y(0)];for(o=0;o<r.numberPoints-1;o++)b=[r.Z(o+1),r.X(o+1),r.Y(o+1)],v=[1,e,t],S=this.projectCoordsToSegment(v,y,b),p=S[1],m=S[0],0<=p&&p<=1?(h=this.distance(m,v),g=o+p):p<0?(m=y,h=this.distance(y,v),g=o):p>1&&o+1==r.numberPoints-1&&(m=b,h=this.distance(m,v),g=r.numberPoints-1),h<c&&(c=h,n=g,s=m),y=b}s=new JXG.Coords(JXG.COORDS_BY_USER,s,i)}else n=e,e=n,t=r.Y(n),s=new JXG.Coords(JXG.COORDS_BY_USER,[e,t],i);return[r.updateTransform(s),n]},projectPointToTurtle:function(e,t,n){var r,i,s,o,u,a=0,f=0,l=Number.POSITIVE_INFINITY,c,h,p,d=t.objects.length;JXG.exists(n)||(n=e.board);for(u=0;u<d;u++)h=t.objects[u],h.elementClass==JXG.OBJECT_CLASS_CURVE&&(r=this.projectPointToCurve(e,h),c=this.distance(r.usrCoords,e.coords.usrCoords),c<l&&(s=r.usrCoords[1],o=r.usrCoords[2],i=e.position,l=c,p=h,f=a),a+=h.numberPoints);return r=new JXG.Coords(JXG.COORDS_BY_USER,[s,o],n),e.position=i+f,p.updateTransform(r)},projectPointToPoint:function(e,t,n){return t.coords},distPointLine:function(e,t){var n=t[1],r=t[2],i=t[0],s;return Math.abs(n)+Math.abs(r)<JXG.Math.eps?Number.POSITIVE_INFINITY:(s=n*e[1]+r*e[2]+i*1,n*=n,r*=r,Math.abs(s)/Math.sqrt(n+r))}}),JXG.Math.Poly={},JXG.Math.Poly.Ring=function(e){this.vars=e},JXG.extend(JXG.Math.Poly.Ring.prototype,{}),JXG.Math.Poly.Monomial=function(e,t,n){var r;if(!JXG.exists(e))throw new Error("JSXGraph error: In JXG.Math.Poly.monomial missing parameter 'ring'.");JXG.isArray(n)||(n=[]),n=n.slice(0,e.vars.length);for(r=n.length;r<e.vars.length;r++)n.push(0);this.ring=e,this.coefficient=t||0,this.exponents=JXG.deepCopy(n)},JXG.extend(JXG.Math.Poly.Monomial.prototype,{copy:function(){return new JXG.Math.Poly.Monomial(this.ring,this.coefficient,this.exponents)},print:function(){var e=[],t;for(t=0;t<this.ring.vars.length;t++)e.push(this.ring.vars[t]+"^"+this.exponents[t]);return this.coefficient+"*"+e.join("*")}}),JXG.Math.Poly.Polynomial=function(e,t){var n=function(){},r;if(!JXG.exists(e))throw new Error("JSXGraph error: In JXG.Math.Poly.polynomial missing parameter 'ring'.");JXG.exists(t)&&typeof t=="string"?r=n(t):r=[],this.ring=e,this.monomials=r},JXG.extend(JXG.Math.Poly.Polynomial.prototype,{findSignature:function(e){var t;for(t=0;t<this.monomials.length;t++)if(JXG.cmpArrays(this.monomials[t].exponents,e))return t;return-1},addSubMonomial:function(e,t){var n;n=this.findSignature(e.exponents),n>-1?this.monomials[n].coefficient+=t*e.coefficient:(e.coefficient*=t,this.monomials.push(e))},add:function(e){var t;if(!JXG.exists(e)||e.ring!==this.ring)throw new Error("JSXGraph error: In JXG.Math.Poly.polynomial.add either summand is undefined or rings don't match.");if(JXG.isArray(e.exponents))this.addSubMonomial(e,1);else for(t=0;t<e.monomials.length;t++)this.addSubMonomial(e.monomials[t],1)},sub:function(e){var t;if(!JXG.exists(e)||e.ring!==this.ring)throw new Error("JSXGraph error: In JXG.Math.Poly.polynomial.sub either summand is undefined or rings don't match.");if(JXG.isArray(e.exponents))this.addSubMonomial(e,-1);else for(t=0;t<e.monomials.length;t++)this.addSubMonomial(e.monomials[t],-1)},copy:function(){var e,t;t=new JXG.Math.Poly.Polynomial(this.ring);for(e=0;e<this.monomials.length;e++)t.monomials.push(this.monomials[e].copy());return t},print:function(){var e=[],t;for(t=0;t<this.monomials.length;t++)e.push("("+this.monomials[t].print()+")");return e.join("+")}}),JXG.Complex=function(e,t){this.isComplex=!0,typeof e=="undefined"&&(e=0),typeof t=="undefined"&&(t=0),e.isComplex&&(t=e.imaginary,e=e.real),this.real=e,this.imaginary=t,this.absval=0,this.angle=0},JXG.extend(JXG.Complex.prototype,{toString:function(){return""+this.real+" + "+this.imaginary+"i"},add:function(e){typeof e=="number"?this.real+=e:(this.real+=e.real,this.imaginary+=e.imaginary)},sub:function(e){typeof e=="number"?this.real-=e:(this.real-=e.real,this.imaginary-=e.imaginary)},mult:function(e){var t,n;typeof e=="number"?(this.real*=e,this.imaginary*=e):(t=this.real,n=this.imaginary,this.real=t*e.real-n*e.imaginary,this.imaginary=t*e.imaginary+n*e.real)},div:function(e){var t,n,r;if(typeof e=="number"){if(Math.abs(e)<Math.eps){this.real=Infinity,this.imaginary=Infinity;return}this.real/=e,this.imaginary/=e}else{if(Math.abs(e.real)<Math.eps&&Math.abs(e.imaginary)<Math.eps){this.real=Infinity,this.imaginary=Infinity;return}t=e.real*e.real+e.imaginary*e.imaginary,r=this.real,n=this.imaginary,this.real=(r*e.real+n*e.imaginary)/t,this.imaginary=(n*e.real-r*e.imaginary)/t}},conj:function(){this.imaginary*=-1}}),JXG.C={},JXG.C.add=function(e,t){var n=new JXG.Complex(e);return n.add(t),n},JXG.C.sub=function(e,t){var n=new JXG.Complex(e);return n.sub(t),n},JXG.C.mult=function(e,t){var n=new JXG.Complex(e);return n.mult(t),n},JXG.C.div=function(e,t){var n=new JXG.Complex(e);return n.div(t),n},JXG.C.conj=function(e){var t=new JXG.Complex(e);return t.conj(),t},JXG.C.abs=function(e){var t=new JXG.Complex(e);return t.conj(),t.mult(e),Math.sqrt(t.real)},JXG.AbstractRenderer=function(){this.vOffsetText=0,this.enhancedRendering=!0,this.container=null,this.type=""},JXG.extend(JXG.AbstractRenderer.prototype,{_updateVisual:function(e,t,n){var r;if(n||this.enhancedRendering)t=t||{},e.visProp.draft?this.setDraft(e):(t.stroke||(this.setObjectStrokeWidth(e,e.visProp.strokewidth),this.setObjectStrokeColor(e,e.visProp.strokecolor,e.visProp.strokeopacity)),t.fill||this.setObjectFillColor(e,e.visProp.fillcolor,e.visProp.fillopacity),t.dash||this.setDashStyle(e,e.visProp),t.shadow||this.setShadow(e),t.gradient||this.setShadow(e))},drawPoint:function(e){var t,n=JXG.Point.prototype.normalizeFace.call(this,e.visProp.face);n==="o"?t="ellipse":n==="[]"?t="rect":t="path",this.appendChildPrim(this.createPrim(t,e.id),e.visProp.layer),this.appendNodesToElement(e,t),this._updateVisual(e,{dash:!0,shadow:!0},!0),this.updatePoint(e)},updatePoint:function(e){var t=e.visProp.size,n=JXG.Point.prototype.normalizeFace.call(this,e.visProp.face);isNaN(e.coords.scrCoords[2]+e.coords.scrCoords[1])||(this._updateVisual(e,{dash:!1,shadow:!1}),t*=!e.board||!e.board.options.point.zoom?1:Math.sqrt(e.board.zoomX*e.board.zoomY),n==="o"?this.updateEllipsePrim(e.rendNode,e.coords.scrCoords[1],e.coords.scrCoords[2],t+1,t+1):n==="[]"?this.updateRectPrim(e.rendNode,e.coords.scrCoords[1]-t,e.coords.scrCoords[2]-t,t*2,t*2):this.updatePathPrim(e.rendNode,this.updatePathStringPoint(e,t,n),e.board),this.setShadow(e))},changePointStyle:function(e){var t=this.getElementById(e.id);JXG.exists(t)&&this.remove(t),this.drawPoint(e),JXG.clearVisPropOld(e),e.visProp.visible||this.hide(e),e.visProp.draft&&this.setDraft(e)},drawLine:function(e){this.appendChildPrim(this.createPrim("line",e.id),e.visProp.layer),this.appendNodesToElement(e,"lines"),this.updateLine(e)},updateLine:function(e){var t=new JXG.Coords(JXG.COORDS_BY_USER,e.point1.coords.usrCoords,e.board),n=new JXG.Coords(JXG.COORDS_BY_USER,e.point2.coords.usrCoords,e.board),r=null;if(e.visProp.firstarrow||e.visProp.lastarrow)r=0;JXG.Math.Geometry.calcStraight(e,t,n,r),this.updateLinePrim(e.rendNode,t.scrCoords[1],t.scrCoords[2],n.scrCoords[1],n.scrCoords[2],e.board),this.makeArrows(e),this._updateVisual(e,{fill:!0})},drawTicks:function(e){var t=this.createPrim("path",e.id);this.appendChildPrim(t,e.visProp.layer),this.appendNodesToElement(e,"path")},updateTicks:function(e,t,n,r,i){},drawCurve:function(e){this.appendChildPrim(this.createPrim("path",e.id),e.visProp.layer),this.appendNodesToElement(e,"path"),this._updateVisual(e,{shadow:!0},!0),this.updateCurve(e)},updateCurve:function(e){this._updateVisual(e),e.visProp.handdrawing?this.updatePathPrim(e.rendNode,this.updatePathStringBezierPrim(e),e.board):this.updatePathPrim(e.rendNode,this.updatePathStringPrim(e),e.board),e.numberPoints>1&&this.makeArrows(e)},drawEllipse:function(e){this.appendChildPrim(this.createPrim("ellipse",e.id),e.visProp.layer),this.appendNodesToElement(e,"ellipse"),this.updateEllipse(e)},updateEllipse:function(e){this._updateVisual(e);var t=e.Radius();t>0&&Math.abs(e.center.coords.usrCoords[0])>JXG.Math.eps&&!isNaN(t+e.center.coords.scrCoords[1]+e.center.coords.scrCoords[2])&&t*e.board.unitX<2e6&&this.updateEllipsePrim(e.rendNode,e.center.coords.scrCoords[1],e.center.coords.scrCoords[2],t*e.board.unitX,t*e.board.unitY)},drawPolygon:function(e){this.appendChildPrim(this.createPrim("polygon",e.id),e.visProp.layer),this.appendNodesToElement(e,"polygon"),this.updatePolygon(e)},updatePolygon:function(e){this._updateVisual(e,{stroke:!0,dash:!0}),this.updatePolygonPrim(e.rendNode,e)},displayCopyright:function(e,t){},drawInternalText:function(e){},updateInternalText:function(e){},drawText:function(e){var t,n;e.visProp.display==="html"?(t=this.container.ownerDocument.createElement("div"),t.style.position="absolute",t.className=e.visProp.cssclass,this.container.style.zIndex==""?n=0:n=parseInt(this.container.style.zIndex),t.style.zIndex=n+e.board.options.layer.text,this.container.appendChild(t),t.setAttribute("id",this.container.id+"_"+e.id)):t=this.drawInternalText(e),e.rendNode=t,e.htmlStr="",this.updateText(e)},updateText:function(e){var t=e.plaintext;e.visProp.visible&&(this.updateTextStyle(e,!1),e.visProp.display==="html"?(isNaN(e.coords.scrCoords[1]+e.coords.scrCoords[2])||(e.visProp.anchorx==="right"?e.rendNode.style.right=parseInt(e.board.canvasWidth-e.coords.scrCoords[1])+"px":e.visProp.anchorx==="middle"?e.rendNode.style.left=parseInt(e.coords.scrCoords[1]-.5*e.size[0])+"px":e.rendNode.style.left=parseInt(e.coords.scrCoords[1])+"px",e.visProp.anchory==="top"?e.rendNode.style.top=parseInt(e.coords.scrCoords[2]+this.vOffsetText)+"px":e.visProp.anchory==="middle"?e.rendNode.style.top=parseInt(e.coords.scrCoords[2]-.5*e.size[1]+this.vOffsetText)+"px":e.rendNode.style.top=parseInt(e.coords.scrCoords[2]-e.size[1]+this.vOffsetText)+"px"),e.htmlStr!==t&&(e.rendNode.innerHTML=t,e.htmlStr=t,e.visProp.usemathjax?MathJax.Hub.Queue(["Typeset",MathJax.Hub,e.rendNode]):e.visProp.useasciimathml&&AMprocessNode(e.rendNode,!1)),this.transformImage(e,e.transformations)):this.updateInternalText(e))},updateTextStyle:function(e,t){var n,r,i,s,o=e.visProp;t?(i=o.highlightstrokecolor,r=o.highlightstrokeopacity,s=o.highlightcssclass):(i=o.strokecolor,r=o.strokeopacity,s=o.cssclass);if(e.visProp.display==="html"||this.type!="canvas"){n=JXG.evaluate(e.visProp.fontsize);if(e.visPropOld.fontsize!=n){try{e.rendNode.style.fontSize=n+"px"}catch(u){e.rendNode.style.fontSize=n}e.visPropOld.fontsize=n}e.visPropOld.cssclass!=s&&(e.rendNode.className=s,e.visPropOld.cssclass=s)}return e.visProp.display==="html"?this.setObjectStrokeColor(e,i,r):this.updateInternalTextStyle(e,i,r),this},updateInternalTextStyle:function(e,t,n){this.setObjectStrokeColor(e,t,n)},drawImage:function(e){},updateImage:function(e){this.updateRectPrim(e.rendNode,e.coords.scrCoords[1],e.coords.scrCoords[2]-e.size[1],e.size[0],e.size[1]),this.updateImageURL(e),this.transformImage(e,e.transformations),this._updateVisual(e,{stroke:!0,dash:!0},!0)},joinTransforms:function(e,t){var n=[[1,0,0],[0,1,0],[0,0,1]],r=e.board.origin.scrCoords[1],i=e.board.origin.scrCoords[2],s=e.board.unitX,o=e.board.unitY,u=[[1,0,0],[-r,1,0],[-i,0,1]],a=[[1,0,0],[0,1/s,0],[0,0,-1/o]],f=[[1,0,0],[0,s,0],[0,0,-o]],l=[[1,0,0],[r,1,0],[i,0,1]],c,h=t.length;for(c=0;c<h;c++)n=JXG.Math.matMatMult(u,n),n=JXG.Math.matMatMult(a,n),n=JXG.Math.matMatMult(t[c].matrix,n),n=JXG.Math.matMatMult(f,n),n=JXG.Math.matMatMult(l,n);return n},transformImage:function(e,t){},updateImageURL:function(e){},updateImageStyle:function(e,t){var n=t?el.visProp.highlightcssclass:el.visProp.cssclass;e.rendNode.className=n},appendChildPrim:function(e,t){},appendNodesToElement:function(e,t){},createPrim:function(e,t){return null},remove:function(e){},makeArrows:function(e){},updateEllipsePrim:function(e,t,n,r,i){},updateLinePrim:function(e,t,n,r,i,s){},updatePathPrim:function(e,t,n){},updatePathStringPoint:function(e,t,n){},updatePathStringPrim:function(e){},updatePathStringBezierPrim:function(e){},updatePolygonPrim:function(e,t){},updateRectPrim:function(e,t,n,r,i){},setPropertyPrim:function(e,t,n){},show:function(e){},hide:function(e){},setBuffering:function(e,t){},setDashStyle:function(e){},setDraft:function(e){if(!e.visProp.draft)return;var t=e.board.options.elements.draft.color,n=e.board.options.elements.draft.opacity;e.type===JXG.OBJECT_TYPE_POLYGON?this.setObjectFillColor(e,t,n):(e.elementClass===JXG.OBJECT_CLASS_POINT?this.setObjectFillColor(e,t,n):this.setObjectFillColor(e,"none",0),this.setObjectStrokeColor(e,t,n),this.setObjectStrokeWidth(e,e.board.options.elements.draft.strokeWidth))},removeDraft:function(e){e.type===JXG.OBJECT_TYPE_POLYGON?this.setObjectFillColor(e,e.visProp.fillcolor,e.visProp.fillopacity):(e.type===JXG.OBJECT_CLASS_POINT&&this.setObjectFillColor(e,e.visProp.fillcolor,e.visProp.fillopacity),this.setObjectStrokeColor(e,e.visProp.strokecolor,e.visProp.strokeopacity),this.setObjectStrokeWidth(e,e.visProp.strokewidth))},setGradient:function(e){},updateGradient:function(e){},setObjectFillColor:function(e,t,n){},setObjectStrokeColor:function(e,t,n){},setObjectStrokeWidth:function(e,t){},setShadow:function(e){},highlight:function(e){var t,n=e.visProp;if(!n.draft){if(e.type===JXG.OBJECT_TYPE_POLYGON){this.setObjectFillColor(e,n.highlightfillcolor,n.highlightfillopacity);for(t=0;t<e.borders.length;t++)this.setObjectStrokeColor(e.borders[t],e.borders[t].visProp.highlightstrokecolor,e.borders[t].visProp.highlightstrokeopacity)}else e.type===JXG.OBJECT_TYPE_TEXT?this.updateTextStyle(e,!0):e.type===JXG.OBJECT_TYPE_IMAGE?this.updateImageStyle(e,!0):(this.setObjectStrokeColor(e,n.highlightstrokecolor,n.highlightstrokeopacity),this.setObjectFillColor(e,n.highlightfillcolor,n.highlightfillopacity));n.highlightstrokewidth&&this.setObjectStrokeWidth(e,Math.max(n.highlightstrokewidth,n.strokewidth))}return this},noHighlight:function(e){var t,n=e.visProp;if(!e.visProp.draft){if(e.type===JXG.OBJECT_TYPE_POLYGON){this.setObjectFillColor(e,n.fillcolor,n.fillopacity);for(t=0;t<e.borders.length;t++)this.setObjectStrokeColor(e.borders[t],e.borders[t].visProp.strokecolor,e.borders[t].visProp.strokeopacity)}else e.type===JXG.OBJECT_TYPE_TEXT?this.updateTextStyle(e,!1):e.type===JXG.OBJECT_TYPE_IMAGE?this.updateImageStyle(e,!1):(this.setObjectStrokeColor(e,n.strokecolor,n.strokeopacity),this.setObjectFillColor(e,n.fillcolor,n.fillopacity));this.setObjectStrokeWidth(e,n.strokewidth)}return this},suspendRedraw:function(){},unsuspendRedraw:function(){},drawZoomBar:function(e){var t,n,r=function(r,i){var s;s=t.createElement("span"),n.appendChild(s),s.appendChild(document.createTextNode(r)),JXG.addEvent(s,"click",i,e)};t=e.containerObj.ownerDocument,n=t.createElement("div"),n.setAttribute("id",e.containerObj.id+"_navigationbar"),n.style.color=e.options.navbar.strokeColor,n.style.backgroundColor=e.options.navbar.fillColor,n.style.padding=e.options.navbar.padding,n.style.position=e.options.navbar.position,n.style.fontSize=e.options.navbar.fontSize,n.style.cursor=e.options.navbar.cursor,n.style.zIndex=e.options.navbar.zIndex,e.containerObj.appendChild(n),n.style.right=e.options.navbar.right,n.style.bottom=e.options.navbar.bottom,r("\u00a0\u2013\u00a0",e.zoomOut),r("\u00a0o\u00a0",e.zoom100),r("\u00a0+\u00a0",e.zoomIn),r("\u00a0\u2190\u00a0",e.clickLeftArrow),r("\u00a0\u2193\u00a0",e.clickUpArrow),r("\u00a0\u2191\u00a0",e.clickDownArrow),r("\u00a0\u2192\u00a0",e.clickRightArrow)},getElementById:function(e){return document.getElementById(this.container.id+"_"+e)},resize:function(e,t){}}),JXG.NoRenderer=function(){this.enhancedRendering=!1,this.type="no"},JXG.extend(JXG.NoRenderer.prototype,{drawPoint:function(e){},updatePoint:function(e){},changePointStyle:function(e){},drawLine:function(e){},updateLine:function(e){},drawTicks:function(e){},updateTicks:function(e,t,n,r,i){},drawCurve:function(e){},updateCurve:function(e){},drawEllipse:function(e){},updateEllipse:function(e){},drawPolygon:function(e){},updatePolygon:function(e){},displayCopyright:function(e,t){},drawInternalText:function(e){},updateInternalText:function(e){},drawText:function(e){},updateText:function(e){},updateTextStyle:function(e,t){},updateInternalTextStyle:function(e,t,n){},drawImage:function(e){},updateImage:function(e){},transformImage:function(e,t){},updateImageURL:function(e){},appendChildPrim:function(e,t){},appendNodesToElement:function(e,t){},createPrim:function(e,t){return null},remove:function(e){},makeArrows:function(e){},updateEllipsePrim:function(e,t,n,r,i){},updateLinePrim:function(e,t,n,r,i,s){},updatePathPrim:function(e,t,n){},updatePathStringPoint:function(e,t,n){},updatePathStringPrim:function(e){},updatePathStringBezierPrim:function(e){},updatePolygonPrim:function(e,t){},updateRectPrim:function(e,t,n,r,i){},setPropertyPrim:function(e,t,n){},show:function(e){},hide:function(e){},setBuffering:function(e,t){},setDashStyle:function(e){},setDraft:function(e){},removeDraft:function(e){},setGradient:function(e){},updateGradient:function(e){},setObjectFillColor:function(e,t,n){},setObjectStrokeColor:function(e,t,n){},setObjectStrokeWidth:function(e,t){},setShadow:function(e){},highlight:function(e){},noHighlight:function(e){},suspendRedraw:function(){},unsuspendRedraw:function(){},drawZoomBar:function(e){},getElementById:function(e){return null},resize:function(e,t){}}),JXG.FileReader={parseFileContent:function(e,t,n,r){var i=!1;JXG.exists(r)||(r=!0);try{i=new XMLHttpRequest,n.toLowerCase()=="raw"?i.overrideMimeType("text/plain; charset=iso-8859-1"):i.overrideMimeType("text/xml; charset=iso-8859-1")}catch(s){try{i=new ActiveXObject("Msxml2.XMLHTTP")}catch(s){try{i=new ActiveXObject("Microsoft.XMLHTTP")}catch(s){i=!1}}}if(!i){alert("AJAX not activated!");return}i.open("GET",e,r),n.toLowerCase()==="raw"?this.cbp=function(){var e=i;e.readyState==4&&t(e.responseText)}:this.cbp=function(){var e=i;if(e.readyState==4){var r="";typeof e.responseStream=="undefined"||e.responseText.slice(0,2)!="PK"&&JXG.Util.asciiCharCodeAt(e.responseText.slice(0,1),0)!=31?r=e.responseText:r=JXG.Util.Base64.decode(BinFileReader(e)),this.parseString(r,t,n,!1)}},this.cb=JXG.bind(this.cbp,this),i.onreadystatechange=this.cb;try{i.send(null)}catch(s){throw new Error("JSXGraph: A problem occurred while trying to read '"+e+"'.")}},cleanWhitespace:function(e){var t=e.firstChild;while(t!=null)t.nodeType==3&&!/\S/.test(t.nodeValue)?e.removeChild(t):t.nodeType==1&&this.cleanWhitespace(t),t=t.nextSibling},stringToXMLTree:function(e){typeof DOMParser=="undefined"&&(DOMParser=function(){},DOMParser.prototype.parseFromString=function(e,t){if(typeof ActiveXObject!="undefined"){var n=new ActiveXObject("MSXML.DomDocument");return n.loadXML(e),n}});var t=new DOMParser,n=t.parseFromString(e,"text/xml");return this.cleanWhitespace(n),n},parseString:function(e,t,n,r){var i,s,o;n=n.toLowerCase();switch(n){case"cdy":case"cinderella":r&&(e=JXG.Util.Base64.decode(e)),e=JXG.CinderellaReader.readCinderella(e,t),t.xmlString=e;break;case"tracenpoche":t.xmlString=JXG.TracenpocheReader.readTracenpoche(e,t);break;case"graph":e=JXG.GraphReader.readGraph(e,t,!1);break;case"digraph":e=JXG.GraphReader.readGraph(e,t,!0);break;case"geonext":e=JXG.GeonextReader.prepareString(e),o=!0;break;case"geogebra":r=e.slice(0,2)!=="PK",e=JXG.GeogebraReader.prepareString(e,r),o=!0;break;case"intergeo":r&&(e=JXG.Util.Base64.decode(e)),e=JXG.IntergeoReader.prepareString(e),o=!0;break;case"sketch":e=JXG.SketchReader.readSketch(e,t)}o&&(t.xmlString=e,i=this.stringToXMLTree(e),this.readElements(i,t,n))},readElements:function(e,t,n){n.toLowerCase()=="geonext"?(t.suspendUpdate(),e.getElementsByTagName("GEONEXT").length!=0&&JXG.GeonextReader.readGeonext(e,t),t.unsuspendUpdate()):e.getElementsByTagName("geogebra").length!=0?JXG.GeogebraReader.readGeogebra(e,t):n.toLowerCase()=="intergeo"&&JXG.IntergeoReader.readIntergeo(e,t)}},!JXG.isMetroApp()&&typeof navigator!="undefined"&&/msie/i.test(navigator.userAgent)&&!/opera/i.test(navigator.userAgent&&document&&document.write)&&document.write('<script type="text/vbscript">\nFunction Base64Encode(inData)\n Const Base64 = "ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789+/"\n Dim cOut, sOut, I\n For I = 1 To LenB(inData) Step 3\n Dim nGroup, pOut, sGroup\n nGroup = &H10000 * AscB(MidB(inData, I, 1)) + _\n &H100 * MyASC(MidB(inData, I + 1, 1)) + MyASC(MidB(inData, I + 2, 1))\n nGroup = Oct(nGroup)\n nGroup = String(8 - Len(nGroup), "0") & nGroup\n pOut = Mid(Base64, CLng("&o" & Mid(nGroup, 1, 2)) + 1, 1) + _\n Mid(Base64, CLng("&o" & Mid(nGroup, 3, 2)) + 1, 1) + _\n Mid(Base64, CLng("&o" & Mid(nGroup, 5, 2)) + 1, 1) + _\n Mid(Base64, CLng("&o" & Mid(nGroup, 7, 2)) + 1, 1)\n sOut = sOut + pOut\n Next\n Select Case LenB(inData) Mod 3\n Case 1: \'8 bit final\n sOut = Left(sOut, Len(sOut) - 2) + "=="\n Case 2: \'16 bit final\n sOut = Left(sOut, Len(sOut) - 1) + "="\n End Select\n Base64Encode = sOut\nEnd Function\n\nFunction MyASC(OneChar)\n If OneChar = "" Then MyASC = 0 Else MyASC = AscB(OneChar)\nEnd Function\n\nFunction BinFileReader(xhr)\n Dim byteString\n Dim b64String\n Dim i\n byteString = xhr.responseBody\n ReDim byteArray(LenB(byteString))\n For i = 1 To LenB(byteString)\n byteArray(i-1) = AscB(MidB(byteString, i, 1))\n Next\n b64String = Base64Encode(byteString)\n BinFileReader = b64String\nEnd Function\n</script>\n'),JXG.GeonextParser={},JXG.GeonextParser.replacePow=function(e){var t,n,r,i,s,o,u,a,f,l,c;e=e.replace(/(\s*)\^(\s*)/g,"^"),f=e.indexOf("^");while(f>=0){a=e.slice(0,f),l=e.slice(f+1);if(a.charAt(a.length-1)==")"){t=1,n=a.length-2;while(n>=0&&t>0)r=a.charAt(n),r==")"?t++:r=="("&&t--,n--;if(t!=0)throw new Error("JSXGraph: Missing '(' in expression");i="",o=a.substring(0,n+1),u=n;while(u>=0&&o.substr(u,1).match(/([\w\.]+)/))i=RegExp.$1+i,u--;i+=a.substring(n+1,a.length),i=i.replace(/([\+\*\%\^\-\/\]\[])/g,"\\$1")}else i="[\\w\\.]+";if(l.match(/^([\w\.]*$)/)){t=1,n=RegExp.$1.length;while(n<l.length&&t>0)r=l.charAt(n),r==")"?t--:r=="("&&t++,n++;if(t!=0)throw new Error("JSXGraph: Missing ')' in expression");s=l.substring(0,n),s=s.replace(/([\($\+\*\%\^\-\/\[\]])/g,"\\$1")}else s="[\\w\\.]+";c=new RegExp("("+i+")\\^("+s+")"),e=e.replace(c,"JXG.Math.pow($1,$2)"),f=e.indexOf("^")}return e},JXG.GeonextParser.replaceIf=function(e){var t="",n,r,i=null,s=null,o=null,u,a,f,l,c,h,p;u=e.indexOf("If(");if(u<0)return e;e=e.replace(/""/g,"0");while(u>=0){n=e.slice(0,u),r=e.slice(u+3),f=1,a=0,l=-1,c=-1;while(a<r.length&&f>0)h=r.charAt(a),h==")"?f--:h=="("?f++:h==","&&f==1&&(l<0?l=a:c=a),a++;p=r.slice(0,a-1),r=r.slice(a);if(l<0)return"";if(c<0)return"";i=p.slice(0,l),s=p.slice(l+1,c),o=p.slice(c+1),i=this.replaceIf(i),s=this.replaceIf(s),o=this.replaceIf(o),t+=n+"(("+i+")?"+"("+s+"):("+o+"))",e=r,i=null,s=null,u=e.indexOf("If(")}return t+=r,t},JXG.GeonextParser.replaceSub=function(e){if(!e.indexOf)return e;var t=e.indexOf("_{"),n;while(t>=0)e=e.substr(0,t)+e.substr(t).replace(/_\{/,""),n=e.substr(t).indexOf("}"),n>=0&&(e=e.substr(0,n)+e.substr(n).replace(/\}/,"")),t=e.indexOf("_{");t=e.indexOf("_");while(t>=0)e=e.substr(0,t)+e.substr(t).replace(/_(.?)/,"$1"),t=e.indexOf("_");return e},JXG.GeonextParser.replaceSup=function(e){if(!e.indexOf)return e;var t=e.indexOf("^{"),n;while(t>=0)e=e.substr(0,t)+e.substr(t).replace(/\^\{/,""),n=e.substr(t).indexOf("}"),n>=0&&(e=e.substr(0,n)+e.substr(n).replace(/\}/,"")),t=e.indexOf("^{");t=e.indexOf("^");while(t>=0)e=e.substr(0,t)+e.substr(t).replace(/\^(.?)/,"$1"),t=e.indexOf("^");return e},JXG.GeonextParser.replaceNameById=function(e,t){var n=0,r,i,s,o,u=["X","Y","L","V"];for(o=0;o<u.length;o++){n=e.indexOf(u[o]+"(");while(n>=0)n>=0&&(r=e.indexOf(")",n+2),r>=0&&(i=e.slice(n+2,r),i=i.replace(/\\(['"])?/g,"$1"),s=t.elementsByName[i],e=e.slice(0,n+2)+s.id+e.slice(r))),r=e.indexOf(")",n+2),n=e.indexOf(u[o]+"(",r)}n=e.indexOf("Dist(");while(n>=0)n>=0&&(r=e.indexOf(",",n+5),r>=0&&(i=e.slice(n+5,r),i=i.replace(/\$['"])?/g,"$1"),s=t.elementsByName[i],e=e.slice(0,n+5)+s.id+e.slice(r))),r=e.indexOf(",",n+5),n=e.indexOf(",",r),r=e.indexOf(")",n+1),r>=0&&(i=e.slice(n+1,r),i=i.replace(/\\(['"])?/g,"$1"),s=t.elementsByName[i],e=e.slice(0,n+1)+s.id+e.slice(r)),r=e.indexOf(")",n+1),n=e.indexOf("Dist(",r);u=["Deg","Rad"];for(o=0;o<u.length;o++){n=e.indexOf(u[o]+"(");while(n>=0)n>=0&&(r=e.indexOf(",",n+4),r>=0&&(i=e.slice(n+4,r),i=i.replace(/\\(['"])?/g,"$1"),s=t.elementsByName[i],e=e.slice(0,n+4)+s.id+e.slice(r))),r=e.indexOf(",",n+4),n=e.indexOf(",",r),r=e.indexOf(",",n+1),r>=0&&(i=e.slice(n+1,r),i=i.replace(/\\(['"])?/g,"$1"),s=t.elementsByName[i],e=e.slice(0,n+1)+s.id+e.slice(r)),r=e.indexOf(",",n+1),n=e.indexOf(",",r),r=e.indexOf(")",n+1),r>=0&&(i=e.slice(n+1,r),i=i.replace(/\\(['"])?/g,"$1"),s=t.elementsByName[i],e=e.slice(0,n+1)+s.id+e.slice(r)),r=e.indexOf(")",n+1),n=e.indexOf(u[o]+"(",r)}return e},JXG.GeonextParser.replaceIdByObj=function(e){var t=/(X|Y|L)\(([\w_]+)$/g;return e=e.replace(t,'this.board.objects["$2"].$1()'),t=/(V)$([\w_]+)$/g,e=e.replace(t,'this.board.objects["$2"].Value()'),t=/(Dist)$([\w_]+),([\w_]+)$/g,e=e.replace(t,'this.board.objects["$2"].Dist(this.board.objects["$3"])'),t=/(Deg)$([\w_]+),([ \w\[\w_]+),([\w_]+)$/g,e=e.replace(t,'JXG.Math.Geometry.trueAngle(this.board.objects["$2"],this.board.objects["$3"],this.board.objects["$4"])'),t=/Rad$([\w_]+),([\w_]+),([\w_]+)$/g,e=e.replace(t,'JXG.Math.Geometry.rad(this.board.objects["$1"],this.board.objects["$2"],this.board.objects["$3"])'),t=/N$(.+)$/g,e=e.replace(t,"($1)"),e},JXG.GeonextParser.geonext2JS=function(e,t){var n,r,i,s=["Abs","ACos","ASin","ATan","Ceil","Cos","Exp","Factorial","Floor","Log","Max","Min","Random","Round","Sin","Sqrt","Tan","Trunc"],o=["Math.abs","Math.acos","Math.asin","Math.atan","Math.ceil","Math.cos","Math.exp","JXG.Math.factorial","Math.floor","Math.log","Math.max","Math.min","Math.random","this.board.round","Math.sin","Math.sqrt","Math.tan","Math.ceil"];e=e.replace(/</g,"<"),e=e.replace(/>/g,">"),e=e.replace(/&/g,"&"),r=e,r=this.replaceNameById(r,t),r=this.replaceIf(r),r=this.replacePow(r),r=this.replaceIdByObj(r);for(i=0;i<s.length;i++)n=new RegExp(["(\\W|^)(",s[i],")"].join(""),"ig"),r=r.replace(n,["$1",o[i]].join(""));return r=r.replace(/True/g,"true"),r=r.replace(/False/g,"false"),r=r.replace(/fasle/g,"false"),r=r.replace(/Pi/g,"Math.PI"),r},JXG.GeonextParser.findDependencies=function(e,t,n){typeof n=="undefined"&&(n=e.board);var r=n.elementsByName,i,s,o;for(i in r)i!=e.name&&(r[i].type==JXG.OBJECT_TYPE_TEXT?r[i].visProp.islabel||(o=i.replace(/\[/g,"\\["),o=o.replace(/\]/g,"\\]"),s=new RegExp("\$([\\w\\[\\]'_ ]+,)*("+o+")(,[\\w\\[\\]'_ ]+)*\$","g"),t.search(s)>=0&&r[i].addChild(e)):(o=i.replace(/\[/g,"\\["),o=o.replace(/\]/g,"\\]"),s=new RegExp("\$([\\w\\[\\]'_ ]+,)*("+o+")(,[\\w\\[\\]'_ ]+)*\$","g"),t.search(s)>=0&&r[i].addChild(e)))},JXG.GeonextParser.gxt2jc=function(e,t){var n,r=["Sqrt"],i=["sqrt"];return e=e.replace(/</g,"<"),e=e.replace(/>/g,">"),e=e.replace(/&/g,"&"),n=e,n=this.replaceNameById2(n,t),n=n.replace(/True/g,"true"),n=n.replace(/False/g,"false"),n=n.replace(/fasle/g,"false"),n},JXG.GeonextParser.replaceNameById2=function(e,t){var n=0,r,i,s,o,u=["X","Y","L","V"];for(o=0;o<u.length;o++){n=e.indexOf(u[o]+"(");while(n>=0)n>=0&&(r=e.indexOf(")",n+2),r>=0&&(i=e.slice(n+2,r),i=i.replace(/\\(['"])?/g,"$1"),s=t.elementsByName[i],e=e.slice(0,n+2)+"$('"+s.id+"')"+e.slice(r))),r=e.indexOf(")",n+2),n=e.indexOf(u[o]+"(",r)}n=e.indexOf("Dist(");while(n>=0)n>=0&&(r=e.indexOf(",",n+5),r>=0&&(i=e.slice(n+5,r),i=i.replace(/\\(['"])?/g,"$1"),s=t.elementsByName[i],e=e.slice(0,n+5)+"$('"+s.id+"')"+e.slice(r))),r=e.indexOf(",",n+5),n=e.indexOf(",",r),r=e.indexOf(")",n+1),r>=0&&(i=e.slice(n+1,r),i=i.replace(/\\(['"])?/g,"$1"),s=t.elementsByName[i],e=e.slice(0,n+1)+"$('"+s.id+"')"+e.slice(r)),r=e.indexOf(")",n+1),n=e.indexOf("Dist(",r);u=["Deg","Rad"];for(o=0;o<u.length;o++){n=e.indexOf(u[o]+"(");while(n>=0)n>=0&&(r=e.indexOf(",",n+4),r>=0&&(i=e.slice(n+4,r),i=i.replace(/\\(['"])?/g,"$1"),s=t.elementsByName[i],e=e.slice(0,n+4)+"$('"+s.id+"')"+e.slice(r))),r=e.indexOf(",",n+4),n=e.indexOf(",",r),r=e.indexOf(",",n+1),r>=0&&(i=e.slice(n+1,r),i=i.replace(/\\(['"])?/g,"$1"),s=t.elementsByName[i],e=e.slice(0,n+1)+"$('"+s.id+"')"+e.slice(r)),r=e.indexOf(",",n+1),n=e.indexOf(",",r),r=e.indexOf(")",n+1),r>=0&&(i=e.slice(n+1,r),i=i.replace(/\\(['"])?/g,"$1"),s=t.elementsByName[i],e=e.slice(0,n+1)+"$('"+s.id+"')"+e.slice(r)),r=e.indexOf(")",n+1),n=e.indexOf(u[o]+"(",r)}return e},JXG.Board=function(e,t,n,r,i,s,o,u,a,f,l){this.BOARD_MODE_NONE=0,this.BOARD_MODE_DRAG=1,this.BOARD_MODE_MOVE_ORIGIN=2,this.BOARD_QUALITY_LOW=1,this.BOARD_QUALITY_HIGH=2,this.BOARD_MODE_ZOOM=17,this.BOARD_MODE_CONSTRUCT=16,this.CONSTRUCTION_TYPE_POINT=1129599060,this.CONSTRUCTION_TYPE_CIRCLE=1129595724,this.CONSTRUCTION_TYPE_LINE=1129598030,this.CONSTRUCTION_TYPE_GLIDER=1129596740,this.CONSTRUCTION_TYPE_MIDPOINT=1129598288,this.CONSTRUCTION_TYPE_PERPENDICULAR=1129599044,this.CONSTRUCTION_TYPE_PARALLEL=1129599052,this.CONSTRUCTION_TYPE_INTERSECTION=1129597267,this.container=e,this.containerObj=typeof document!="undefined"?document.getElementById(this.container):null;if(typeof document!="undefined"&&this.containerObj==null)throw new Error("\nJSXGraph: HTML container element '"+e+"' not found.");this.renderer=t,this.grids=[],this.options=JXG.deepCopy(JXG.Options),this.dimension=2,this.jc=new JXG.JessieCode,this.jc.use(this),this.origin={},this.origin.usrCoords=[1,0,0],this.origin.scrCoords=[1,r[0],r[1]],this.zoomX=i,this.zoomY=s,this.unitX=o*this.zoomX,this.unitY=u*this.zoomY,this.canvasWidth=a,this.canvasHeight=f,JXG.exists(n)&&n!==""&&typeof document!="undefined"&&!JXG.exists(document.getElementById(n))?this.id=n:this.id=this.generateId(),JXG.EventEmitter.eventify(this),this.hooks=[],this.dependentBoards=[],this.inUpdate=!1,this.objects={},this.objectsList=[],this.groups={},this.animationObjects={},this.highlightedObjects={},this.numObjects=0,this.elementsByName={},this.mode=this.BOARD_MODE_NONE,this.updateQuality=this.BOARD_QUALITY_HIGH,this.isSuspendedRedraw=!1,this.calculateSnapSizes(),this.drag_dx=0,this.drag_dy=0,this.mouse=null,this.touches=[],this.xmlString="",this.cPos=[],this.touchMoveLast=0,this.downObjects=[],this.showCopyright=!1;if(l!=null&&l||l==null&&this.options.showCopyright)this.showCopyright=!0,this.renderer.displayCopyright(JXG.JSXGraph.licenseText,parseInt(this.options.text.fontSize));this.needsFullUpdate=!1,this.reducedUpdate=!1,this.currentCBDef="none",this.geonextCompatibilityMode=!1,this.options.text.useASCIIMathML&&translateASCIIMath?init():this.options.text.useASCIIMathML=!1,this.hasMouseHandlers=!1,this.hasTouchHandlers=!1,this.hasMouseUp=!1,this.hasTouchEnd=!1,this.addEventHandlers(),this.methodMap={update:"update",on:"on",off:"off",setView:"setBoundingBox",setBoundingBox:"setBoundingBox",migratePoint:"migratePoint",colorblind:"emulateColorblindness"}},JXG.extend(JXG.Board.prototype,{generateName:function(e){if(e.type==JXG.OBJECT_TYPE_TICKS)return"";var t,n=2,r="",i="",s=[],o="",u,a;e.elementClass==JXG.OBJECT_CLASS_POINT?t=["","A","B","C","D","E","F","G","H","I","J","K","L","M","N","O","P","Q","R","S","T","U","V","W","X","Y","Z"]:e.type==JXG.OBJECT_TYPE_ANGLE?t=["","α","β","γ","δ","ε","ζ","η","θ","ι","κ","λ","μ","ν","ξ","ο","π","ρ","σ","τ","υ","φ","χ","ψ","ω"]:t=["","a","b","c","d","e","f","g","h","i","j","k","l","m","n","o","p","q","r","s","t","u","v","w","x","y","z"],e.elementClass!==JXG.OBJECT_CLASS_POINT&&e.elementClass!=JXG.OBJECT_CLASS_LINE&&e.type!=JXG.OBJECT_TYPE_ANGLE&&(e.type===JXG.OBJECT_TYPE_POLYGON?r="P_{":e.elementClass===JXG.OBJECT_CLASS_CIRCLE?r="k_{":e.type===JXG.OBJECT_TYPE_TEXT?r="t_{":r="s_{",i="}");for(u=0;u<n;u++)s[u]=0;while(s[n-1]<t.length){for(s[0]=1;s[0]<t.length;s[0]++){o=r;for(u=n;u>0;u--)o+=t[s[u-1]];if(this.elementsByName[o+i]==null)return o+i}s[0]=t.length;for(u=1;u<n;u++)s[u-1]==t.length&&(s[u-1]=1,s[u]++)}return""},generateId:function(){var e=1;while(JXG.JSXGraph.boards["jxgBoard"+e]!=null)e=Math.round(Math.random()*65535);return"jxgBoard"+e},setId:function(e,t){var n=this.numObjects++,r=e.id;if(r==""||!JXG.exists(r))r=this.id+t+n;return e.id=r,this.objects[r]=e,e._pos=this.objectsList.length,this.objectsList[this.objectsList.length]=e,r},finalizeAdding:function(e){e.visProp.visible||this.renderer.hide(e)},finalizeLabel:function(e){e.hasLabel&&!e.label.content.visProp.islabel&&!e.label.content.visProp.visible&&this.renderer.hide(e.label.content)},getCoordsTopLeftCorner:function(){var e=this.containerObj,t=JXG.getOffset(e),n=document.documentElement.ownerDocument,r=function(t){var n=parseInt(JXG.getStyle(e,t));return isNaN(n)?0:n};return this.cPos.length>0&&(this.mode===JXG.BOARD_MODE_DRAG||this.mode===JXG.BOARD_MODE_MOVE_ORIGIN)?this.cPos:(!e.currentStyle&&n.defaultView&&(e=document.documentElement,t[0]+=r("margin-left"),t[1]+=r("margin-top"),t[0]+=r("border-left-width"),t[1]+=r("border-top-width"),t[0]+=r("padding-left"),t[1]+=r("padding-top"),e=this.containerObj),t[0]+=r("border-left-width"),t[1]+=r("border-top-width"),this.renderer.type!=="vml"&&(t[0]+=r("padding-left"),t[1]+=r("padding-top")),this.cPos=t,t)},getMousePosition:function(e,t){var n=this.getCoordsTopLeftCorner(),r,i;return r=JXG.getPosition(e,t),[r[0]-n[0],r[1]-n[1]]},initMoveOrigin:function(e,t){this.drag_dx=e-this.origin.scrCoords[1],this.drag_dy=t-this.origin.scrCoords[2],this.mode=this.BOARD_MODE_MOVE_ORIGIN},initMoveObject:function(e,t,n,r){var i,s,o=[],u,a=this.objectsList.length,f={visProp:{layer:-1e4}};for(s=0;s<a;s++){i=this.objectsList[s],u=i.hasPoint&&i.hasPoint(e,t),i.visProp.visible&&u&&(i.triggerEventHandlers([r+"down","down"],n),this.downObjects.push(i));if((this.geonextCompatibilityMode&&(i.elementClass==JXG.OBJECT_CLASS_POINT||i.type==JXG.OBJECT_TYPE_TEXT)||!this.geonextCompatibilityMode)&&i.isDraggable&&i.visProp.visible&&!i.visProp.fixed&&!i.visProp.frozen&&u&&i.visProp.layer>=f.visProp.layer){if(JXG.exists(f.label)&&i==f.label.content)continue;f=i,o[0]=f}}return o.length>0&&(this.mode=this.BOARD_MODE_DRAG),this.options.takeFirst&&(o.length=1),o},moveObject:function(e,t,n,r,i){var s=new JXG.Coords(JXG.COORDS_BY_SCREEN,this.getScrCoordsOfMouse(e,t),this),o=n.obj,u;o.type!=JXG.OBJECT_TYPE_GLIDER?(isNaN(n.targets[0].Xprev+n.targets[0].Yprev)||o.setPositionDirectly(JXG.COORDS_BY_SCREEN,s.scrCoords.slice(1),[n.targets[0].Xprev,n.targets[0].Yprev]),n.targets[0].Xprev=s.scrCoords[1],n.targets[0].Yprev=s.scrCoords[2],this.update(o)):o.type==JXG.OBJECT_TYPE_GLIDER&&(u=o.coords,o.setPositionDirectly(JXG.COORDS_BY_USER,s.usrCoords.slice(1)),o.slideObject.elementClass==JXG.OBJECT_CLASS_CIRCLE?o.coords=JXG.Math.Geometry.projectPointToCircle(o,o.slideObject,this):o.slideObject.elementClass==JXG.OBJECT_CLASS_LINE&&(o.coords=JXG.Math.Geometry.projectPointToLine(o,o.slideObject,this)),o.group.length!=0?(o.group[o.group.length-1].dX=o.coords.scrCoords[1]-u.scrCoords[1],o.group[o.group.length-1].dY=o.coords.scrCoords[2]-u.scrCoords[2],o.group[o.group.length-1].update(this)):this.update(o)),o.triggerEventHandlers([i+"drag","drag"],r),this.updateInfobox(o),this.update(),o.highlight(!0)},twoFingerMove:function(e,t,n,r){var i,s,o;if(!JXG.exists(n)||!JXG.exists(n.obj))return;o=n.obj,i=new JXG.Coords(JXG.COORDS_BY_SCREEN,this.getScrCoordsOfMouse(e[0],e[1]),this),s=new JXG.Coords(JXG.COORDS_BY_SCREEN,this.getScrCoordsOfMouse(t[0],t[1]),this),o.elementClass===JXG.OBJECT_CLASS_LINE||o.type===JXG.OBJECT_TYPE_POLYGON?this.twoFingerTouchObject(i,s,n,o):o.elementClass===JXG.OBJECT_CLASS_CIRCLE&&this.twoFingerTouchCircle(i,s,n,o),o.triggerEventHandlers(["touchdrag","drag"],r),n.targets[0].Xprev=i.scrCoords[1],n.targets[0].Yprev=i.scrCoords[2],n.targets[1].Xprev=s.scrCoords[1],n.targets[1].Yprev=s.scrCoords[2]},twoFingerTouchObject:function(e,t,n,r){var i,s,o,u,a,f,l,c,h,p,d,v,m,g,y,b;if(JXG.exists(n.targets[0])&&JXG.exists(n.targets[1])&&!isNaN(n.targets[0].Xprev+n.targets[0].Yprev+n.targets[1].Xprev+n.targets[1].Yprev)){i=e.usrCoords,s=t.usrCoords,o=(new JXG.Coords(JXG.COORDS_BY_SCREEN,[n.targets[0].Xprev,n.targets[0].Yprev],this)).usrCoords,u=(new JXG.Coords(JXG.COORDS_BY_SCREEN,[n.targets[1].Xprev,n.targets[1].Yprev],this)).usrCoords,f=[1,(o[1]+u[1])*.5,(o[2]+u[2])*.5],a=[1,(i[1]+s[1])*.5,(i[2]+s[2])*.5],c=JXG.Math.crossProduct(o,u),l=JXG.Math.crossProduct(i,s),p=JXG.Math.crossProduct(c,l);if(Math.abs(p[0])<JXG.Math.eps)return;p[1]/=p[0],p[2]/=p[0],d=JXG.Math.Geometry.rad(f.slice(1),p.slice(1),a.slice(1)),v=this.create("transform",[d,p[1],p[2]],{type:"rotate"}),v.update(),f=JXG.Math.matVecMult(v.matrix,f),f[1]/=f[0],f[2]/=f[0],m=this.create("transform",[a[1]-f[1],a[2]-f[2]],{type:"translate"}),m.update(),v.melt(m),r.visProp.scalable&&(h=JXG.Math.Geometry.distance(i,s)/JXG.Math.Geometry.distance(o,u),g=this.create("transform",[-a[1],-a[2]],{type:"translate"}),y=this.create("transform",[h,h],{type:"scale"}),b=this.create("transform",[a[1],a[2]],{type:"translate"}),v.melt(g).melt(y).melt(b)),r.elementClass===JXG.OBJECT_CLASS_LINE?v.applyOnce([r.point1,r.point2]):r.type===JXG.OBJECT_TYPE_POLYGON&&v.applyOnce(r.vertices.slice(0,-1)),this.update(),r.highlight(!0)}},twoFingerTouchCircle:function(e,t,n,r){var i,s,o,u,a,f,l,c,h,p,d;if(r.method==="pointCircle"||r.method==="pointLine")return;JXG.exists(n.targets[0])&&JXG.exists(n.targets[1])&&!isNaN(n.targets[0].Xprev+n.targets[0].Yprev+n.targets[1].Xprev+n.targets[1].Yprev)&&(i=e.usrCoords,s=t.usrCoords,o=(new JXG.Coords(JXG.COORDS_BY_SCREEN,[n.targets[0].Xprev,n.targets[0].Yprev],this)).usrCoords,u=(new JXG.Coords(JXG.COORDS_BY_SCREEN,[n.targets[1].Xprev,n.targets[1].Yprev],this)).usrCoords,l=this.create("transform",[i[1]-o[1],i[2]-o[2]],{type:"translate"}),f=JXG.Math.Geometry.rad(u.slice(1),i.slice(1),s.slice(1)),c=this.create("transform",[-i[1],-i[2]],{type:"translate"}),h=this.create("transform",[f],{type:"rotate"}),l.melt(c).melt(h),r.visProp.scalable&&(a=JXG.Math.Geometry.distance(i,s)/JXG.Math.Geometry.distance(o,u),p=this.create("transform",[a,a],{type:"scale"}),l.melt(p)),d=this.create("transform",[i[1],i[2]],{type:"translate"}),l.melt(d),l.applyOnce([r.center]),r.method==="twoPoints"?l.applyOnce([r.point2]):r.method==="pointRadius"&&JXG.isNumber(r.updateRadius.origin)&&r.setRadius(r.radius*a),this.update(r.center),r.highlight(!0))},highlightElements:function(e,t,n,r){var i,s,o,u=this.objectsList.length;for(i=0;i<u;i++)s=this.objectsList[i],o=s.id,s.visProp.highlight&&JXG.exists(s.hasPoint)&&s.visProp.visible&&s.hasPoint(e,t)&&(this.updateInfobox(s),JXG.exists(this.highlightedObjects[o])||(this.highlightedObjects[o]=s,s.highlight(),this.triggerEventHandlers(["mousehit","hit"],n,s,r)),s.mouseover?s.triggerEventHandlers(["mousemove","move"],n):(s.triggerEventHandlers(["mouseover","over"],n),s.mouseover=!0));for(i=0;i<u;i++)s=this.objectsList[i],o=s.id,s.mouseover&&(this.highlightedObjects[o]||(s.triggerEventHandlers(["mouseout","out"],n),s.mouseover=!1))},saveStartPos:function(e,t){var n=[],r,i;if(e.elementClass==JXG.OBJECT_CLASS_LINE)n.push(e.point1.coords.usrCoords),n.push(e.point2.coords.usrCoords);else if(e.elementClass==JXG.OBJECT_CLASS_CIRCLE)n.push(e.center.coords.usrCoords);else if(e.type==JXG.OBJECT_TYPE_GLIDER)n.push([e.position,e.position,e.position]);else if(e.type==JXG.OBJECT_TYPE_POLYGON){i=e.vertices.length-1;for(r=0;r<i;r++)n.push(e.vertices[r].coords.usrCoords)}else if(e.elementClass==JXG.OBJECT_CLASS_POINT)n.push(e.coords.usrCoords);else try{n.push(e.coords.usrCoords)}catch(s){JXG.debug("JSXGraph+ saveStartPos: obj.coords.usrCoords not available: "+s)}i=n.length;for(r=0;r<i;r++)t.Zstart.push(n[r][0]),t.Xstart.push(n[r][1]),t.Ystart.push(n[r][2])},mouseOriginMoveStart:function(e){var t=this.options.pan.enabled&&(!this.options.pan.needShift||e.shiftKey);if(t){var n=this.getMousePosition(e);this.initMoveOrigin(n[0],n[1])}return t},mouseOriginMove:function(e){var t=this.mode===this.BOARD_MODE_MOVE_ORIGIN;if(t){var n=this.getMousePosition(e);this.moveOrigin(n[0],n[1],!0)}return t},touchOriginMoveStart:function(e){var t=e[JXG.touchProperty],n=t.length==2&&JXG.Math.Geometry.distance([t[0].screenX,t[0].screenY],[t[1].screenX,t[1].screenY])<80,r=this.options.pan.enabled&&(!this.options.pan.needTwoFingers||n);if(r){var i=this.getMousePosition(e,0);this.initMoveOrigin(i[0],i[1])}return r},touchOriginMove:function(e){var t=this.mode===this.BOARD_MODE_MOVE_ORIGIN;if(t){var n=this.getMousePosition(e,0);this.moveOrigin(n[0],n[1],!0)}return t},originMoveEnd:function(){this.mode=this.BOARD_MODE_NONE},addEventHandlers:function(){this.addMouseEventHandlers(),this.addTouchEventHandlers()},addMouseEventHandlers:function(){!this.hasMouseHandlers&&typeof document!="undefined"&&(JXG.addEvent(this.containerObj,"mousedown",this.mouseDownListener,this),JXG.addEvent(this.containerObj,"mousemove",this.mouseMoveListener,this),JXG.addEvent(this.containerObj,"mousewheel",this.mouseWheelListener,this),JXG.addEvent(this.containerObj,"DOMMouseScroll",this.mouseWheelListener,this),this.hasMouseHandlers=!0,this.containerObj.oncontextmenu=function(e){return JXG.exists(e)&&e.preventDefault(),!1})},addTouchEventHandlers:function(){!this.hasTouchHandlers&&typeof document!="undefined"&&(JXG.addEvent(this.containerObj,"touchstart",this.touchStartListener,this),JXG.addEvent(this.containerObj,"touchmove",this.touchMoveListener,this),JXG.addEvent(this.containerObj,"gesturestart",this.gestureStartListener,this),JXG.addEvent(this.containerObj,"gesturechange",this.gestureChangeListener,this),this.hasTouchHandlers=!0)},removeMouseEventHandlers:function(){this.hasMouseHandlers&&typeof document!="undefined"&&(JXG.removeEvent(this.containerObj,"mousedown",this.mouseDownListener,this),JXG.removeEvent(this.containerObj,"mousemove",this.mouseMoveListener,this),this.hasMouseUp&&(JXG.removeEvent(document,"mouseup",this.mouseUpListener,this),this.hasMouseUp=!1),JXG.removeEvent(this.containerObj,"mousewheel",this.mouseWheelListener,this),JXG.removeEvent(this.containerObj,"DOMMouseScroll",this.mouseWheelListener,this),this.hasMouseHandlers=!1)},removeTouchEventHandlers:function(){this.hasTouchHandlers&&typeof document!="undefined"&&(JXG.removeEvent(this.containerObj,"touchstart",this.touchStartListener,this),JXG.removeEvent(this.containerObj,"touchmove",this.touchMoveListener,this),this.hasTouchEnd&&(JXG.removeEvent(document,"touchend",this.touchEndListener,this),this.hasTouchEnd=!1),JXG.removeEvent(this.containerObj,"gesturestart",this.gestureStartListener,this),JXG.removeEvent(this.containerObj,"gesturechange",this.gestureChangeListener,this),this.hasTouchHandlers=!1)},removeEventHandlers:function(){this.removeMouseEventHandlers(),this.removeTouchEventHandlers()},clickLeftArrow:function(){return this.moveOrigin(this.origin.scrCoords[1]+this.canvasWidth*.1,this.origin.scrCoords[2]),this},clickRightArrow:function(){return this.moveOrigin(this.origin.scrCoords[1]-this.canvasWidth*.1,this.origin.scrCoords[2]),this},clickUpArrow:function(){return this.moveOrigin(this.origin.scrCoords[1],this.origin.scrCoords[2]-this.canvasHeight*.1),this},clickDownArrow:function(){return this.moveOrigin(this.origin.scrCoords[1],this.origin.scrCoords[2]+this.canvasHeight*.1),this},gestureChangeListener:function(e){var t,n=this.options.zoom.factorX,r=this.options.zoom.factorY;return this.options.zoom.wheel?(e.preventDefault(),this.mode===this.BOARD_MODE_NONE&&(t=new JXG.Coords(JXG.COORDS_BY_SCREEN,this.getMousePosition(e),this),this.options.zoom.factorX=e.scale/this.prevScale,this.options.zoom.factorY=e.scale/this.prevScale,this.zoomIn(t.usrCoords[1],t.usrCoords[2]),this.prevScale=e.scale,this.options.zoom.factorX=n,this.options.zoom.factorY=r),!1):!0},gestureStartListener:function(e){return this.options.zoom.wheel?(e.preventDefault(),this.prevScale=1,!1):!0},touchStartListener:function(e,t){var n,r,i,s,o,u=this.options.precision.touch,a,f,l,c=e[JXG.touchProperty];this.hasTouchEnd||(JXG.addEvent(document,"touchend",this.touchEndListener,this),this.hasTouchEnd=!0),this.hasMouseHandlers&&this.removeMouseEventHandlers(),document.selection&&typeof document.selection.empty=="function"?document.selection.empty():window.getSelection&&window.getSelection().removeAllRanges(),this.options.precision.hasPoint=this.options.precision.touch;for(n=0;n<c.length;n++)c[n].jxg_isused=!1;for(n=0;n<this.touches.length;n++)for(s=0;s<this.touches[n].targets.length;s++){this.touches[n].targets[s].num=-1,u=this.options.precision.touch;do{for(o=0;o<c.length;o++)if(Math.abs(Math.pow(c[o].screenX-this.touches[n].targets[s].X,2)+Math.pow(c[o].screenY-this.touches[n].targets[s].Y,2))<u*u){this.touches[n].targets[s].num=o,this.touches[n].targets[s].X=c[o].screenX,this.touches[n].targets[s].Y=c[o].screenY,c[o].jxg_isused=!0;break}u*=2}while(this.touches[n].targets[s].num==-1&&u<this.options.precision.touchMax);this.touches[n].targets[s].num===-1&&(JXG.debug("i couldn't find a targettouches for target no "+s+" on "+this.touches[n].obj.name+" ("+this.touches[n].obj.id+"). Removed the target."),JXG.debug("eps = "+u+", touchMax = "+JXG.Options.precision.touchMax),this.touches[n].targets.splice(n,1))}for(n=0;n<c.length;n++)if(t||!c[n].jxg_isused){r=this.getMousePosition(e,n),t?(i=[t],this.mode=this.BOARD_MODE_DRAG):i=this.initMoveObject(r[0],r[1],e,"touch");if(i.length!=0){a=i[i.length-1];if(JXG.isPoint(a)||a.type===JXG.OBJECT_TYPE_TEXT||a.type===JXG.OBJECT_TYPE_TICKS)l=[{num:n,X:c[n].screenX,Y:c[n].screenY,Xprev:NaN,Yprev:NaN,Xstart:[],Ystart:[],Zstart:[]}],this.saveStartPos(a,l[0]),this.touches.push({obj:a,targets:l}),this.highlightedObjects[a.id]=a,a.highlight(!0);else if(a.elementClass===JXG.OBJECT_CLASS_LINE||a.elementClass===JXG.OBJECT_CLASS_CIRCLE||a.type===JXG.OBJECT_TYPE_POLYGON){f=!1;for(s=0;s<this.touches.length;s++)if(a.id===this.touches[s].obj.id){f=!0;if(this.touches[s].targets.length===1){var h={num:n,X:c[n].screenX,Y:c[n].screenY,Xprev:NaN,Yprev:NaN,Xstart:[],Ystart:[],Zstart:[]};this.saveStartPos(a,h),this.touches[s].targets.push(h)}c[n].jxg_isused=!0}f||(l=[{num:n,X:c[n].screenX,Y:c[n].screenY,Xprev:NaN,Yprev:NaN,Xstart:[],Ystart:[],Zstart:[]}],this.saveStartPos(a,l[0]),this.touches.push({obj:a,targets:l}),this.highlightedObjects[a.id]=a,a.highlight(!0))}}c[n].jxg_isused=!0}this.touches.length>0&&(e.preventDefault(),e.stopPropagation());if(this.mode===this.BOARD_MODE_NONE&&this.touchOriginMoveStart(e))return this.triggerEventHandlers(["touchstart","down"],e),!1;if(JXG.isWebkitAndroid()){var p=new Date;this.touchMoveLast=p.getTime()-200}return this.options.precision.hasPoint=this.options.precision.mouse,this.triggerEventHandlers(["touchstart","down"],e),this.touches.length>0},touchMoveListener:function(e){var t,n=0,r,i=e[JXG.touchProperty];this.mode!==this.BOARD_MODE_NONE&&(e.preventDefault(),e.stopPropagation());if(JXG.isWebkitAndroid()){var s=new Date;s=s.getTime();if(s-this.touchMoveLast<80)return this.updateQuality=this.BOARD_QUALITY_HIGH,this.triggerEventHandlers(["touchmove","move"],e,this.mode),!1;this.touchMoveLast=s}this.mode!=this.BOARD_MODE_DRAG&&this.renderer.hide(this.infobox),this.options.precision.hasPoint=this.options.precision.touch;if(!this.touchOriginMove(e)&&this.mode==this.BOARD_MODE_DRAG)for(t=0;t<this.touches.length;t++)this.touches[t].targets.length===1?i[this.touches[t].targets[0].num]&&(this.touches[t].targets[0].X=i[this.touches[t].targets[0].num].screenX,this.touches[t].targets[0].Y=i[this.touches[t].targets[0].num].screenY,r=this.getMousePosition(e,this.touches[t].targets[0].num),this.moveObject(r[0],r[1],this.touches[t],e,"touch")):this.touches[t].targets.length===2&&this.touches[t].targets[0].num>-1&&this.touches[t].targets[1].num>-1&&i[this.touches[t].targets[0].num]&&i[this.touches[t].targets[1].num]&&(this.touches[t].targets[0].X=i[this.touches[t].targets[0].num].screenX,this.touches[t].targets[0].Y=i[this.touches[t].targets[0].num].screenY,this.touches[t].targets[1].X=i[this.touches[t].targets[1].num].screenX,this.touches[t].targets[1].Y=i[this.touches[t].targets[1].num].screenY,this.twoFingerMove(this.getMousePosition(e,this.touches[t].targets[0].num),this.getMousePosition(e,this.touches[t].targets[1].num),this.touches[t],e));return this.mode!=this.BOARD_MODE_DRAG&&this.renderer.hide(this.infobox),this.options.precision.hasPoint=this.options.precision.mouse,this.triggerEventHandlers(["touchmove","move"],e,this.mode),this.mode===this.BOARD_MODE_NONE},touchEndListener:function(e){var t,n,r,i=this.options.precision.touch,s=[],o,u,a=e[JXG.touchProperty];this.triggerEventHandlers(["touchend","up"],e),this.renderer.hide(this.infobox);if(a.length>0){for(t=0;t<this.touches.length;t++)s[t]=this.touches[t];this.touches.length=0;for(t=0;t<a.length;t++)a[t].jxg_isused=!1;for(t=0;t<s.length;t++){o=!1,u=0;for(n=0;n<s[t].targets.length;n++){s[t].targets[n].found=!1;for(r=0;r<a.length;r++)if(Math.abs(Math.pow(a[r].screenX-s[t].targets[n].X,2)+Math.pow(a[r].screenY-s[t].targets[n].Y,2))<i*i){s[t].targets[n].found=!0,s[t].targets[n].num=r,s[t].targets[n].X=a[r].screenX,s[t].targets[n].Y=a[r].screenY,u++;break}}JXG.isPoint(s[t].obj)?o=s[t].targets[0]&&s[t].targets[0].found:s[t].obj.elementClass===JXG.OBJECT_CLASS_LINE?o=s[t].targets[0]&&s[t].targets[0].found||s[t].targets[1]&&s[t].targets[1].found:s[t].obj.elementClass===JXG.OBJECT_CLASS_CIRCLE&&(o=u===1||u===3);if(o){this.touches.push({obj:s[t].obj,targets:[]});for(n=0;n<s[t].targets.length;n++)s[t].targets[n].found&&this.touches[this.touches.length-1].targets.push({num:s[t].targets[n].num,X:s[t].targets[n].screenX,Y:s[t].targets[n].screenY,Xprev:NaN,Yprev:NaN,Xstart:s[t].targets[n].Xstart,Ystart:s[t].targets[n].Ystart,Zstart:s[t].targets[n].Zstart})}else delete this.highlightedObjects[s[t].obj.id],s[t].obj.noHighlight()}}else this.touches.length=0;for(t=0;t<this.downObjects.length;t++){o=!1;for(n=0;n<this.touches.length;n++)this.touches[n].obj.id==this.downObjects[t].id&&(o=!0);o||(this.downObjects[t].triggerEventHandlers(["touchup","up"],e),this.downObjects[t].snapToGrid(),this.downObjects.splice(t,1))}if(!a||a.length===0)JXG.removeEvent(document,"touchend",this.touchEndListener,this),this.hasTouchEnd=!1,this.dehighlightAll(),this.updateQuality=this.BOARD_QUALITY_HIGH,this.originMoveEnd(),this.update();return!0},mouseDownListener:function(e,t){var n,r,i,s,o;return document.selection&&typeof document.selection.empty=="function"?document.selection.empty():window.getSelection&&window.getSelection().removeAllRanges(),this.hasMouseUp||(JXG.addEvent(document,"mouseup",this.mouseUpListener,this),this.hasMouseUp=!0),n=this.getMousePosition(e),t?(r=[t],this.mode=this.BOARD_MODE_DRAG):r=this.initMoveObject(n[0],n[1],e,"mouse"),r.length==0?(this.mode=this.BOARD_MODE_NONE,s=!0):(this.mouse={obj:null,targets:[{X:n[0],Y:n[1],Xprev:NaN,Yprev:NaN}]},this.mouse.obj=r[r.length-1],this.dehighlightAll(),this.highlightedObjects[this.mouse.obj.id]=this.mouse.obj,this.mouse.obj.highlight(!0),this.mouse.targets[0].Xstart=[],this.mouse.targets[0].Ystart=[],this.mouse.targets[0].Zstart=[],this.saveStartPos(this.mouse.obj,this.mouse.targets[0]),e&&e.preventDefault?e.preventDefault():window.event&&(window.event.returnValue=!1)),this.mode===this.BOARD_MODE_NONE&&(s=this.mouseOriginMoveStart(e)),t||this.triggerEventHandlers(["mousedown","down"],e),s},mouseUpListener:function(e){var t;this.triggerEventHandlers(["mouseup","up"],e),this.updateQuality=this.BOARD_QUALITY_HIGH,this.mouse&&this.mouse.obj&&this.mouse.obj.snapToGrid(),this.originMoveEnd(),this.dehighlightAll(),this.update();for(t=0;t<this.downObjects.length;t++)this.downObjects[t].triggerEventHandlers(["mouseup","up"],e);this.downObjects.length=0,this.hasMouseUp&&(JXG.removeEvent(document,"mouseup",this.mouseUpListener,this),this.hasMouseUp=!1),this.mouse=null},mouseMoveListener:function(e){var t;t=this.getMousePosition(e),this.updateQuality=this.BOARD_QUALITY_LOW,this.mode!=this.BOARD_MODE_DRAG&&(this.dehighlightAll(),this.renderer.hide(this.infobox)),this.mouseOriginMove(e)||(this.mode==this.BOARD_MODE_DRAG?this.moveObject(t[0],t[1],this.mouse,e,"mouse"):this.highlightElements(t[0],t[1],e,-1)),this.updateQuality=this.BOARD_QUALITY_HIGH,this.triggerEventHandlers(["mousemove","move"],e,this.mode)},mouseWheelListener:function(e){if(!this.options.zoom.wheel||this.options.zoom.needShift&&!e.shiftKey)return!0;e=e||window.event;var t=e.detail?e.detail*-1:e.wheelDelta/40,n=new JXG.Coords(JXG.COORDS_BY_SCREEN,this.getMousePosition(e),this);return t>0?this.zoomIn(n.usrCoords[1],n.usrCoords[2]):this.zoomOut(n.usrCoords[1],n.usrCoords[2]),e.preventDefault(),!1},updateInfobox:function(e){var t,n,r,i;return e.visProp.showinfobox?(e.elementClass==JXG.OBJECT_CLASS_POINT&&(r=e.coords.usrCoords[1],i=e.coords.usrCoords[2],this.infobox.setCoords(r+this.infobox.distanceX/this.unitX,i+this.infobox.distanceY/this.unitY),typeof e.infoboxText!="string"?(e.visProp.infoboxdigits==="auto"?(t=JXG.autoDigits(r),n=JXG.autoDigits(i)):JXG.isNumber(e.visProp.infoboxdigits)?(t=r.toFixed(e.visProp.infoboxdigits),n=i.toFixed(e.visProp.infoboxdigits)):(t=r,n=i),this.highlightInfobox(t,n,e)):this.highlightCustomInfobox(e.infoboxText,e),this.renderer.show(this.infobox)),this):this},highlightCustomInfobox:function(e){return this.infobox.setText(e),this},highlightInfobox:function(e,t,n){return this.highlightCustomInfobox("("+e+", "+t+")"),this},dehighlightAll:function(){var e,t,n=!1;for(e in this.highlightedObjects)t=this.highlightedObjects[e],this.hasMouseHandlers&&t.noHighlight(),n=!0;return this.highlightedObjects={},this.options.renderer=="canvas"&&n&&(this.prepareUpdate(),this.renderer.suspendRedraw(this),this.updateRenderer(),this.renderer.unsuspendRedraw()),this},getScrCoordsOfMouse:function(e,t){return[e,t]},getUsrCoordsOfMouse:function(e){var t=this.getCoordsTopLeftCorner(),n=JXG.getPosition(e),r=n[0]-t[0],i=n[1]-t[1],s=new JXG.Coords(JXG.COORDS_BY_SCREEN,[r,i],this);return s.usrCoords.slice(1)},getAllUnderMouse:function(e){var t=this.getAllObjectsUnderMouse(e);return t.push(this.getUsrCoordsOfMouse(e)),t},getAllObjectsUnderMouse:function(e){var t=this.getCoordsTopLeftCorner(),n=JXG.getPosition(e),r=n[0]-t[0],i=n[1]-t[1],s=[],o,u,a=this.objectsList.length;for(o=0;o<a;o++)u=this.objectsList[o],u.visProp.visible&&u.hasPoint&&u.hasPoint(r,i)&&(s[s.length]=u);return s},moveOrigin:function(e,t,n){var r,i,s=this.objectsList.length;JXG.exists(e)&&JXG.exists(t)&&(this.origin.scrCoords[1]=e,this.origin.scrCoords[2]=t,n&&(this.origin.scrCoords[1]-=this.drag_dx,this.origin.scrCoords[2]-=this.drag_dy));for(i=0;i<s;i++)r=this.objectsList[i],!r.visProp.frozen&&(r.elementClass==JXG.OBJECT_CLASS_POINT||r.elementClass==JXG.OBJECT_CLASS_CURVE||r.type==JXG.OBJECT_TYPE_AXIS||r.type==JXG.OBJECT_TYPE_TEXT)&&r.elementClass!=JXG.OBJECT_CLASS_CURVE&&r.type!=JXG.OBJECT_TYPE_AXIS&&r.coords.usr2screen();return this.clearTraces(),this.fullUpdate(),this},addConditions:function(e){var t="var el, x, y, c, rgbo;\n",n=e.indexOf("<data>"),r=e.indexOf("</data>"),i,s,o,u,a,f;if(n<0)return;while(n>=0){i=e.slice(n+6,r),s=i.indexOf("="),o=i.slice(0,s),u=i.slice(s+1),s=o.indexOf("."),a=o.slice(0,s),f=this.elementsByName[JXG.unescapeHTML(a)];var l=o.slice(s+1).replace(/\s+/g,"").toLowerCase();u=JXG.GeonextParser.geonext2JS(u,this),u=u.replace(/this\.board\./g,"this."),JXG.exists(this.elementsByName[a])||JXG.debug("debug conditions: |"+a+"| undefined"),t+='el = this.objects["'+f.id+'"];\n';switch(l){case"x":t+="var y=el.coords.usrCoords[2];\n",t+="el.setPositionDirectly(JXG.COORDS_BY_USER,["+u+",y]);\n",t+="el.prepareUpdate().update();\n";break;case"y":t+="var x=el.coords.usrCoords[1];\n",t+="el.coords=new JXG.Coords(JXG.COORDS_BY_USER,[x,"+u+"],this);\n",t+="el.setPositionDirectly(JXG.COORDS_BY_USER,[x,"+u+"]);\n",t+="el.prepareUpdate().update();\n";break;case"visible":t+="var c="+u+";\n",t+="el.visProp.visible = c;\n",t+="if (c) {el.showElement();} else {el.hideElement();}\n";break;case"position":t+="el.position = "+u+";\n",t+="el.prepareUpdate().update(true);\n";break;case"stroke":t+="rgbo = JXG.rgba2rgbo("+u+");\n",t+="el.visProp.strokecolor = rgbo[0];\n",t+="el.visProp.strokeopacity = rgbo[1];\n";break;case"style":t+="el.setStyle("+u+");\n";break;case"strokewidth":t+="el.strokeWidth = "+u+";\n";break;case"fill":t+="var rgbo = JXG.rgba2rgbo("+u+");\n",t+="el.visProp.fillcolor = rgbo[0];\n",t+="el.visProp.fillopacity = rgbo[1];\n";break;case"label":break;default:JXG.debug("property '"+l+"' in conditions not yet implemented:"+u)}e=e.slice(r+7),n=e.indexOf("<data>"),r=e.indexOf("</data>")}t+="this.prepareUpdate().updateElements();\n",t+="return true;\n",t=t.replace(/</g,"<"),t=t.replace(/>/g,">"),t=t.replace(/&/g,"&"),this.updateConditions=new Function(t),this.updateConditions()},updateConditions:function(){return!1},calculateSnapSizes:function(){var e=new JXG.Coords(JXG.COORDS_BY_USER,[0,0],this),t=new JXG.Coords(JXG.COORDS_BY_USER,[this.options.grid.gridX,this.options.grid.gridY],this),n=e.scrCoords[1]-t.scrCoords[1],r=e.scrCoords[2]-t.scrCoords[2];this.options.grid.snapSizeX=this.options.grid.gridX;while(Math.abs(n)>25)this.options.grid.snapSizeX*=2,n/=2;this.options.grid.snapSizeY=this.options.grid.gridY;while(Math.abs(r)>25)this.options.grid.snapSizeY*=2,r/=2;return this},applyZoom:function(){var e,t,n=this.objectsList.length;for(t=0;t<n;t++)e=this.objectsList[t],!e.visProp.frozen&&(e.elementClass==JXG.OBJECT_CLASS_POINT||e.elementClass==JXG.OBJECT_CLASS_CURVE||e.type==JXG.OBJECT_TYPE_AXIS||e.type==JXG.OBJECT_TYPE_TEXT)&&e.elementClass!=JXG.OBJECT_CLASS_CURVE&&e.type!=JXG.OBJECT_TYPE_AXIS&&e.coords.usr2screen();return this.calculateSnapSizes(),this.clearTraces(),this.fullUpdate(),this},zoomIn:function(e,t){var n=this.getBoundingBox(),r=this.options.zoom.factorX,i=this.options.zoom.factorY,s=(n[2]-n[0])*(1-1/r),o=(n[1]-n[3])*(1-1/i),u=.5,a=.5;return typeof e=="number"&&typeof t=="number"&&(u=(e-n[0])/(n[2]-n[0]),a=(n[1]-t)/(n[1]-n[3])),this.setBoundingBox([n[0]+s*u,n[1]-o*a,n[2]-s*(1-u),n[3]+o*(1-a)],!1),this.zoomX*=r,this.zoomY*=i,this.applyZoom(),this},zoomOut:function(e,t){var n=this.getBoundingBox(),r=this.options.zoom.factorX,i=this.options.zoom.factorY,s=(n[2]-n[0])*(1-r),o=(n[1]-n[3])*(1-i),u=.5,a=.5;return this.zoomX<JXG.Options.zoom.eps||this.zoomY<JXG.Options.zoom.eps?this:(typeof e=="number"&&typeof t=="number"&&(u=(e-n[0])/(n[2]-n[0]),a=(n[1]-t)/(n[1]-n[3])),this.setBoundingBox([n[0]+s*u,n[1]-o*a,n[2]-s*(1-u),n[3]+o*(1-a)],!1),this.zoomX/=r,this.zoomY/=i,this.applyZoom(),this)},zoom100:function(){var e=this.getBoundingBox(),t=(e[2]-e[0])*(1-this.zoomX)*.5,n=(e[1]-e[3])*(1-this.zoomY)*.5;return this.setBoundingBox([e[0]+t,e[1]-n,e[2]-t,e[3]+n],!1),this.zoomX=1,this.zoomY=1,this.applyZoom(),this},zoomAllPoints:function(){var e=0,t=0,n=0,r=0,i,s,o,u,a=this.objectsList.length,f;for(i=0;i<a;i++)f=this.objectsList[i],JXG.isPoint(f)&&f.visProp.visible&&(f.coords.usrCoords[1]<e?e=f.coords.usrCoords[1]:f.coords.usrCoords[1]>t&&(t=f.coords.usrCoords[1]),f.coords.usrCoords[2]>r?r=f.coords.usrCoords[2]:f.coords.usrCoords[2]<n&&(n=f.coords.usrCoords[2]));return s=50,o=s/this.unitX,u=s/this.unitY,this.zoomX=1,this.zoomY=1,this.setBoundingBox([e-o,r+u,t+o,n-u],!0),this.applyZoom(),this},zoomElements:function(e){var t,n,r,i,s=[0,0,0,0],o=[1,-1,-1,1];if(!JXG.isArray(e)||e.length===0)return this;for(t=0;t<e.length;t++){r=JXG.getRef(this,e[t]),i=r.bounds();if(JXG.isArray(i))if(JXG.isArray(s))for(n=0;n<4;n++)o[n]*i[n]<o[n]*s[n]&&(s[n]=i[n]);else s=i}if(JXG.isArray(s)){for(n=0;n<4;n++)s[n]-=o[n];this.zoomX=1,this.zoomY=1,this.setBoundingBox(s,!0)}return this},setZoom:function(e,t){var n=this.options.zoom.factorX,r=this.options.zoom.factorY;return this.options.zoom.factorX=e/this.zoomX,this.options.zoom.factorY=t/this.zoomY,this.zoomIn(),this.options.zoom.factorX=n,this.options.zoom.factorY=r,this},removeObject:function(e){var t,n;if(JXG.isArray(e)){for(n=0;n<e.length;n++)this.removeObject(e[n]);return this}e=JXG.getReference(this,e);if(!JXG.exists(e))return this;try{for(t in e.childElements)e.childElements[t].board.removeObject(e.childElements[t]);for(t in this.objects)JXG.exists(this.objects[t].childElements)&&(delete this.objects[t].childElements[e.id],delete this.objects[t].descendants[e.id]);if(e._pos>-1){this.objectsList.splice(e._pos,1);for(t=e._pos;t<this.objectsList.length;t++)this.objectsList[t]._pos--}else JXG.debug("object "+e.id+" not found in list.");delete this.objects[e.id],delete this.elementsByName[e.name],e.visProp&&e.visProp.trace&&e.clearTrace(),JXG.exists(e.remove)&&e.remove()}catch(r){JXG.debug(e.id+": Could not be removed: "+r)}return this.update(),this},removeAncestors:function(e){for(var t in e.ancestors)this.removeAncestors(e.ancestors[t]);return this.removeObject(e),this},initGeonextBoard:function(){var e,t,n,r,i;return e=this.create("point",[0,0],{id:this.id+"g00e0",name:"Ursprung",withLabel:!1,visible:!1,fixed:!0}),t=this.create("point",[1,0],{id:this.id+"gX0e0",name:"Punkt_1_0",withLabel:!1,visible:!1,fixed:!0}),n=this.create("point",[0,1],{id:this.id+"gY0e0",name:"Punkt_0_1",withLabel:!1,visible:!1,fixed:!0}),r=this.create("line",[e,t],{id:this.id+"gXLe0",name:"X-Achse",withLabel:!1,visible:!1}),i=this.create("line",[e,n],{id:this.id+"gYLe0",name:"Y-Achse",withLabel:!1,visible:!1}),this},initInfobox:function(){var e=JXG.copyAttributes({},this.options,"infobox");return e.id=this.id+"_infobox",this.infobox=this.create("text",[0,0,"0,0"],e),this.infobox.distanceX=-20,this.infobox.distanceY=25,this.infobox.needsUpdateSize=!1,this.infobox.dump=!1,this.renderer.hide(this.infobox),this},resizeContainer:function(e,t){return this.canvasWidth=parseFloat(e),this.canvasHeight=parseFloat(t),this.containerObj.style.width=this.canvasWidth+"px",this.containerObj.style.height=this.canvasHeight+"px",this.renderer.resize(this.canvasWidth,this.canvasHeight),this},showDependencies:function(){var e,t,n,r,i;t="\n";for(e in this.objects){i=0;for(n in this.objects[e].childElements)i++;i>=0&&(t+=""+this.objects[e].id+":<"+"/b> ");for(n in this.objects[e].childElements)t+=this.objects[e].childElements[n].id+"("+this.objects[e].childElements[n].name+")"+", ";t+="\n"}return t+="\n",r=window.open(),r.document.open(),r.document.write(t),r.document.close(),this},showXML:function(){var e=window.open("");return e.document.open(),e.document.write("<pre>"+JXG.escapeHTML(this.xmlString)+"<"+"/pre>"),e.document.close(),this},prepareUpdate:function(){var e,t,n=this.objectsList.length;for(e=0;e<n;e++)t=this.objectsList[e],t.needsUpdate=t.needsRegularUpdate||this.needsFullUpdate;return this},updateElements:function(e){var t,n;e=JXG.getRef(this,e);for(t=0;t<this.objectsList.length;t++)n=this.objectsList[t],n.update(!JXG.exists(e)||n.id!==e.id);return this},updateRenderer:function(e){var t,n,r=this.objectsList.length;if(this.options.renderer=="canvas")this.updateRendererCanvas(e);else for(t=0;t<r;t++)n=this.objectsList[t],n.updateRenderer();return this},updateRendererCanvas:function(e){var t,n,r,i=this.objectsList.length,s=this.options.layer,o=this.options.layer.numlayers,u=Number.NEGATIVE_INFINITY,a,f;for(r=0;r<o;r++){a=Number.POSITIVE_INFINITY;for(f in s)s[f]>u&&s[f]<a&&(a=s[f]);u=a;for(t=0;t<i;t++)n=this.objectsList[t],n.visProp.layer===a&&n.prepareUpdate().updateRenderer()}return this},addHook:function(e,t,n){return t=JXG.def(t,"update"),n=JXG.def(n,this),this.hooks.push([t,e]),this.on(t,e,n),this.hooks.length-1},addEvent:JXG.shortcut(JXG.Board.prototype,"on"),removeHook:function(e){return this.hooks[e]&&(this.off(this.hooks[e][0],this.hooks[e][1]),this.hooks[e]=null),this},removeEvent:JXG.shortcut(JXG.Board.prototype,"off"),updateHooks:function(e){return arguments[0]=JXG.def(arguments[0],"update"),this.triggerEventHandlers.apply(this,arguments),this},addChild:function(e){return e!==null&&JXG.exists(e.containerObj)&&(this.dependentBoards.push(e),this.update()),this},removeChild:function(e){var t;for(t=this.dependentBoards.length-1;t>=0;t--)this.dependentBoards[t]==e&&this.dependentBoards.splice(t,1);return this},update:function(e){var t,n,r,i;if(this.inUpdate||this.isSuspendedUpdate)return this;this.inUpdate=!0,this.prepareUpdate(e).updateElements(e).updateConditions(),this.renderer.suspendRedraw(this),this.updateRenderer(e),this.renderer.unsuspendRedraw(),this.triggerEventHandlers("update"),n=this.dependentBoards.length;for(t=0;t<n;t++)r=this.dependentBoards[t].id,i=JXG.JSXGraph.boards[r],i!=this&&(i.updateQuality=this.updateQuality,i.prepareUpdate().updateElements().updateConditions(),i.renderer.suspendRedraw(),i.updateRenderer(),i.renderer.unsuspendRedraw(),i.triggerEventHandlers("update"));return this.inUpdate=!1,this},fullUpdate:function(){return this.needsFullUpdate=!0,this.update(),this.needsFullUpdate=!1,this},addGrid:function(){return this.create("grid",[]),this},removeGrids:function(){var e;for(e=0;e<this.grids.length;e++)this.removeObject(this.grids[e]);return this.grids.length=0,this.update(),this},create:function(e,t,n){var 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in h)c[l.toLowerCase()]=h[l];return c}(),JXG.useStandardOptions=function(e){var t=JXG.Options,n=e.hasGrid,r,i,s,o;e.options.grid.hasGrid=t.grid.hasGrid,e.options.grid.gridX=t.grid.gridX,e.options.grid.gridY=t.grid.gridY,e.options.grid.gridColor=t.grid.gridColor,e.options.grid.gridOpacity=t.grid.gridOpacity,e.options.grid.gridDash=t.grid.gridDash,e.options.grid.snapToGrid=t.grid.snapToGrid,e.options.grid.snapSizeX=t.grid.SnapSizeX,e.options.grid.snapSizeY=t.grid.SnapSizeY,e.takeSizeFromFile=t.takeSizeFromFile,o=function(e,t){e.visProp.fillcolor=t.fillColor,e.visProp.highlightfillcolor=t.highlightFillColor,e.visProp.strokecolor=t.strokeColor,e.visProp.highlightstrokecolor=t.highlightStrokeColor};for(r in e.objects){s=e.objects[r];if(s.elementClass==JXG.OBJECT_CLASS_POINT)o(s,t.point);else if(s.elementClass==JXG.OBJECT_CLASS_LINE){o(s,t.line);for(i in s.ticks)i.majorTicks=t.line.ticks.majorTicks,i.minTicksDistance=t.line.ticks.minTicksDistance,i.visProp.minorheight=t.line.ticks.minorHeight,i.visProp.majorheight=t.line.ticks.majorHeight}else s.elementClass==JXG.OBJECT_CLASS_CIRCLE?o(s,t.circle):s.type==JXG.OBJECT_TYPE_ANGLE?o(s,t.angle):s.type==JXG.OBJECT_TYPE_ARC?o(s,t.arc):s.type==JXG.OBJECT_TYPE_POLYGON?o(s,t.polygon):s.type==JXG.OBJECT_TYPE_CONIC?o(s,t.conic):s.type==JXG.OBJECT_TYPE_CURVE?o(s,t.curve):s.type==JXG.OBJECT_TYPE_SECTOR&&(s.arc.visProp.fillcolor=t.sector.fillColor,s.arc.visProp.highlightfillcolor=t.sector.highlightFillColor,s.arc.visProp.fillopacity=t.sector.fillOpacity,s.arc.visProp.highlightfillopacity=t.sector.highlightFillOpacity)}e.fullUpdate(),n&&!e.hasGrid?e.removeGrids(e):!n&&e.hasGrid&&e.create("grid",[])},JXG.useBlackWhiteOptions=function(e){var t=JXG.Options;t.point.fillColor=JXG.rgb2bw(t.point.fillColor),t.point.highlightFillColor=JXG.rgb2bw(t.point.highlightFillColor),t.point.strokeColor=JXG.rgb2bw(t.point.strokeColor),t.point.highlightStrokeColor=JXG.rgb2bw(t.point.highlightStrokeColor),t.line.fillColor=JXG.rgb2bw(t.line.fillColor),t.line.highlightFillColor=JXG.rgb2bw(t.line.highlightFillColor),t.line.strokeColor=JXG.rgb2bw(t.line.strokeColor),t.line.highlightStrokeColor=JXG.rgb2bw(t.line.highlightStrokeColor),t.circle.fillColor=JXG.rgb2bw(t.circle.fillColor),t.circle.highlightFillColor=JXG.rgb2bw(t.circle.highlightFillColor),t.circle.strokeColor=JXG.rgb2bw(t.circle.strokeColor),t.circle.highlightStrokeColor=JXG.rgb2bw(t.circle.highlightStrokeColor),t.arc.fillColor=JXG.rgb2bw(t.arc.fillColor),t.arc.highlightFillColor=JXG.rgb2bw(t.arc.highlightFillColor),t.arc.strokeColor=JXG.rgb2bw(t.arc.strokeColor),t.arc.highlightStrokeColor=JXG.rgb2bw(t.arc.highlightStrokeColor),t.polygon.fillColor=JXG.rgb2bw(t.polygon.fillColor),t.polygon.highlightFillColor=JXG.rgb2bw(t.polygon.highlightFillColor),t.sector.fillColor=JXG.rgb2bw(t.sector.fillColor),t.sector.highlightFillColor=JXG.rgb2bw(t.sector.highlightFillColor),t.curve.strokeColor=JXG.rgb2bw(t.curve.strokeColor),t.grid.gridColor=JXG.rgb2bw(t.grid.gridColor),JXG.useStandardOptions(e)},JXG.JSXGraph={licenseText:"JSXGraph v0.96 Copyright (C) see http://jsxgraph.org",boards:{},elements:{},rendererType:function(){var e=function(e){var t,n;if(JXG.rendererFiles[e]){t=JXG.rendererFiles[e].split(",");for(n=0;n<t.length;n++)(function(e){JXG.require(JXG.requirePath+e+".js")})(t[n]);delete JXG.rendererFiles[e]}};JXG.Options.renderer="no";if(JXG.supportsVML()){JXG.Options.renderer="vml";function t(){document.body&&(document.body.scrollLeft,document.body.scrollTop)}document.onmousemove=t,e("vml")}return JXG.supportsCanvas()&&(JXG.Options.renderer="canvas",e("canvas")),JXG.supportsSVG()&&(JXG.Options.renderer="svg",e("svg")),JXG.isNode()&&(JXG.Options.renderer="canvas",e("canvas")),JXG.Options.renderer}(),initBoard:function(e,t){var n,r,i,s,o,u,a,f,l,c,h,p,d,v,m,g,y,b,w;return f=JXG.getDimensions(e),typeof document!="undefined"&&e!==null?w=document.getElementById(e):w=e,typeof t=="undefined"&&(t={}),typeof t["boundingbox"]!="undefined"?(l=t.boundingbox,u=parseInt(f.width),a=parseInt(f.height),t.keepaspectratio?(s=u/(l[2]-l[0]),o=a/(-l[3]+l[1]),Math.abs(s)<Math.abs(o)?o=Math.abs(s)*o/Math.abs(o):s=Math.abs(o)*s/Math.abs(s)):(s=u/(l[2]-l[0]),o=a/(-l[3]+l[1])),r=-s*l[0],i=o*l[1]):(r=typeof t["originX"]=="undefined"?150:t.originX,i=typeof t["originY"]=="undefined"?150:t.originY,s=typeof t["unitX"]=="undefined"?50:t.unitX,o=typeof t["unitY"]=="undefined"?50:t.unitY),c=typeof t["zoomfactor"]=="undefined"?1:t.zoom,h=c*(typeof t["zoomX"]=="undefined"?1:t.zoomX),p=c*(typeof t["zoomY"]=="undefined"?1:t.zoomY),d=typeof t["showCopyright"]=="undefined"?JXG.Options.showCopyright:t.showCopyright,g=typeof t["zoom"]=="undefined"?JXG.Options.zoom.wheel:t.zoom,y=typeof t["pan"]=="undefined"?JXG.Options.pan:t.pan,JXG.Options.renderer=="svg"?n=new JXG.SVGRenderer(w):JXG.Options.renderer=="vml"?n=new JXG.VMLRenderer(w):JXG.Options.renderer=="silverlight"?n=new JXG.SilverlightRenderer(w,f.width,f.height):JXG.Options.renderer=="canvas"?n=new JXG.CanvasRenderer(w):n=new JXG.NoRenderer,m=new JXG.Board(e,n,"",[r,i],h,p,s,o,f.width,f.height,d),this.boards[m.id]=m,m.keepaspectratio=t.keepaspectratio,m.options.zoom.wheel=g,m.options.pan=y,m.suspendUpdate(),m.initInfobox(),t.axis&&(b=typeof t.axis=="object"?t.axis:{ticks:{drawZero:!0}},m.defaultAxes={},m.defaultAxes.x=m.create("axis",[[0,0],[1,0]],b),m.defaultAxes.y=m.create("axis",[[0,0],[0,1]],b)),t.grid&&m.create("grid",[],typeof t.grid=="object"?t.grid:{}),typeof t["shownavigation"]!="undefined"&&(t.showNavigation=t.shownavigation),v=typeof t["showNavigation"]=="undefined"?m.options.showNavigation:t.showNavigation,v&&m.renderer.drawZoomBar(m),m.unsuspendUpdate(),m},loadBoardFromFile:function(e,t,n){var r,i,s;return JXG.Options.renderer=="svg"?r=new JXG.SVGRenderer(document.getElementById(e)):JXG.Options.renderer=="vml"?r=new JXG.VMLRenderer(document.getElementById(e)):JXG.Options.renderer=="silverlight"?r=new JXG.SilverlightRenderer(document.getElementById(e),s.width,s.height):r=new JXG.CanvasRenderer(document.getElementById(e)),s=JXG.getDimensions(e),i=new JXG.Board(e,r,"",[150,150],1,1,50,50,s.width,s.height),i.initInfobox(),JXG.FileReader.parseFileContent(t,i,n),i.options.showNavigation&&i.renderer.drawZoomBar(i),this.boards[i.id]=i,i},loadBoardFromString:function(e,t,n){var r,i,s;return JXG.Options.renderer=="svg"?r=new JXG.SVGRenderer(document.getElementById(e)):JXG.Options.renderer=="vml"?r=new JXG.VMLRenderer(document.getElementById(e)):JXG.Options.renderer=="silverlight"?r=new JXG.SilverlightRenderer(document.getElementById(e),i.width,i.height):r=new JXG.CanvasRenderer(document.getElementById(e)),i=JXG.getDimensions(e),s=new JXG.Board(e,r,"",[150,150],1,1,50,50,i.width,i.height),s.initInfobox(),JXG.FileReader.parseString(t,s,n,!0),s.options.showNavigation&&s.renderer.drawZoomBar(s),this.boards[s.id]=s,s},freeBoard:function(e){var t,n;typeof e=="string"&&(e=this.boards[e]),e.removeEventHandlers(),e.suspendUpdate();for(t in e.objects)e.objects[t].remove();while(e.containerObj.firstChild)e.containerObj.removeChild(e.containerObj.firstChild);for(t in e.objects)delete e.objects[t];delete e.renderer,delete e.algebra,e.jc.creator.clearCache(),delete e.jc,delete this.boards[e.id]},registerElement:function(e,t){e=e.toLowerCase(),this.elements[e]=t;if(JXG.Board.prototype["_"+e])throw new Error("JSXGraph: Can't create wrapper method in JXG.Board because member '_"+e+"' already exists'");JXG.Board.prototype["_"+e]=function(t,n){return this.create(e,t,n)}},unregisterElement:function(e){delete this.elements[e.toLowerCase()],delete JXG.Board.prototype["_"+e.toLowerCase()]}},JXG.extend(JXG,{OBJECT_TYPE_ARC:1,OBJECT_TYPE_ARROW:2,OBJECT_TYPE_AXIS:3,OBJECT_TYPE_AXISPOINT:4,OBJECT_TYPE_TICKS:5,OBJECT_TYPE_CIRCLE:6,OBJECT_TYPE_CONIC:7,OBJECT_TYPE_CURVE:8,OBJECT_TYPE_GLIDER:9,OBJECT_TYPE_IMAGE:10,OBJECT_TYPE_LINE:11,OBJECT_TYPE_POINT:12,OBJECT_TYPE_SLIDER:13,OBJECT_TYPE_CAS:14,OBJECT_TYPE_GXTCAS:15,OBJECT_TYPE_POLYGON:16,OBJECT_TYPE_SECTOR:17,OBJECT_TYPE_TEXT:18,OBJECT_TYPE_ANGLE:19,OBJECT_TYPE_INTERSECTION:20,OBJECT_TYPE_TURTLE:21,OBJECT_TYPE_VECTOR:22,OBJECT_TYPE_OPROJECT:23,OBJECT_TYPE_GRID:24,OBJECT_CLASS_POINT:1,OBJECT_CLASS_LINE:2,OBJECT_CLASS_CIRCLE:3,OBJECT_CLASS_CURVE:4,OBJECT_CLASS_AREA:5,OBJECT_CLASS_OTHER:6}),JXG.GeometryElement=function(e,t,n,r){var i,s;this.needsUpdate=!0,this.isDraggable=!1,this.isReal=!0,this.childElements={},this.hasLabel=!1,this.highlighted=!1,this.notExistingParents={},this.traces={},this.numTraces=0,this.transformations=[],this.baseElement=null,this.descendants={},this.ancestors={},this.symbolic={},this.elType="",this.dump=!0,this.subs={},this._pos=-1,this.stdform=[1,0,0,0,1,1,0,0],this.methodMap={setLabel:"setLabelText",getName:"getName",addTransform:"addTransform",setProperty:"setProperty",setAttribute:"setAttribute"},this.quadraticform=[[1,0,0],[0,1,0],[0,0,1]],this.visProp={},JXG.EventEmitter.eventify(this),this.mouseover=!1;if(arguments.length>0){this.board=e,this.type=n,this.elementClass=r||JXG.OBJECT_CLASS_OTHER,this.id=t.id,i=t.name,JXG.exists(i)||(i=this.board.generateName(this)),this.board.elementsByName[i]=this,this.name=i,this.needsRegularUpdate=t.needsregularupdate,JXG.clearVisPropOld(this),t=this.resolveShortcuts(t);for(s in t)this._set(s,t[s]);this.visProp.draft=t.draft&&t.draft.draft,this.visProp.gradientangle="270",this.visProp.gradientsecondopacity=this.visProp.fillopacity,this.visProp.gradientpositionx=.5,this.visProp.gradientpositiony=.5}},JXG.extend(JXG.GeometryElement.prototype,{addChild:function(e){var t,n;this.childElements[e.id]=e,this.addDescendants(e),e.ancestors[this.id]=this;for(t in this.descendants){this.descendants[t].ancestors[this.id]=this;for(n in this.ancestors)this.descendants[t].ancestors[this.ancestors[n].id]=this.ancestors[n]}for(t in this.ancestors)for(n in this.descendants)this.ancestors[t].descendants[this.descendants[n].id]=this.descendants[n];return this},addDescendants:function(e){var t;this.descendants[e.id]=e;for(t in e.childElements)this.addDescendants(e.childElements[t]);return this},countChildren:function(){var e,t=0,n;n=this.childElements;for(e in n)n.hasOwnProperty(e)&&e.indexOf("Label")<0&&t++;return t},getName:function(){return this.name},addTransform:function(){},draggable:function(){return this.isDraggable&&!this.visProp.fixed&&!this.visProp.frozen&&this.type!=JXG.OBJECT_TYPE_GLIDER},generatePolynomial:function(){return[]},animate:function(e,t,n){n=n||{};var r,i,s=this.board.options.animationDelay,o=Math.ceil(t/(s*1)),u,a=this,f=!1;this.animationData={};var l=function(e,t,n){var r,i,s,f,l;r=JXG.rgb2hsv(e),i=JXG.rgb2hsv(t),s=(i[0]-r[0])/(1*o),f=(i[1]-r[1])/(1*o),l=(i[2]-r[2])/(1*o),a.animationData[n]=new Array(o);for(u=0;u<o;u++)a.animationData[n][o-u-1]=JXG.hsv2rgb(r[0]+(u+1)*s,r[1]+(u+1)*f,r[2]+(u+1)*l)},c=function(e,t,n,r){var i;e=parseFloat(e),t=parseFloat(t);if(isNaN(e)||isNaN(t))return;var s=(t-e)/(1*o);a.animationData[n]=new Array(o);for(u=0;u<o;u++)i=e+(u+1)*s,a.animationData[n][o-u-1]=r?Math.floor(i):i};for(r in e){i=r.toLowerCase();switch(i){case"strokecolor":case"fillcolor":l(this.visProp[i],e[r],i);break;case"size":if(this.elementClass!==JXG.OBJECT_CLASS_POINT)break;f=!0;case"strokeopacity":case"strokewidth":case"fillopacity":c(this.visProp[i],e[r],i,f)}}return this.animationCallback=n.callback,this.board.addAnimation(this),this},update:function(){return this.visProp.trace&&this.cloneToBackground(!0),this},updateRenderer:function(){return this},hideElement:function(){return this.visProp.visible=!1,this.board.renderer.hide(this),this.label!=null&&this.hasLabel&&(this.label.hiddenByParent=!0,this.label.content.visProp.visible&&this.board.renderer.hide(this.label.content)),this},showElement:function(){return this.visProp.visible=!0,this.board.renderer.show(this),this.label!=null&&this.hasLabel&&this.label.hiddenByParent&&(this.label.hiddenByParent=!1,this.label.content.visProp.visible&&this.board.renderer.show(this.label.content)),this},_set:function(e,t){e=e.toLocaleLowerCase(),this.visProp.hasOwnProperty(e)&&e.indexOf("color")>=0&&JXG.isString(t)&&t.length==9&&t.charAt(0)==="#"?(t=JXG.rgba2rgbo(t),this.visProp[e]=t[0],this.visProp[e.replace("color","opacity")]=t[1]):this.visProp[e]=t},resolveShortcuts:function(e){var t,n;for(t in JXG.Options.shortcuts)if(JXG.exists(e[t]))for(n=0;n<JXG.Options.shortcuts[t].length;n++)JXG.exists(e[JXG.Options.shortcuts[t][n]])||(e[JXG.Options.shortcuts[t][n]]=e[t]);return e},setLabelText:function(e){return e=e.replace(/</g,"<").replace(/>/g,">"),this.label!==null&&this.label.content.setText(e),this},setAttribute:JXG.shortcut(JXG.GeometryElement.prototype,"setProperty"),setProperty:function(){var e,t,n,r,i,s,o={},u;for(e=0;e<arguments.length;e++)r=arguments[e],JXG.isString(r)?(s=r.split(":"),o[JXG.trim(s[0])]=JXG.trim(s[1])):JXG.isArray(r)?o[r[0]]=r[1]:JXG.extend(o,r);o=this.resolveShortcuts(o);for(e in o){t=e.replace(/\s+/g,"").toLowerCase(),n=o[e],u=this.visProp[t];switch(t){case"name":delete this.board.elementsByName[this.name],this.name=n,this.board.elementsByName[this.name]=this;break;case"needsregularupdate":this.needsRegularUpdate=n!="false"&&n!=0,this.board.renderer.setBuffering(this,this.needsRegularUpdate?"auto":"static");break;case"labelcolor":n=JXG.rgba2rgbo(n),i=n[1],n=n[0],i==0&&this.label!=null&&this.hasLabel&&this.label.content.hideElement(),this.label!=null&&this.hasLabel&&(this.label.color=n,this.board.renderer.setObjectStrokeColor(this.label.content,n,i)),this.type==JXG.OBJECT_TYPE_TEXT&&(this.visProp.strokecolor=n,this.visProp.strokeopacity=i,this.board.renderer.setObjectStrokeColor(this,this.visProp.strokecolor,this.visProp.strokeopacity));break;case"infoboxtext":typeof n=="string"?this.infoboxText=n:this.infoboxText=!1;break;case"visible":if(n=="false"||n==0)this.visProp.visible=!1,this.hideElement();else if(n=="true"||n==1)this.visProp.visible=!0,this.showElement();break;case"face":this.elementClass==JXG.OBJECT_CLASS_POINT&&(this.visProp.face=n,this.board.renderer.changePointStyle(this));break;case"trace":n=="false"||n==0?(this.clearTrace(),this.visProp.trace=!1):this.visProp.trace=!0;break;case"gradient":this.visProp.gradient=n,this.board.renderer.setGradient(this);break;case"gradientsecondcolor":n=JXG.rgba2rgbo(n),this.visProp.gradientsecondcolor=n[0],this.visProp.gradientsecondopacity=n[1],this.board.renderer.updateGradient(this);break;case"gradientsecondopacity":this.visProp.gradientsecondopacity=n,this.board.renderer.updateGradient(this);break;case"withlabel":this.visProp.withlabel=n,n?this.label&&this.label.content?this.visProp.visible&&this.label.content.showElement():(this.createLabel(),this.visProp.visible||this.label.content.hideElement()):this.label&&this.label.content&&this.hasLabel&&this.label.content.hideElement(),this.hasLabel=n;break;case"rotate":(this.type===JXG.OBJECT_TYPE_TEXT&&this.visProp.display=="internal"||this.type===JXG.OBJECT_TYPE_IMAGE)&&this.addRotation(n);break;case"ticksdistance":this.type===JXG.OBJECT_TYPE_TICKS&&typeof n=="number"&&(this.ticksFunction=function(e){return function(t){return e}}(n));break;default:JXG.exists(this.visProp[t])&&(!JXG.Validator[t]||JXG.Validator[t]&&JXG.Validator[t](n)||JXG.Validator[t]&&JXG.isFunction(n)&&JXG.Validator[t](n()))&&(n=n.toLowerCase&&n.toLowerCase()==="false"?!1:n,this._set(t,n))}this.triggerEventHandlers("attribute:"+t,u)}return this.triggerEventHandlers("attribute",o),this.visProp.needsregularupdate?this.board.update(this):this.board.fullUpdate(),this},getAttribute:JXG.shortcut(JXG.GeometryElement.prototype,"getProperty"),getProperty:function(e){var t;e=e.toLowerCase();switch(e){case"needsregularupdate":t=this.needsRegularUpdate;break;case"labelcolor":t=this.label.color;break;case"infoboxtext":t=this.infoboxText;break;case"withlabel":t=this.hasLabel;break;default:t=this.visProp[e]}return t},setDash:function(e){return this.setProperty({dash:e}),this},prepareUpdate:function(){return this.needsUpdate=!0,this},remove:function(){return this.board.renderer.remove(this.board.renderer.getElementById(this.id)),this.hasLabel&&this.board.renderer.remove(this.board.renderer.getElementById(this.label.content.id)),this},getTextAnchor:function(){return new JXG.Coords(JXG.COORDS_BY_USER,[0,0],this.board)},getLabelAnchor:function(){return new JXG.Coords(JXG.COORDS_BY_USER,[0,0],this.board)},setStraight:function(e,t){return this},setArrow:function(e,t){return this.visProp.firstarrow=e,this.visProp.lastarrow=t,this.prepareUpdate().update(),this},createGradient:function(){(this.visProp.gradient==="linear"||this.visProp.gradient==="radial")&&this.board.renderer.setGradient(this)},createLabel:function(){var e={};return e=JXG.deepCopy(this.visProp.label,null),e.id=this.id+"Label",e.isLabel=!0,e.visible=this.visProp.visible,e.anchor=this,e.priv=this.visProp.priv,this.nameHTML=JXG.GeonextParser.replaceSup(JXG.GeonextParser.replaceSub(this.name)),this.label={},this.visProp.withlabel&&(this.label.relativeCoords=[0,0],this.label.content=JXG.createText(this.board,[this.label.relativeCoords[0],-this.label.relativeCoords[1],this.name],e),this.label.content.needsUpdate=!0,this.label.content.update(),this.label.content.dump=!1,this.label.color=this.label.content.visProp.strokecolor,this.visProp.visible||(this.label.hiddenByParent=!0,this.label.content.visProp.visible=!1),this.hasLabel=!0),this},highlight:function(e){e=JXG.def(e,!1);if(!this.highlighted||e)this.highlighted=!0,this.board.renderer.highlight(this);return this},noHighlight:function(){return this.highlighted&&(this.highlighted=!1,this.board.renderer.noHighlight(this)),this},clearTrace:function(){var e;for(e in this.traces)this.board.renderer.remove(this.traces[e]);return this.numTraces=0,this},cloneToBackground:function(){return this},bounds:function(){},normalize:function(){return this.stdform=JXG.Math.normalize(this.stdform),this},toJSON:function(){var e='{"name":'+this.name;e+=', "id":'+this.id;var t=[];for(var n in this.visProp)this.visProp[n]!=null&&t.push('"'+n+'":'+this.visProp[n]);return e+=', "visProp":{'+t.toString()+"}",e+="}",e},addRotation:function(e){var t,n,r,i,s,o=this;if((this.type===JXG.OBJECT_TYPE_TEXT&&this.visProp.display==="internal"||this.type===JXG.OBJECT_TYPE_IMAGE)&&e!=0){var t,n,r,i,s,o=this;t=this.board.create("transform",[function(){return-o.X()},function(){return-o.Y()}],{type:"translate"}),n=this.board.create("transform",[function(){return o.X()},function(){return o.Y()}],{type:"translate"}),r=this.board.create("transform",[function(){return o.board.unitX/o.board.unitY},function(){return 1}],{type:"scale"}),i=this.board.create("transform",[function(){return o.board.unitY/o.board.unitX},function(){return 1}],{type:"scale"}),s=this.board.create("transform",[e*Math.PI/180],{type:"rotate"}),t.bindTo(this),r.bindTo(this),s.bindTo(this),i.bindTo(this),n.bindTo(this)}return this},highlightStrokeColor:function(e){return this.setProperty({highlightStrokeColor:e}),this},strokeColor:function(e){return this.setProperty({strokeColor:e}),this},strokeWidth:function(e){return this.setProperty({strokeWidth:e}),this},fillColor:function(e){return this.setProperty({fillColor:e}),this},highlightFillColor:function(e){return this.setProperty({highlightFillColor:e}),this},labelColor:function(e){return this.setProperty({labelColor:e}),this},dash:function(e){return this.setProperty({dash:e}),this},visible:function(e){return this.setProperty({visible:e}),this},shadow:function(e){return this.setProperty({shadow:e}),this},getType:function(){return this.elType},getParents:function(){return this.parents},snapToGrid:function(){return this},getAttributes:function(){var e=JXG.deepCopy(this.visProp),t=["attractors","attractordistance","snatchdistance","traceattributes","frozen","shadow","gradientangle","gradientsecondopacity","gradientpositionx","gradientpositiony","needsregularupdate","zoom","layer","offset"],n;e.id=this.id,e.name=this.name;for(n=0;n<t.length;n++)delete e[t[n]];return e},hasPoint:function(e,t){return!1},addEvent:JXG.shortcut(JXG.GeometryElement.prototype,"on"),removeEvent:JXG.shortcut(JXG.GeometryElement.prototype,"off"),__evt__:function(e){},__evt__:function(e){},__evt__:function(e){},__evt__:function(e){},__evt__:function(e){},__evt__:function(e){},__evt__:function(e){},__evt__:function(e){},__evt__:function(e){},__evt__:function(e){},__evt__:function(e){},__evt__:function(e){},__evt__:function(e){},__evt__:function(e){},__evt__:function(e){},__evt__:function(e){},__evt__:function(e){},__evt__:function(){}}),JXG.COORDS_BY_USER=1,JXG.COORDS_BY_SCREEN=2,JXG.Coords=function(e,t,n){this.board=n,this.usrCoords=[],this.scrCoords=[],JXG.EventEmitter.eventify(this),this.setCoordinates(e,t)},JXG.extend(JXG.Coords.prototype,{normalizeUsrCoords:function(){var e=JXG.Math.eps;Math.abs(this.usrCoords[0])>e&&(this.usrCoords[1]/=this.usrCoords[0],this.usrCoords[2]/=this.usrCoords[0],this.usrCoords[0]=1)},usr2screen:function(e){var t=Math.round,n=this.board,r=this.usrCoords,i=n.origin.scrCoords;e===null||e?(this.scrCoords[0]=t(r[0]),this.scrCoords[1]=t(r[0]*i[1]+r[1]*n.unitX),this.scrCoords[2]=t(r[0]*i[2]-r[2]*n.unitY)):(this.scrCoords[0]=r[0],this.scrCoords[1]=r[0]*i[1]+r[1]*n.unitX,this.scrCoords[2]=r[0]*i[2]-r[2]*n.unitY)},screen2usr:function(){var e=this.board.origin.scrCoords,t=this.scrCoords,n=this.board;this.usrCoords[0]=1,this.usrCoords[1]=(t[1]-e[1])/n.unitX,this.usrCoords[2]=(e[2]-t[2])/n.unitY},distance:function(e,t){var n=0,r,i=this.usrCoords,s=this.scrCoords,o;if(e===JXG.COORDS_BY_USER){r=t.usrCoords,o=i[0]-r[0],n=o*o;if(n>JXG.Math.eps)return Number.POSITIVE_INFINITY;o=i[1]-r[1],n+=o*o,o=i[2]-r[2],n+=o*o}else r=t.scrCoords,o=s[1]-r[1],n+=o*o,o=s[2]-r[2],n+=o*o;return Math.sqrt(n)},setCoordinates:function(e,t,n){var r=this.usrCoords,i=this.scrCoords,s=this.usrCoords.slice(0),o=this.scrCoords.slice(0);return e===JXG.COORDS_BY_USER?(t.length===2?(r[0]=1,r[1]=t[0],r[2]=t[1]):(r[0]=t[0],r[1]=t[1],r[2]=t[2],this.normalizeUsrCoords()),this.usr2screen(n)):(i[1]=t[0],i[2]=t[1],this.screen2usr()),this.triggerEventHandlers("update",s,o),this},__evt__:function(e,t){},__evt__:function(){}}),JXG.Point=function(e,t,n){this.constructor(e,n,JXG.OBJECT_TYPE_POINT,JXG.OBJECT_CLASS_POINT),t==null&&(t=[0,0]),this.coords=new JXG.Coords(JXG.COORDS_BY_USER,t,this.board),this.initialCoords=new JXG.Coords(JXG.COORDS_BY_USER,t,this.board),this.position=null,this.onPolygon=!1,this.slideObject=null,this.Xjc=null,this.Yjc=null,this.methodMap=JXG.deepCopy(this.methodMap,{move:"moveTo",glide:"makeGlider",X:"X",Y:"Y",free:"free",setPosition:"setGliderPosition"}),this.group=[],this.elType="point",this.id=this.board.setId(this,"P"),this.board.renderer.drawPoint(this),this.board.finalizeAdding(this),this.createLabel()},JXG.Point.prototype=new JXG.GeometryElement,JXG.extend(JXG.Point.prototype,{hasPoint:function(e,t){var n=this.coords.scrCoords,r;return r=parseFloat(this.visProp.size)+parseFloat(this.visProp.strokewidth)*.5,r<this.board.options.precision.hasPoint&&(r=this.board.options.precision.hasPoint),Math.abs(n[1]-e)<r+2&&Math.abs(n[2]-t)<r+2},updateConstraint:function(){return this},update:function(e){return this.needsUpdate?(typeof e=="undefined"&&(e=!1),this.type==JXG.OBJECT_TYPE_GLIDER&&(e?this.updateGliderFromParent():this.updateGlider()),(this.type==JXG.OBJECT_TYPE_CAS||this.type==JXG.OBJECT_TYPE_AXISPOINT)&&this.updateConstraint(),this.updateTransform(),this.visProp.trace&&this.cloneToBackground(!0),this):this},updateGlider:function(){var e,t,n,r,i,s,o,u,a,f=this.slideObject,l,c,h,p,d,v;if(f.elementClass==JXG.OBJECT_CLASS_CIRCLE)this.coords=JXG.Math.Geometry.projectPointToCircle(this,f,this.board),this.position=JXG.Math.Geometry.rad([f.center.X()+1,f.center.Y()],f.center,this);else if(f.elementClass==JXG.OBJECT_CLASS_LINE){if(this.onPolygon){t=f.point1.coords.usrCoords,n=f.point2.coords.usrCoords,e=1,r=n[e]-t[e],Math.abs(r)<JXG.Math.eps&&(e=2,r=n[e]-t[e]),o=JXG.Math.Geometry.projectPointToLine(this,f,this.board),u=(o.usrCoords[e]-t[e])/r,s=f.parentPolygon;if(u<0){for(e=0;e<s.borders.length;e++)if(f==s.borders[e]){f=s.borders[(e-1+s.borders.length)%s.borders.length];break}}else if(u>1)for(e=0;e<s.borders.length;e++)if(f==s.borders[e]){f=s.borders[(e+1+s.borders.length)%s.borders.length];break}}t=f.point1.coords,n=f.point2.coords,r=t.distance(JXG.COORDS_BY_USER,n),t=t.usrCoords.slice(0),n=n.usrCoords.slice(0),r<JXG.Math.eps?(this.coords.setCoordinates(JXG.COORDS_BY_USER,t),this.position=0):(this.coords=JXG.Math.Geometry.projectPointToLine(this,f,this.board),Math.abs(n[0])<JXG.Math.eps?(e=1,r=n[e],Math.abs(r)<JXG.Math.eps&&(e=2,r=n[e]),r=(this.coords.usrCoords[e]-t[e])/r,a=r>=0?1:-1,r=Math.abs(r),this.position=a*r/(r+1)):Math.abs(t[0])<JXG.Math.eps?(e=1,r=t[e],Math.abs(r)<JXG.Math.eps&&(e=2,r=t[e]),r=(this.coords.usrCoords[e]-n[e])/r,r<0?this.position=(1-2*r)/(1-r):this.position=1/(r+1)):(e=1,r=n[e]-t[e],Math.abs(r)<JXG.Math.eps&&(e=2,r=n[e]-t[e]),this.position=(this.coords.usrCoords[e]-t[e])/r)),this.visProp.snapwidth>0&&Math.abs(this._smax-this._smin)>=JXG.Math.eps&&(this.position<0&&(this.position=0),this.position>1&&(this.position=1),i=this.position*(this._smax-this._smin)+this._smin,i=Math.round(i/this.visProp.snapwidth)*this.visProp.snapwidth,this.position=(i-this._smin)/(this._smax-this._smin),this.update(!0)),t=f.point1.coords.usrCoords,!f.visProp.straightfirst&&Math.abs(t[0])>JXG.Math.eps&&this.position<0&&(this.coords.setCoordinates(JXG.COORDS_BY_USER,t),this.position=0),n=f.point2.coords.usrCoords,!f.visProp.straightlast&&Math.abs(n[0])>JXG.Math.eps&&this.position>1&&(this.coords.setCoordinates(JXG.COORDS_BY_USER,n),this.position=1)}else if(f.type==JXG.OBJECT_TYPE_TURTLE)this.updateConstraint(),this.coords=JXG.Math.Geometry.projectPointToTurtle(this,f,this.board);else if(f.elementClass==JXG.OBJECT_CLASS_CURVE)if(f.type==JXG.OBJECT_TYPE_ARC||f.type==JXG.OBJECT_TYPE_SECTOR){this.coords=JXG.Math.Geometry.projectPointToCircle(this,f,this.board),h=JXG.Math.Geometry.rad(f.radiuspoint,f.center,this),l=0,c=JXG.Math.Geometry.rad(f.radiuspoint,f.center,f.anglepoint),this.position=h;if(f.visProp.type=="minor"&&c>Math.PI||f.visProp.type=="major"&&c<Math.PI)l=c,c=2*Math.PI;if(h<l||h>c){this.position=c;if(h<l&&h>l*.5||h>c&&h>c*.5+Math.PI)this.position=l;this.updateGliderFromParent()}}else this.updateConstraint(),f.transformations.length>0?(f.updateTransformMatrix(),v=JXG.Math.inverse(f.transformMat),d=JXG.Math.matVecMult(v,this.coords.usrCoords),p=(new JXG.Coords(JXG.COORDS_BY_USER,d,this.board)).usrCoords,d=JXG.Math.Geometry.projectCoordsToCurve(p[1],p[2],this.position||0,f,this.board),this.position=d[1],this.coords=d[0]):this.coords=JXG.Math.Geometry.projectPointToCurve(this,f,this.board);else f.elementClass==JXG.OBJECT_CLASS_POINT&&(this.coords=JXG.Math.Geometry.projectPointToPoint(this,f,this.board))},updateGliderFromParent:function(){var e,t,n,r,i,s=this.slideObject,o;s.elementClass==JXG.OBJECT_CLASS_CIRCLE?(n=s.Radius(),this.coords.setCoordinates(JXG.COORDS_BY_USER,[s.center.X()+n*Math.cos(this.position),s.center.Y()+n*Math.sin(this.position)])):s.elementClass==JXG.OBJECT_CLASS_LINE?(e=s.point1.coords.usrCoords,t=s.point2.coords.usrCoords,Math.abs(t[0])<JXG.Math.eps?(r=Math.min(Math.abs(this.position),1-JXG.Math.eps),r/=1-r,this.position<0&&(r*=-1),this.coords.setCoordinates(JXG.COORDS_BY_USER,[e[0]+r*t[0],e[1]+r*t[1],e[2]+r*t[2]])):Math.abs(e[0])<JXG.Math.eps?(r=Math.max(this.position,JXG.Math.eps),r=Math.min(r,2-JXG.Math.eps),r>1?r=(r-1)/(r-2):r=(1-r)/r,this.coords.setCoordinates(JXG.COORDS_BY_USER,[t[0]+r*e[0],t[1]+r*e[1],t[2]+r*e[2]])):(r=this.position,this.coords.setCoordinates(JXG.COORDS_BY_USER,[e[0]+r*(t[0]-e[0]),e[1]+r*(t[1]-e[1]),e[2]+r*(t[2]-e[2])]))):s.type==JXG.OBJECT_TYPE_TURTLE?(this.coords.setCoordinates(JXG.COORDS_BY_USER,[s.Z(this.position),s.X(this.position),s.Y(this.position)]),this.updateConstraint(),this.coords=JXG.Math.Geometry.projectPointToTurtle(this,s,this.board)):s.elementClass==JXG.OBJECT_CLASS_CURVE?(this.coords.setCoordinates(JXG.COORDS_BY_USER,[s.Z(this.position),s.X(this.position),s.Y(this.position)]),s.type==JXG.OBJECT_TYPE_ARC||s.type==JXG.OBJECT_TYPE_SECTOR?(o=JXG.Math.Geometry.rad([s.center.X()+1,s.center.Y()],s.center,s.radiuspoint),n=s.Radius(),this.coords.setCoordinates(JXG.COORDS_BY_USER,[s.center.X()+n*Math.cos(this.position+o),s.center.Y()+n*Math.sin(this.position+o)])):(this.updateConstraint(),this.coords=JXG.Math.Geometry.projectPointToCurve(this,s,this.board))):s.elementClass==JXG.OBJECT_CLASS_POINT&&(this.coords=JXG.Math.Geometry.projectPointToPoint(this,s,this.board))},updateRenderer:function(){if(!this.needsUpdate)return this;if(this.visProp.visible&&this.visProp.size>0){var e=this.isReal;this.isReal=!isNaN(this.coords.usrCoords[1]+this.coords.usrCoords[2]),this.isReal=Math.abs(this.coords.usrCoords[0])>JXG.Math.eps?this.isReal:!1,this.isReal?(e!=this.isReal&&(this.board.renderer.show(this),this.hasLabel&&this.label.content.visProp.visible&&this.board.renderer.show(this.label.content)),this.board.renderer.updatePoint(this)):e!=this.isReal&&(this.board.renderer.hide(this),this.hasLabel&&this.label.content.visProp.visible&&this.board.renderer.hide(this.label.content))}return this.hasLabel&&this.visProp.visible&&this.label.content&&this.label.content.visProp.visible&&this.isReal&&(this.label.content.update(),this.board.renderer.updateText(this.label.content)),this.needsUpdate=!1,this},X:function(){return this.coords.usrCoords[1]},Y:function(){return this.coords.usrCoords[2]},Z:function(){return this.coords.usrCoords[0]},XEval:function(){return this.coords.usrCoords[1]},YEval:function(){return this.coords.usrCoords[2]},ZEval:function(){return this.coords.usrCoords[0]},bounds:function(){return this.coords.usrCoords.slice(1).concat(this.coords.usrCoords.slice(1))},Dist:function(e){var t,n=e.coords.usrCoords,r=this.coords.usrCoords,i;return i=r[0]-n[0],t=i*i,i=r[1]-n[1],t+=i*i,i=r[2]-n[2],t+=i*i,Math.sqrt(t)},snapToGrid:function(){return this.handleSnapToGrid()},handleSnapToGrid:function(){var e,t,n=this.visProp.snapsizex,r=this.visProp.snapsizey;return this.visProp.snaptogrid&&(e=this.coords.usrCoords[1],t=this.coords.usrCoords[2],n<=0&&this.board.defaultAxes&&this.board.defaultAxes.x.defaultTicks&&(n=this.board.defaultAxes.x.defaultTicks.ticksDelta*(this.board.defaultAxes.x.defaultTicks.visProp.minorticks+1)),r<=0&&this.board.defaultAxes&&this.board.defaultAxes.y.defaultTicks&&(r=this.board.defaultAxes.y.defaultTicks.ticksDelta*(this.board.defaultAxes.y.defaultTicks.visProp.minorticks+1)),n>0&&r>0&&this.coords.setCoordinates(JXG.COORDS_BY_USER,[Math.round(e/n)*n,Math.round(t/r)*r])),this},handleSnapToPoints:function(){var e,t,n,r=0,i=Infinity,s=null;if(this.visProp.snaptopoints){for(e in this.board.objects)t=this.board.objects[e],t.elementClass==JXG.OBJECT_CLASS_POINT&&t!==this&&t.visProp.visible&&(n=JXG.Math.Geometry.projectPointToPoint(this,t,this.board),r=n.distance(JXG.COORDS_BY_USER,this.coords),r<this.visProp.attractordistance&&r<i&&(i=r,s=n));s!=null&&this.coords.setCoordinates(JXG.COORDS_BY_USER,s.usrCoords)}return this},handleAttractors:function(){var e=this.visProp.attractors.length,t,n,r,i=0;if(this.visProp.attractordistance==0)return;for(t=0;t<e;t++){n=JXG.getRef(this.board,this.visProp.attractors[t]);if(!JXG.exists(n)||n===this)continue;n.elementClass==JXG.OBJECT_CLASS_POINT?r=JXG.Math.Geometry.projectPointToPoint(this,n,this.board):n.elementClass==JXG.OBJECT_CLASS_LINE?r=JXG.Math.Geometry.projectPointToLine(this,n,this.board):n.elementClass==JXG.OBJECT_CLASS_CIRCLE?r=JXG.Math.Geometry.projectPointToCircle(this,n,this.board):n.elementClass==JXG.OBJECT_CLASS_CURVE?r=JXG.Math.Geometry.projectPointToCurve(this,n,this.board):n.type==JXG.OBJECT_TYPE_TURTLE&&(r=JXG.Math.Geometry.projectPointToTurtle(this,n,this.board)),i=r.distance(JXG.COORDS_BY_USER,this.coords);if(i<this.visProp.attractordistance){found=!0,(this.type!=JXG.OBJECT_TYPE_GLIDER||this.slideObject!=n)&&this.makeGlider(n);break}n==this.slideObject&&i>=this.visProp.snatchdistance&&(this.type=JXG.OBJECT_TYPE_POINT)}return this},setPositionDirectly:function(e,t){var n,r,i,s,o,u,a=this.coords,f;this.coords.setCoordinates(e,t),this.handleSnapToGrid(),this.handleSnapToPoints(),this.handleAttractors();if(!(this.group.length>0)){for(n=this.transformations.length-1;n>=0;n--)e===JXG.COORDS_BY_SCREEN?f=(new JXG.Coords(e,t,this.board)).usrCoords:(t.length===2&&(t=[1].concat(t)),f=t),this.initialCoords.setCoordinates(JXG.COORDS_BY_USER,JXG.Math.matVecMult(JXG.Math.inverse(this.transformations[n].matrix),f));this.update()}return this},setPositionByTransform:function(e,t){var n;return t=new JXG.Coords(e,t,this.board),n=this.board.create("transform",t.usrCoords.slice(1),{type:"translate"}),this.transformations.length>0&&this.transformations[this.transformations.length-1].isNumericMatrix?this.transformations[this.transformations.length-1].melt(n):this.addTransform(this,n),this.update(),this},setPosition:function(e,t){return this.setPositionDirectly(e,t)},setGliderPosition:function(e){if(this.type=JXG.OBJECT_TYPE_GLIDER)this.position=e,this.board.update();return this},makeGlider:function(e){return this.slideObject=JXG.getRef(this.board,e),this.type=JXG.OBJECT_TYPE_GLIDER,this.elType="glider",this.visProp.snapwidth=-1,this.slideObject.addChild(this),this.isDraggable=!0,this.generatePolynomial=function(){return this.slideObject.generatePolynomial(this)},this.updateGlider(),this},free:function(){var e,t;if(this.type!==JXG.OBJECT_TYPE_GLIDER){if(!!this.isDraggable)return;this.isDraggable=!0,this.type=JXG.OBJECT_TYPE_POINT,this.XEval=function(){return this.coords.usrCoords[1]},this.YEval=function(){return this.coords.usrCoords[2]},this.ZEval=function(){return this.coords.usrCoords[0]},this.Xjc=null,this.Yjc=null}for(e in this.ancestors){this.ancestors[e].descendants[this.id]&&delete this.ancestors[e].descendants[this.id],this.ancestors[e].childElements[this.id]&&delete this.ancestors[e].childElements[this.id];for(t in this.descendants)this.ancestors[e].descendants[t]&&delete this.ancestors[e].descendants[t],this.ancestors[e].childElements[t]&&delete this.ancestors[e].childElements[t]}this.ancestors=[],this.slideObject=null,this.elType="point",this.type=JXG.OBJECT_TYPE_POINT},addConstraint:function(e){this.type=JXG.OBJECT_TYPE_CAS;var t=[],n,r,i,s,o=["X","Y"];this.isDraggable=!1;for(r=0;r<e.length;r++)i=e[r],typeof i=="string"?(t[r]=this.board.jc.snippet(i,!0,null,!0),e.length===2&&(this[o[r]+"jc"]=e[r])):typeof i=="function"?t[r]=i:typeof i=="number"?t[r]=function(e){return function(){return e}}(i):typeof i=="object"&&typeof i.Value=="function"&&(t[r]=function(e){return function(){return e.Value()}}(i)),t[r].origin=i;return e.length==1?this.updateConstraint=function(){var e=t[0]();JXG.isArray(e)?this.coords.setCoordinates(JXG.COORDS_BY_USER,e):this.coords=e}:e.length==2?(this.XEval=t[0],this.YEval=t[1],n="this.coords.setCoordinates("+JXG.COORDS_BY_USER+",[this.XEval(),this.YEval()]);",this.updateConstraint=new Function("",n)):(this.ZEval=t[0],this.XEval=t[1],this.YEval=t[2],n="this.coords.setCoordinates("+JXG.COORDS_BY_USER+",[this.ZEval(),this.XEval(),this.YEval()]);",this.updateConstraint=new Function("",n)),this.board.isSuspendedUpdate||this.prepareUpdate().update().updateRenderer(),this},updateTransform:function(){if(this.transformations.length==0||this.baseElement==null)return this;var e,t;this===this.baseElement?e=this.transformations[0].apply(this.baseElement,"self"):e=this.transformations[0].apply(this.baseElement),this.coords.setCoordinates(JXG.COORDS_BY_USER,e);for(t=1;t<this.transformations.length;t++)this.coords.setCoordinates(JXG.COORDS_BY_USER,this.transformations[t].apply(this));return this},addTransform:function(e,t){var n,r=JXG.isArray(t)?t:[t],i=r.length;this.transformations.length===0&&(this.baseElement=e);for(n=0;n<i;n++)this.transformations.push(r[n]);return this},startAnimation:function(e,t){return this.type==JXG.OBJECT_TYPE_GLIDER&&typeof this.intervalCode=="undefined"&&(this.intervalCode=window.setInterval("JXG.JSXGraph.boards['"+this.board.id+"'].objects['"+this.id+"']._anim("+e+", "+t+")",250),typeof this.intervalCount=="undefined"&&(this.intervalCount=0)),this},stopAnimation:function(){return typeof this.intervalCode!="undefined"&&(window.clearInterval(this.intervalCode),delete this.intervalCode),this},moveAlong:function(e,t,n){n=n||{};var r=[],i=this.board.options.animationDelay,s=function(t,n){return function(){return e[t][n]}},o=[],u,a,f=t/i;if(JXG.isArray(e)){for(u=0;u<e.length;u++)JXG.isPoint(e[u])?o[u]=e[u]:o[u]={elementClass:JXG.OBJECT_CLASS_POINT,X:s(u,0),Y:s(u,1)};t=t||0;if(t===0)return this.setPosition(JXG.COORDS_BY_USER,[o[o.length-1].X(),o[o.length-1].Y()]),this.board.update(this);a=JXG.Math.Numerics.Neville(o);for(u=0;u<f;u++)r[u]=[],r[u][0]=a[0]((f-u)/f*a[3]()),r[u][1]=a[1]((f-u)/f*a[3]());this.animationPath=r}else JXG.isFunction(e)&&(this.animationPath=e,this.animationStart=(new Date).getTime());return this.animationCallback=n.callback,this.board.addAnimation(this),this},moveTo:function(e,t,n){e=new JXG.Coords(JXG.COORDS_BY_USER,e,this.board);if(typeof t=="undefined"||t==0||Math.abs(e.usrCoords[0]-this.coords.usrCoords[0])>JXG.Math.eps)return this.setPosition(JXG.COORDS_BY_USER,e.usrCoords),this.board.update(this);n=n||{};var r=this.board.options.animationDelay,i=Math.ceil(t/(r*1)),s=new Array(i+1),o=this.coords.usrCoords[1],u=this.coords.usrCoords[2],a=e.usrCoords[1]-o,f=e.usrCoords[2]-u,l,c=function(e){return n.effect&&n.effect=="<>"?Math.pow(Math.sin(e/(i*1)*Math.PI/2),2):e/i};if(Math.abs(a)<JXG.Math.eps&&Math.abs(f)<JXG.Math.eps)return this;for(l=i;l>=0;l--)s[i-l]=[e.usrCoords[0],o+a*c(l),u+f*c(l)];return this.animationPath=s,this.animationCallback=n.callback,this.board.addAnimation(this),this},visit:function(e,t,n){typeof n=="number"?n={repeat:n}:(n=n||{},typeof n.repeat=="undefined"&&(n.repeat=1));var r=this.board.options.animationDelay,i=Math.ceil(t/(r*n.repeat)),s=new Array(n.repeat*(i+1)),o=this.coords.usrCoords[1],u=this.coords.usrCoords[2],a=e[0]-o,f=e[1]-u,l,c,h=function(e){var t=e<i/2?2*e/i:2*(i-e)/i;return n.effect&&n.effect=="<>"?Math.pow(Math.sin(t*Math.PI/2),2):t};for(c=0;c<n.repeat;c++)for(l=i;l>=0;l--)s[c*(i+1)+i-l]=[e[0],o+a*h(l),u+f*h(l)];return this.animationPath=s,this.animationCallback=n.callback,this.board.addAnimation(this),this},_anim:function(e,t){var n,r,i,s,o,u,a=1,f,l;return this.intervalCount++,this.intervalCount>t&&(this.intervalCount=0),this.slideObject.elementClass==JXG.OBJECT_CLASS_LINE?(n=this.slideObject.point1.coords.distance(JXG.COORDS_BY_SCREEN,this.slideObject.point2.coords),r=this.slideObject.getSlope(),r!="INF"?(o=Math.atan(r),i=Math.round(this.intervalCount/t*n*Math.cos(o)),s=Math.round(this.intervalCount/t*n*Math.sin(o))):(i=0,s=Math.round(this.intervalCount/t*n)),e<0?(u=this.slideObject.point2,this.slideObject.point2.coords.scrCoords[1]-this.slideObject.point1.coords.scrCoords[1]>0?a=-1:this.slideObject.point2.coords.scrCoords[1]-this.slideObject.point1.coords.scrCoords[1]==0&&this.slideObject.point2.coords.scrCoords[2]-this.slideObject.point1.coords.scrCoords[2]>0&&(a=-1)):(u=this.slideObject.point1,this.slideObject.point1.coords.scrCoords[1]-this.slideObject.point2.coords.scrCoords[1]>0?a=-1:this.slideObject.point1.coords.scrCoords[1]-this.slideObject.point2.coords.scrCoords[1]==0&&this.slideObject.point1.coords.scrCoords[2]-this.slideObject.point2.coords.scrCoords[2]>0&&(a=-1)),this.coords.setCoordinates(JXG.COORDS_BY_SCREEN,[u.coords.scrCoords[1]+a*i,u.coords.scrCoords[2]+a*s])):this.slideObject.elementClass==JXG.OBJECT_CLASS_CURVE?(e>0?f=Math.round(this.intervalCount/t*this.board.canvasWidth):f=Math.round((t-this.intervalCount)/t*this.board.canvasWidth),this.coords.setCoordinates(JXG.COORDS_BY_SCREEN,[f,0]),this.coords=JXG.Math.Geometry.projectPointToCurve(this,this.slideObject,this.board)):this.slideObject.elementClass==JXG.OBJECT_CLASS_CIRCLE&&(e<0?o=this.intervalCount/t*2*Math.PI:o=(t-this.intervalCount)/t*2*Math.PI,l=this.slideObject.Radius(),this.coords.setCoordinates(JXG.COORDS_BY_USER,[this.slideObject.center.coords.usrCoords[1]+l*Math.cos(o),this.slideObject.center.coords.usrCoords[2]+l*Math.sin(o)])),this.board.update(this),this},setStyle:function(e){var t=["cross","cross","cross","circle","circle","circle","circle","square","square","square","plus","plus","plus"],n=[2,3,4,1,2,3,4,2,3,4,2,3,4];return this.visProp.face=t[e],this.visProp.size=n[e],this.board.renderer.changePointStyle(this),this},normalizeFace:function(e){var t={cross:"x",x:"x",circle:"o",o:"o",square:"[]","[]":"[]",plus:"+","+":"+",diamond:"<>","<>":"<>",triangleup:"^",a:"^","^":"^",triangledown:"v",v:"v",triangleleft:"<","<":"<",triangleright:">",">":">"};return t[e]},remove:function(){this.hasLabel&&this.board.renderer.remove(this.board.renderer.getElementById(this.label.content.id)),this.board.renderer.remove(this.board.renderer.getElementById(this.id))},getTextAnchor:function(){return this.coords},getLabelAnchor:function(){return this.coords},face:function(e){this.setProperty({face:e})},size:function(e){this.setProperty({size:e})},cloneToBackground:function(){var e={};return e.id=this.id+"T"+this.numTraces,this.numTraces++,e.coords=this.coords,e.visProp=JXG.deepCopy(this.visProp,this.visProp.traceattributes,!0),e.visProp.layer=this.board.options.layer.trace,e.elementClass=JXG.OBJECT_CLASS_POINT,e.board=this.board,JXG.clearVisPropOld(e),this.board.renderer.drawPoint(e),this.traces[e.id]=e.rendNode,this},getParents:function(){var e=[this.Z(),this.X(),this.Y()];return this.parents&&(e=this.parents),this.type==JXG.OBJECT_TYPE_GLIDER&&(e=[this.X(),this.Y(),this.slideObject.id]),e}}),JXG.createPoint=function(e,t,n){var r,i=!1,s,o;o=JXG.copyAttributes(n,e.options,"point");for(s=0;s<t.length;s++)if(typeof t[s]=="function"||typeof t[s]=="string")i=!0;if(!i)if(JXG.isNumber(t[0])&&JXG.isNumber(t[1]))r=new JXG.Point(e,t,o),JXG.exists(o.slideobject)?r.makeGlider(o.slideobject):r.baseElement=r,r.isDraggable=!0;else{if(typeof t[0]!="object"||typeof t[1]!="object")throw new Error("JSXGraph: Can't create point with parent types '"+typeof t[0]+"' and '"+typeof t[1]+"'."+"\nPossible parent types: [x,y], [z,x,y], [point,transformation]");r=new JXG.Point(e,[0,0],o),r.addTransform(t[0],t[1]),r.isDraggable=!1,r.parents=[t[0].id]}else r=new JXG.Point(e,[NaN,NaN],o),r.addConstraint(t);return r},JXG.createGlider=function(e,t,n){var r,i=JXG.copyAttributes(n,e.options,"glider");return t.length===1?r=e.create("point",[0,0],i):r=e.create("point",t.slice(0,2),i),r.makeGlider(t[t.length-1]),r},JXG.createIntersectionPoint=function(e,t,n){var r,i=JXG.copyAttributes(n,e.options,"intersection"),s;t.push(0,0),r=e.create("point",[0,0,0],i),s=new e.intersection(t[0],t[1],t[2],t[3],{point:r}),r.addConstraint([s]);try{t[0].addChild(r),t[1].addChild(r)}catch(o){throw new Error("JSXGraph: Can't create 'intersection' with parent types '"+typeof t[0]+"' and '"+typeof t[1]+"'.")}return r.elType="intersection",r.parents=[t[0].id,t[1].id,t[2]],t[3]!=null&&r.parents.push(t[3]),r.generatePolynomial=function(){var e=t[0].generatePolynomial(r),n=t[1].generatePolynomial(r);return e.length==0||n.length==0?[]:[e[0],n[0]]},r},JXG.createOtherIntersectionPoint=function(e,t,n){var r;if(t.length!=3||!JXG.isPoint(t[2])||t[0].elementClass!=JXG.OBJECT_CLASS_LINE&&t[0].elementClass!=JXG.OBJECT_CLASS_CIRCLE||t[1].elementClass!=JXG.OBJECT_CLASS_LINE&&t[1].elementClass!=JXG.OBJECT_CLASS_CIRCLE)throw new Error("JSXGraph: Can't create 'other intersection point' with parent types '"+typeof t[0]+"', '"+typeof t[1]+"'and '"+typeof t[2]+"'."+"\nPossible parent types: [circle|line,circle|line,point]");return r=e.create("point",[e.otherIntersection(t[0],t[1],t[2])],n),r.elType="otherintersection",r.parents=[t[0].id,t[1].id,t[2]],t[0].addChild(r),t[1].addChild(r),r.generatePolynomial=function(){var e=t[0].generatePolynomial(r),n=t[1].generatePolynomial(r);return e.length==0||n.length==0?[]:[e[0],n[0]]},r},JXG.JSXGraph.registerElement("point",JXG.createPoint),JXG.JSXGraph.registerElement("glider",JXG.createGlider),JXG.JSXGraph.registerElement("intersection",JXG.createIntersectionPoint),JXG.JSXGraph.registerElement("otherintersection",JXG.createOtherIntersectionPoint),JXG.Line=function(e,t,n,r){this.constructor(e,r,JXG.OBJECT_TYPE_LINE,JXG.OBJECT_CLASS_LINE),this.point1=JXG.getReference(this.board,t),this.point2=JXG.getReference(this.board,n),this.ticks=[],this.defaultTicks=null,this.parentPolygon=null,this.id=this.board.setId(this,"L"),this.board.renderer.drawLine(this),this.board.finalizeAdding(this),this.elType="line",this.point1.addChild(this),this.point2.addChild(this),this.updateStdform(),this.createLabel()},JXG.Line.prototype=new JXG.GeometryElement,JXG.extend(JXG.Line.prototype,{hasPoint:function(e,t){var n=[],r,i=[1,e,t],s,o,u,a,f,l;return n[0]=this.stdform[0]-this.stdform[1]*this.board.origin.scrCoords[1]/this.board.unitX+this.stdform[2]*this.board.origin.scrCoords[2]/this.board.unitY,n[1]=this.stdform[1]/this.board.unitX,n[2]=this.stdform[2]/-this.board.unitY,r=JXG.Math.Geometry.distPointLine(i,n),isNaN(r)||r>this.board.options.precision.hasPoint?!1:this.visProp.straightfirst&&this.visProp.straightlast?!0:(o=this.point1.coords,u=this.point2.coords,s=[0,n[1],n[2]],s=JXG.Math.crossProduct(s,i),s=JXG.Math.crossProduct(s,n),s[1]/=s[0],s[2]/=s[0],s[0]=1,s=(new JXG.Coords(JXG.COORDS_BY_SCREEN,s.slice(1),this.board)).usrCoords,a=o.distance(JXG.COORDS_BY_USER,u),o=o.usrCoords.slice(0),u=u.usrCoords.slice(0),a<JXG.Math.eps?f=0:(a==Number.POSITIVE_INFINITY&&(a=1/JXG.Math.eps,Math.abs(u[0])<JXG.Math.eps?(a/=JXG.Math.Geometry.distance([0,0,0],u),u=[1,o[1]+u[1]*a,o[2]+u[2]*a]):(a/=JXG.Math.Geometry.distance([0,0,0],o),o=[1,u[1]+o[1]*a,u[2]+o[2]*a])),l=1,a=u[l]-o[l],Math.abs(a)<JXG.Math.eps&&(l=2,a=u[l]-o[l]),f=(s[l]-o[l])/a),!this.visProp.straightfirst&&f<0?!1:!this.visProp.straightlast&&f>1?!1:!0)},update:function(){var e;return this.needsUpdate?(this.constrained&&(typeof this.funps!="undefined"?(e=this.funps(),e&&e.length&&e.length===2&&(this.point1=e[0],this.point2=e[1])):(typeof this.funp1=="function"&&(e=this.funp1(),JXG.isPoint(e)?this.point1=e:e&&e.length&&e.length===2&&this.point1.setPositionDirectly(JXG.COORDS_BY_USER,e)),typeof this.funp2=="function"&&(e=this.funp2(),JXG.isPoint(e)?this.point2=e:e&&e.length&&e.length===2&&this.point2.setPositionDirectly(JXG.COORDS_BY_USER,e)))),this.updateSegmentFixedLength(),this.updateStdform(),this.visProp.trace&&this.cloneToBackground(!0),this):this},updateSegmentFixedLength:function(){var e,t,n,r,i,s,o,u;if(!this.hasFixedLength)return this;e=this.point1.Dist(this.point2),t=this.fixedLength(),n=this.fixedLengthOldCoords[0].distance(JXG.COORDS_BY_USER,this.point1.coords),r=this.fixedLengthOldCoords[1].distance(JXG.COORDS_BY_USER,this.point2.coords);if(n>JXG.Math.eps||r>JXG.Math.eps||e!=t){i=this.point1.isDraggable&&this.point1.type!=JXG.OBJECT_TYPE_GLIDER&&!this.point1.visProp.fixed,s=this.point2.isDraggable&&this.point2.type!=JXG.OBJECT_TYPE_GLIDER&&!this.point2.visProp.fixed;if(e>JXG.Math.eps){if(n>r&&s||n<=r&&s&&!i)this.point2.setPositionDirectly(JXG.COORDS_BY_USER,[this.point1.X()+(this.point2.X()-this.point1.X())*t/e,this.point1.Y()+(this.point2.Y()-this.point1.Y())*t/e]),this.point2.prepareUpdate().updateRenderer();else if(n<=r&&i||n>r&&i&&!s)this.point1.setPositionDirectly(JXG.COORDS_BY_USER,[this.point2.X()+(this.point1.X()-this.point2.X())*t/e,this.point2.Y()+(this.point1.Y()-this.point2.Y())*t/e]),this.point1.prepareUpdate().updateRenderer()}else o=Math.random()-.5,u=Math.random()-.5,e=Math.sqrt(o*o+u*u),s?(this.point2.setPositionDirectly(JXG.COORDS_BY_USER,[this.point1.X()+o*t/e,this.point1.Y()+u*t/e]),this.point2.prepareUpdate().updateRenderer()):i&&(this.point1.setPositionDirectly(JXG.COORDS_BY_USER,[this.point2.X()+o*t/e,this.point2.Y()+u*t/e]),this.point1.prepareUpdate().updateRenderer());this.fixedLengthOldCoords[0].setCoordinates(JXG.COORDS_BY_USER,this.point1.coords.usrCoords),this.fixedLengthOldCoords[1].setCoordinates(JXG.COORDS_BY_USER,this.point2.coords.usrCoords)}return this},updateStdform:function(){var e=JXG.Math.crossProduct(this.point1.coords.usrCoords,this.point2.coords.usrCoords);this.stdform[0]=e[0],this.stdform[1]=e[1],this.stdform[2]=e[2],this.stdform[3]=0,this.normalize()},updateRenderer:function(){var e;return this.needsUpdate&&this.visProp.visible&&(e=this.isReal,this.isReal=!isNaN(this.point1.coords.usrCoords[1]+this.point1.coords.usrCoords[2]+this.point2.coords.usrCoords[1]+this.point2.coords.usrCoords[2])&&JXG.Math.innerProduct(this.stdform,this.stdform,3)>=JXG.Math.eps*JXG.Math.eps,this.isReal?(e!=this.isReal&&(this.board.renderer.show(this),this.hasLabel&&this.label.content.visProp.visible&&this.board.renderer.show(this.label.content)),this.board.renderer.updateLine(this)):e!=this.isReal&&(this.board.renderer.hide(this),this.hasLabel&&this.label.content.visProp.visible&&this.board.renderer.hide(this.label.content)),this.needsUpdate=!1),this.hasLabel&&this.label.content.visProp.visible&&this.isReal&&(this.label.content.update(),this.board.renderer.updateText(this.label.content)),this},generatePolynomial:function(e){var t=this.point1.symbolic.x,n=this.point1.symbolic.y,r=this.point2.symbolic.x,i=this.point2.symbolic.y,s=e.symbolic.x,o=e.symbolic.y;return[["(",n,")*(",s,")-(",n,")*(",r,")+(",o,")*(",r,")-(",t,")*(",o,")+(",t,")*(",i,")-(",s,")*(",i,")"].join("")]},getRise:function(){return Math.abs(this.stdform[2])>=JXG.Math.eps?-this.stdform[0]/this.stdform[2]:Infinity},getSlope:function(){return Math.abs(this.stdform[2])>=JXG.Math.eps?-this.stdform[1]/this.stdform[2]:Infinity},getAngle:function(){return Math.atan2(this.point2.Y()-this.point1.Y(),this.point2.X()-this.point1.X())},setStraight:function(e,t){return this.visProp.straightfirst=e,this.visProp.straightlast=t,this.board.renderer.updateLine(this),this},getTextAnchor:function(){return new JXG.Coords(JXG.COORDS_BY_USER,[.5*(this.point2.X()+this.point1.X()),.5*(this.point2.Y()+this.point1.Y())],this.board)},setLabelRelativeCoords:function(e){JXG.exists(this.label.content)&&(this.label.content.relativeCoords=new JXG.Coords(JXG.COORDS_BY_SCREEN,[e[0],-e[1]],this.board))},getLabelAnchor:function(){var e,t,n=0,r=0,i=0,s=new JXG.Coords(JXG.COORDS_BY_USER,this.point1.coords.usrCoords,this.board),o=new JXG.Coords(JXG.COORDS_BY_USER,this.point2.coords.usrCoords,this.board);(this.visProp.straightfirst||this.visProp.straightlast)&&JXG.Math.Geometry.calcStraight(this,s,o,0),s=s.scrCoords,o=o.scrCoords;if(!JXG.exists(this.label.content))return new JXG.Coords(JXG.COORDS_BY_SCREEN,[NaN,NaN],this.board);switch(this.label.content.visProp.position){case"lft":case"llft":case"ulft":s[1]<=o[1]?(e=s[1],t=s[2]):(e=o[1],t=o[2]);break;case"rt":case"lrt":case"urt":s[1]>o[1]?(e=s[1],t=s[2]):(e=o[1],t=o[2]);break;default:e=.5*(s[1]+o[1]),t=.5*(s[2]+o[2])}if(this.visProp.straightfirst||this.visProp.straightlast)JXG.exists(this.label.content)&&(r=parseFloat(this.label.content.visProp.offset[0]),i=parseFloat(this.label.content.visProp.offset[1]),n=this.label.content.visProp.fontsize),Math.abs(e)<JXG.Math.eps?e=r:this.board.canvasWidth+JXG.Math.eps>e&&e>this.board.canvasWidth-n-JXG.Math.eps?e=this.board.canvasWidth-r-n:e+=r,JXG.Math.eps+n>t&&t>-JXG.Math.eps?t=i+n:this.board.canvasHeight+JXG.Math.eps>t&&t>this.board.canvasHeight-n-JXG.Math.eps?t=this.board.canvasHeight-i:t+=i;return new JXG.Coords(JXG.COORDS_BY_SCREEN,[e,t],this.board)},cloneToBackground:function(){var e={},t,n,r;return e.id=this.id+"T"+this.numTraces,e.elementClass=JXG.OBJECT_CLASS_LINE,this.numTraces++,e.point1=this.point1,e.point2=this.point2,e.stdform=this.stdform,e.board=this.board,e.visProp=JXG.deepCopy(this.visProp,this.visProp.traceattributes,!0),e.visProp.layer=this.board.options.layer.trace,JXG.clearVisPropOld(e),n=this.getSlope(),t=this.getRise(),e.getSlope=function(){return n},e.getRise=function(){return t},r=this.board.renderer.enhancedRendering,this.board.renderer.enhancedRendering=!0,this.board.renderer.drawLine(e),this.board.renderer.enhancedRendering=r,this.traces[e.id]=e.rendNode,delete e,this},addTransform:function(e){var t,n=JXG.isArray(e)?e:[e],r=n.length;for(t=0;t<r;t++)this.point1.transformations.push(n[t]),this.point2.transformations.push(n[t]);return this},setPosition:function(e,t){var n;return t=new JXG.Coords(e,t,this.board),n=this.board.create("transform",t.usrCoords.slice(1),{type:"translate"}),this.point1.transformations.length>0&&this.point1.transformations[this.point1.transformations.length-1].isNumericMatrix?this.point1.transformations[this.point1.transformations.length-1].melt(n):this.point1.addTransform(this.point1,n),this.point2.transformations.length>0&&this.point2.transformations[this.point2.transformations.length-1].isNumericMatrix?this.point2.transformations[this.point2.transformations.length-1].melt(n):this.point2.addTransform(this.point2,n),this},setPositionDirectly:function(e,t,n){var r,i,s=new JXG.Coords(e,t,this.board),o=new JXG.Coords(e,n,this.board);return!this.point1.draggable()||!this.point2.draggable()?this:(r=JXG.Math.Statistics.subtract(s.usrCoords,o.usrCoords),i=this.board.create("transform",r.slice(1),{type:"translate"}),i.applyOnce([this.point1,this.point2]),this)},snapToGrid:function(){return this.visProp.snaptogrid&&(this.point1.snapToGrid(),this.point2.snapToGrid()),this},X:function(e){var t=this.stdform[2],n;return n=Math.abs(this.point1.coords.usrCoords[0])>JXG.Math.eps?this.point1.coords.usrCoords[1]:this.point2.coords.usrCoords[1],e=(e-.5)*2,e<0?(e*=-1,(1-e)*n+e*t):(1-e)*n-e*t},Y:function(e){var t=this.stdform[1],n;return n=Math.abs(this.point1.coords.usrCoords[0])>JXG.Math.eps?this.point1.coords.usrCoords[2]:this.point2.coords.usrCoords[2],e=(e-.5)*2,e<0?(e*=-1,(1-e)*n-e*t):(1-e)*n+e*t},Z:function(e){var t=Math.abs(this.point1.coords.usrCoords[0])>JXG.Math.eps?this.point1.coords.usrCoords[0]:this.point2.coords.usrCoords[0];return e=(e-.5)*2,e<0&&(e*=-1),(1-e)*t},L:function(){return this.point1.Dist(this.point2)},minX:function(){return 0},maxX:function(){return 1},bounds:function(){var e=this.point1.coords.usrCoords,t=this.point2.coords.usrCoords;return[Math.min(e[1],t[1]),Math.max(e[2],t[2]),Math.max(e[1],t[1]),Math.min(e[2],t[2])]},addTicks:function(e){if(e.id==""||typeof e.id=="undefined")e.id=this.id+"_ticks_"+(this.ticks.length+1);return this.board.renderer.drawTicks(e),this.ticks.push(e),e.id},remove:function(){this.removeAllTicks(),JXG.GeometryElement.prototype.remove.call(this)},removeAllTicks:function(){var e,t;for(t=this.ticks.length;t>0;t--)this.removeTicks(this.ticks[t-1]);this.ticks=new Array,this.board.update()},removeTicks:function(e){var t,n;this.defaultTicks!=null&&this.defaultTicks==e&&(this.defaultTicks=null);for(t=this.ticks.length;t>0;t--)if(this.ticks[t-1]==e){this.board.removeObject(this.ticks[t-1]);if(this.ticks[t-1].ticks)for(n=0;n<this.ticks[t-1].ticks.length;n++)this.ticks[t-1].labels[n]!=null&&this.board.removeObject(this.ticks[t-1].labels[n]);delete this.ticks[t-1];break}},hideElement:function(){var e;JXG.GeometryElement.prototype.hideElement.call(this);for(e=0;e<this.ticks.length;e++)this.ticks[e].hideElement()},showElement:function(){var e;JXG.GeometryElement.prototype.showElement.call(this);for(e=0;e<this.ticks.length;e++)this.ticks[e].showElement()}}),JXG.createLine=function(e,t,n){var r,i,s,o,u,a=[],f=!1,l;if(t.length==2){if(JXG.isArray(t[0])&&t[0].length>1)u=JXG.copyAttributes(n,e.options,"line","point1"),i=e.create("point",t[0],u);else if(JXG.isString(t[0])||t[0].elementClass==JXG.OBJECT_CLASS_POINT)i=JXG.getReference(e,t[0]);else if(typeof t[0]=="function"&&t[0]().elementClass==JXG.OBJECT_CLASS_POINT)i=t[0](),f=!0;else{if(typeof t[0]!="function"||!t[0]().length||t[0]().length!==2)throw new Error("JSXGraph: Can't create line with parent types '"+typeof t[0]+"' and '"+typeof t[1]+"'."+"\nPossible parent types: [point,point], [[x1,y1],[x2,y2]], [a,b,c]");u=JXG.copyAttributes(n,e.options,"line","point1"),i=JXG.createPoint(e,t[0](),u),f=!0}if(JXG.isArray(t[1])&&t[1].length>1)u=JXG.copyAttributes(n,e.options,"line","point2"),s=e.create("point",t[1],u);else if(JXG.isString(t[1])||t[1].elementClass==JXG.OBJECT_CLASS_POINT)s=JXG.getReference(e,t[1]);else if(typeof t[1]=="function"&&t[1]().elementClass==JXG.OBJECT_CLASS_POINT)s=t[1](),f=!0;else{if(typeof t[1]!="function"||!t[1]().length||t[1]().length!==2)throw new Error("JSXGraph: Can't create line with parent types '"+typeof t[0]+"' and '"+typeof t[1]+"'."+"\nPossible parent types: [point,point], [[x1,y1],[x2,y2]], [a,b,c]");u=JXG.copyAttributes(n,e.options,"line","point2"),s=JXG.createPoint(e,t[1](),u),f=!0}u=JXG.copyAttributes(n,e.options,"line"),r=new JXG.Line(e,i,s,u),f?(r.constrained=!0,r.funp1=t[0],r.funp2=t[1]):r.isDraggable=!0,r.constrained||(r.parents=[i.id,s.id])}else if(t.length==3){l=!0;for(o=0;o<3;o++)if(typeof t[o]=="number")a[o]=function(e){return function(){return e}}(t[o]);else{if(typeof t[o]!="function")throw new Error("JSXGraph: Can't create line with parent types '"+typeof t[0]+"' and '"+typeof t[1]+"' and '"+typeof t[2]+"'."+"\nPossible parent types: [point,point], [[x1,y1],[x2,y2]], [a,b,c]");a[o]=t[o],l=!1}u=JXG.copyAttributes(n,e.options,"line","point1"),l?i=e.create("point",[a[2]()*a[2]()+a[1]()*a[1](),a[2]()-a[1]()*a[0]()+a[2](),-a[1]()-a[2]()*a[0]()-a[1]()],u):i=e.create("point",[function(){return(0+a[2]()*a[2]()+a[1]()*a[1]())*.5},function(){return(a[2]()-a[1]()*a[0]()+a[2]())*.5},function(){return(-a[1]()-a[2]()*a[0]()-a[1]())*.5}],u),u=JXG.copyAttributes(n,e.options,"line","point2"),l?s=e.create("point",[a[2]()*a[2]()+a[1]()*a[1](),-a[1]()*a[0]()+a[2](),-a[2]()*a[0]()-a[1]()],u):s=e.create("point",[function(){return a[2]()*a[2]()+a[1]()*a[1]()},function(){return-a[1]()*a[0]()+a[2]()},function(){return-a[2]()*a[0]()-a[1]()}],u),i.prepareUpdate().update(),s.prepareUpdate().update(),u=JXG.copyAttributes(n,e.options,"line"),r=new JXG.Line(e,i,s,u),r.isDraggable=l,l&&(r.parents=[a[0](),a[1](),a[2]()])}else if(t.length==1&&typeof t[0]=="function"&&t[0]().length==2&&t[0]()[0].elementClass==JXG.OBJECT_CLASS_POINT&&t[0]()[1].elementClass==JXG.OBJECT_CLASS_POINT){var c=t[0]();u=JXG.copyAttributes(n,e.options,"line"),r=new JXG.Line(e,c[0],c[1],u),r.constrained=!0,r.funps=t[0]}else{if(t.length!=1||typeof t[0]!="function"||t[0]().length!=3||typeof t[0]()[0]!="number"||typeof t[0]()[1]!="number"||typeof t[0]()[2]!="number")throw new Error("JSXGraph: Can't create line with parent types '"+typeof t[0]+"' and '"+typeof t[1]+"'."+"\nPossible parent types: [point,point], [[x1,y1],[x2,y2]], [a,b,c]");c=t[0],u=JXG.copyAttributes(n,e.options,"line","point1"),i=e.create("point",[function(){var e=c();return[(0+e[2]*e[2]+e[1]*e[1])*.5,(e[2]-e[1]*e[0]+e[2])*.5,(-e[1]-e[2]*e[0]-e[1])*.5]}],u),u=JXG.copyAttributes(n,e.options,"line","point2"),s=e.create("point",[function(){var e=c();return[e[2]*e[2]+e[1]*e[1],-e[1]*e[0]+e[2],-e[2]*e[0]-e[1]]}],u),u=JXG.copyAttributes(n,e.options,"line"),r=new JXG.Line(e,i,s,u),r.constrained=!0,r.funps=t[0]}return r},JXG.JSXGraph.registerElement("line",JXG.createLine),JXG.createSegment=function(e,t,n){var r,i,s;n.straightFirst=!1,n.straightLast=!1,s=JXG.copyAttributes(n,e.options,"segment"),r=e.create("line",t.slice(0,2),s);if(t.length==3){r.hasFixedLength=!0;if(JXG.isNumber(t[2]))r.fixedLength=function(){return t[2]};else{if(!JXG.isFunction(t[2]))throw new Error("JSXGraph: Can't create segment with third parent type '"+typeof t[2]+"'."+"\nPossible third parent types: number or function");r.fixedLength=t[2]}r.fixedLengthOldCoords=[],r.fixedLengthOldCoords[0]=new JXG.Coords(JXG.COORDS_BY_USER,r.point1.coords.usrCoords.slice(1,3),e),r.fixedLengthOldCoords[1]=new JXG.Coords(JXG.COORDS_BY_USER,r.point2.coords.usrCoords.slice(1,3),e)}return r.elType="segment",r},JXG.JSXGraph.registerElement("segment",JXG.createSegment),JXG.createArrow=function(e,t,n){var r;return n.firstArrow=!1,n.lastArrow=!0,r=e.create("line",t,n).setStraight(!1,!1),r.type=JXG.OBJECT_TYPE_VECTOR,r.elType="arrow",r},JXG.JSXGraph.registerElement("arrow",JXG.createArrow),JXG.createAxis=function(e,t,n){var r,i,s;if(!JXG.isArray(t[0])&&!JXG.isPoint(t[0])||!JXG.isArray(t[1])&&!JXG.isPoint(t[1]))throw new Error("JSXGraph: Can't create axis with parent types '"+typeof t[0]+"' and '"+typeof t[1]+"'."+"\nPossible parent types: [point,point], [[x1,y1],[x2,y2]]");r=JXG.copyAttributes(n,e.options,"axis"),i=e.create("line",t,r),i.type=JXG.OBJECT_TYPE_AXIS,i.isDraggable=!1,i.point1.isDraggable=!1,i.point2.isDraggable=!1;for(var o in i.ancestors)i.ancestors[o].type=JXG.OBJECT_TYPE_AXISPOINT;return r=JXG.copyAttributes(n,e.options,"axis","ticks"),JXG.exists(r.ticksdistance)?s=r.ticksdistance:JXG.isArray(r.ticks)?s=r.ticks:s=1,i.defaultTicks=e.create("ticks",[i,s],r),i.defaultTicks.dump=!1,i.elType="axis",i.subs={ticks:i.defaultTicks},i},JXG.JSXGraph.registerElement("axis",JXG.createAxis),JXG.createTangent=function(e,t,n){var r,i,s,o,u,a,f,l;if(t.length==1)r=t[0],i=r.slideObject;else{if(t.length!=2)throw new Error("JSXGraph: Can't create tangent with parent types '"+typeof t[0]+"' and '"+typeof t[1]+"'."+"\nPossible parent types: [glider], [point,line|curve|circle|conic]");if(JXG.isPoint(t[0]))r=t[0],i=t[1];else{if(!JXG.isPoint(t[1]))throw new Error("JSXGraph: Can't create tangent with parent types '"+typeof t[0]+"' and '"+typeof t[1]+"'."+"\nPossible parent types: [glider], [point,line|curve|circle|conic]");i=t[0],r=t[1]}}if(i.elementClass==JXG.OBJECT_CLASS_LINE)l=e.create("line",[i.point1,i.point2],n);else if(i.elementClass==JXG.OBJECT_CLASS_CURVE&&i.type!=JXG.OBJECT_TYPE_CONIC)i.visProp.curvetype!="plot"?(s=i.X,o=i.Y,l=e.create("line",[function(){return-r.X()*e.D(o)(r.position)+r.Y()*e.D(s)(r.position)},function(){return e.D(o)(r.position)},function(){return-e.D(s)(r.position)}],n),r.addChild(l),l.glider=r):(l=e.create("line",[function(){return u=Math.floor(r.position),u==i.numberPoints-1&&u--,u<0?1:i.Y(u)*i.X(u+1)-i.X(u)*i.Y(u+1)},function(){return u=Math.floor(r.position),u==i.numberPoints-1&&u--,u<0?0:i.Y(u+1)-i.Y(u)},function(){return u=Math.floor(r.position),u==i.numberPoints-1&&u--,u<0?0:i.X(u)-i.X(u+1)}],n),r.addChild(l),l.glider=r);else if(i.type==JXG.OBJECT_TYPE_TURTLE)l=e.create("line",[function(){u=Math.floor(r.position);for(a=0;a<i.objects.length;a++){f=i.objects[a];if(f.type==JXG.OBJECT_TYPE_CURVE){if(u<f.numberPoints)break;u-=f.numberPoints}}return u==f.numberPoints-1&&u--,u<0?1:f.Y(u)*f.X(u+1)-f.X(u)*f.Y(u+1)},function(){u=Math.floor(r.position);for(a=0;a<i.objects.length;a++){f=i.objects[a];if(f.type==JXG.OBJECT_TYPE_CURVE){if(u<f.numberPoints)break;u-=f.numberPoints,moveTo(funps)}}return u==f.numberPoints-1&&u--,u<0?0:f.Y(u+1)-f.Y(u)},function(){u=Math.floor(r.position);for(a=0;a<i.objects.length;a++){f=i.objects[a];if(f.type==JXG.OBJECT_TYPE_CURVE){if(u<f.numberPoints)break;u-=f.numberPoints}}return u==f.numberPoints-1&&u--,u<0?0:f.X(u)-f.X(u+1)}],n),r.addChild(l),l.glider=r;else if(i.elementClass==JXG.OBJECT_CLASS_CIRCLE||i.type==JXG.OBJECT_TYPE_CONIC)l=e.create("line",[function(){return JXG.Math.matVecMult(i.quadraticform,r.coords.usrCoords)[0]},function(){return JXG.Math.matVecMult(i.quadraticform,r.coords.usrCoords)[1]},function(){return JXG.Math.matVecMult(i.quadraticform,r.coords.usrCoords)[2]}],n),r.addChild(l),l.glider=r;if(!JXG.exists(l))throw new Error("JSXGraph: Couldn't create tangent with the given parents.");l.elType="tangent",l.parents=[];for(u=0;u<t.length;u++)l.parents.push(t[u].id);return l},JXG.JSXGraph.registerElement("tangent",JXG.createTangent),JXG.JSXGraph.registerElement("polar",JXG.createTangent),JXG.Group=function(e,t,n){var r,i,s,o,u;this.board=e,this.objects={},r=this.board.numObjects,this.board.numObjects++,t==""||!JXG.exists(t)?this.id=this.board.id+"Group"+r:this.id=t,this.board.groups[this.id]=this,this.type=JXG.OBJECT_TYPE_POINT,this.elementClass=JXG.OBJECT_CLASS_POINT,n==""||!JXG.exists(n)?this.name="group_"+this.board.generateName(this):this.name=n,delete this.type,arguments.length==4&&JXG.isArray(arguments[3])?i=arguments[3]:i=Array.prototype.slice.call(arguments,3);for(s=0;s<i.length;s++)o=JXG.getReference(this.board,i[s]),!o.visProp.fixed&&(o.type==JXG.OBJECT_TYPE_POINT||o.type==JXG.OBJECT_TYPE_GLIDER)&&(o.group.length!=0?this.addGroup(o.group[o.group.length-1]):this.addPoint(o));this.suspendUpdate=!1,this.dX=0,this.dY=0},JXG.extend(JXG.Group.prototype,{ungroup:function(){var e;for(e in this.objects)JXG.isArray(this.objects[e].point.group)&&this.objects[e].point.group[this.objects[e].point.group.length-1]==this&&this.objects[e].point.group.pop(),this.removePoint(this.objects[e].point)},suspendUpdate:function(){this.suspendUpdate=!0},unsuspendUpdate:function(){this.suspendUpdate=!1},update:function(e,t,n,r){var i=null,s;if(!this.suspendUpdate){this.suspendUpdate=!0;for(s in this.objects)JXG.exists(this.board.objects[s])?(i=this.objects[s].point,i.id!=e.id&&i.coords.setCoordinates(JXG.COORDS_BY_USER,[i.coords.usrCoords[1]+t,i.coords.usrCoords[2]+n]),this.objects[s].point.prepareUpdate().update(!1).updateRenderer()):delete this.objects[s];this.suspendUpdate=!1}return this},addPoint:function(e){this.objects[e.id]={point:e,handler:function(t,n){this.update(e,e.coords.usrCoords[1]-t[1],e.coords.usrCoords[2]-t[2],e.coords.usrCoords[0]-t[0])}},e.coords.on("update",this.objects[e.id].handler,this)},addPoints:function(e){var t;for(t=0;t<e.length;t++)this.addPoint(e[t])},addGroup:function(e){var t;for(t in e.objects)this.addPoint(e.objects[t].point)},removePoint:function(e){var t;this.objects[e.id].point.coords.off("update",this.objects[e.id].handler),delete this.objects[e.id]},setProperty:function(){var e;for(e in this.objects)this.objects[e].point.setProperty.apply(this.objects[e].point,arguments)}}),JXG.createGroup=function(e,t,n){var r,i=new JXG.Group(e,n.id,n.name,t);i.elType="group",i.parents=[];for(r=0;r<t.length;r++)i.parents.push(t[r].id);return i},JXG.JSXGraph.registerElement("group",JXG.createGroup),JXG.Circle=function(e,t,n,r,i){this.constructor(e,i,JXG.OBJECT_TYPE_CIRCLE,JXG.OBJECT_CLASS_CIRCLE),this.method=t,this.midpoint=JXG.getReference(this.board,n),this.center=JXG.getReference(this.board,n),this.point2=null,this.radius=0,this.line=null,this.circle=null,t=="twoPoints"?(this.point2=JXG.getReference(e,r),this.radius=this.Radius()):t=="pointRadius"?(this.gxtterm=r,this.updateRadius=JXG.createFunction(r,this.board,null,!0),this.updateRadius()):t=="pointLine"?(this.line=JXG.getReference(e,r),this.radius=this.line.point1.coords.distance(JXG.COORDS_BY_USER,this.line.point2.coords)):t=="pointCircle"&&(this.circle=JXG.getReference(e,r),this.radius=this.circle.Radius()),this.id=this.board.setId(this,"C"),this.board.renderer.drawEllipse(this),this.board.finalizeAdding(this),this.createGradient(),this.elType="circle",this.createLabel(),this.center.addChild(this),t=="pointRadius"?this.notifyParents(r):t=="pointLine"?this.line.addChild(this):t=="pointCircle"?this.circle.addChild(this):t=="twoPoints"&&this.point2.addChild(this),this.methodMap=JXG.deepCopy(this.methodMap,{setRadius:"setRadius",getRadius:"getRadius",radius:"Radius"})},JXG.Circle.prototype=new JXG.GeometryElement,JXG.extend(JXG.Circle.prototype,{hasPoint:function(e,t){var n=this.board.options.precision.hasPoint/this.board.unitX,r=this.center.coords.usrCoords,i=new JXG.Coords(JXG.COORDS_BY_SCREEN,[e,t],this.board),s=this.Radius(),o=Math.sqrt((r[1]-i.usrCoords[1])*(r[1]-i.usrCoords[1])+(r[2]-i.usrCoords[2])*(r[2]-i.usrCoords[2]));return this.visProp.hasinnerpoints?o<s+n:Math.abs(o-s)<n},generatePolynomial:function(e){var t=this.center.symbolic.x,n=this.center.symbolic.y,r=e.symbolic.x,i=e.symbolic.y,s=this.generateRadiusSquared();if(s=="")return[];var o="(("+r+")-("+t+"))^2 + (("+i+")-("+n+"))^2 - ("+s+")";return[o]},generateRadiusSquared:function(){var e="",t,n,r,i,s,o;return this.method=="twoPoints"?(t=this.center.symbolic.x,n=this.center.symbolic.y,r=this.point2.symbolic.x,i=this.point2.symbolic.y,e="(("+r+")-("+t+"))^2 + (("+i+")-("+n+"))^2"):this.method=="pointRadius"?typeof this.radius=="number"&&(e=""+this.radius*this.radius):this.method=="pointLine"?(r=this.line.point1.symbolic.x,i=this.line.point1.symbolic.y,s=this.line.point2.symbolic.x,o=this.line.point2.symbolic.y,e="(("+r+")-("+s+"))^2 + (("+i+")-("+o+"))^2"):this.method=="pointCircle"&&(e=this.circle.Radius()),e},update:function(){return this.needsUpdate&&(this.visProp.trace&&this.cloneToBackground(!0),this.method=="pointLine"?this.radius=this.line.point1.coords.distance(JXG.COORDS_BY_USER,this.line.point2.coords):this.method=="pointCircle"?this.radius=this.circle.Radius():this.method=="pointRadius"&&(this.radius=this.updateRadius()),this.updateStdform(),this.updateQuadraticform()),this},updateQuadraticform:function(){var e=this.center,t=e.X(),n=e.Y(),r=this.Radius();this.quadraticform=[[t*t+n*n-r*r,-t,-n],[-t,1,0],[-n,0,1]]},updateStdform:function(){this.stdform[3]=.5,this.stdform[4]=this.Radius(),this.stdform[1]=-this.center.coords.usrCoords[1],this.stdform[2]=-this.center.coords.usrCoords[2],this.normalize()},updateRenderer:function(){if(this.needsUpdate&&this.visProp.visible){var e=this.isReal;this.isReal=!isNaN(this.center.coords.usrCoords[1]+this.center.coords.usrCoords[2]+this.Radius())&&this.center.isReal,this.isReal?(e!=this.isReal&&(this.board.renderer.show(this),this.hasLabel&&this.label.content.visProp.visible&&this.board.renderer.show(this.label.content)),this.board.renderer.updateEllipse(this)):e!=this.isReal&&(this.board.renderer.hide(this),this.hasLabel&&this.label.content.visProp.visible&&this.board.renderer.hide(this.label.content)),this.needsUpdate=!1}this.hasLabel&&this.label.content.visProp.visible&&this.isReal&&(this.label.content.update(),this.board.renderer.updateText(this.label.content))},notifyParents:function(e){typeof e=="string"&&JXG.GeonextParser.findDependencies(this,e+"",this.board)},setRadius:function(e){return this.updateRadius=JXG.createFunction(e,this.board,null,!0),this.board.update(),this},Radius:function(e){if(JXG.exists(e))return this.setRadius(e),this.Radius();if(this.method=="twoPoints")return JXG.Math.Geometry.distance(this.point2.coords.usrCoords,[0,0,0])==0||JXG.Math.Geometry.distance(this.center.coords.usrCoords,[0,0,0])==0?NaN:this.center.Dist(this.point2);if(this.method=="pointLine"||this.method=="pointCircle")return this.radius;if(this.method=="pointRadius")return this.updateRadius()},getRadius:function(){return this.Radius()},getTextAnchor:function(){return this.center.coords},getLabelAnchor:function(){var e=this.Radius(),t=this.center.coords.usrCoords,n,r;switch(this.visProp.label.position){case"lft":n=t[1]-e,r=t[2];break;case"llft":n=t[1]-Math.sqrt(.5)*e,r=t[2]-Math.sqrt(.5)*e;break;case"rt":n=t[1]+e,r=t[2];break;case"lrt":n=t[1]+Math.sqrt(.5)*e,r=t[2]-Math.sqrt(.5)*e;break;case"urt":n=t[1]+Math.sqrt(.5)*e,r=t[2]+Math.sqrt(.5)*e;break;case"top":n=t[1],r=t[2]+e;break;case"bot":n=t[1],r=t[2]-e;break;case"ulft":default:n=t[1]-Math.sqrt(.5)*e,r=t[2]+Math.sqrt(.5)*e}return new JXG.Coords(JXG.COORDS_BY_USER,[n,r],this.board)},cloneToBackground:function(){var e={},t,n;return e.id=this.id+"T"+this.numTraces,e.elementClass=JXG.OBJECT_CLASS_CIRCLE,this.numTraces++,e.center={},e.center.coords=this.center.coords,t=this.Radius(),e.Radius=function(){return t},e.getRadius=function(){return t},e.board=this.board,e.visProp=JXG.deepCopy(this.visProp,this.visProp.traceattributes,!0),e.visProp.layer=this.board.options.layer.trace,JXG.clearVisPropOld(e),n=this.board.renderer.enhancedRendering,this.board.renderer.enhancedRendering=!0,this.board.renderer.drawEllipse(e),this.board.renderer.enhancedRendering=n,this.traces[e.id]=e.rendNode,this},addTransform:function(e){var t,n=JXG.isArray(e)?e:[e],r=n.length;for(t=0;t<r;t++)this.center.transformations.push(n[t]),this.method==="twoPoints"&&this.point2.transformations.push(n[t]);return this},snapToGrid:function(){return this.visProp.snaptogrid&&(this.center.snapToGrid(),this.method==="twoPoints"&&this.point2.snapToGrid()),this},setPosition:function(e,t){var n;return t=new JXG.Coords(e,t,this.board),n=this.board.create("transform",t.usrCoords.slice(1),{type:"translate"}),this.addTransform(n),this},setPositionDirectly:function(e,t,n){t=new JXG.Coords(e,t,this.board),n=new JXG.Coords(e,n,this.board);var r=JXG.Math.Statistics.subtract(t.usrCoords,n.usrCoords),i=this.parents.length,s,o;for(s=0;s<i;s++)if(!JXG.getRef(this.board,this.parents[s]).draggable())return this;for(s=0;s<i;s++)o=JXG.getRef(this.board,this.parents[s]),o.coords.setCoordinates(JXG.COORDS_BY_USER,JXG.Math.Statistics.add(o.coords.usrCoords,r));return this.update(),this},X:function(e){return this.Radius()*Math.cos(e*2*Math.PI)+this.center.coords.usrCoords[1]},Y:function(e){return this.Radius()*Math.sin(e*2*Math.PI)+this.center.coords.usrCoords[2]},Z:function(e){return 1},minX:function(){return 0},maxX:function(){return 1},Area:function(){var e=this.Radius();return e*e*Math.PI},bounds:function(){var e=this.center.coords.usrCoords,t=this.Radius();return[e[1]-t,e[2]+t,e[1]+t,e[2]-t]}}),JXG.createCircle=function(e,t,n){var r,i,s,o,u=!0;i=[];for(s=0;s<t.length;s++)JXG.isPoint(t[s])?i[s]=t[s]:JXG.isArray(t[s])&&t[s].length>1?(o=JXG.copyAttributes(n,e.options,"circle","center"),i[s]=e.create("point",t[s],o)):i[s]=t[s];o=JXG.copyAttributes(n,e.options,"circle");if(t.length==2&&JXG.isPoint(i[0])&&JXG.isPoint(i[1]))r=new JXG.Circle(e,"twoPoints",i[0],i[1],o);else if((JXG.isNumber(i[0])||JXG.isFunction(i[0])||JXG.isString(i[0]))&&JXG.isPoint(i[1]))r=new JXG.Circle(e,"pointRadius",i[1],i[0],o);else if((JXG.isNumber(i[1])||JXG.isFunction(i[1])||JXG.isString(i[1]))&&JXG.isPoint(i[0]))r=new JXG.Circle(e,"pointRadius",i[0],i[1],o);else if(i[0].elementClass==JXG.OBJECT_CLASS_CIRCLE&&JXG.isPoint(i[1]))r=new JXG.Circle(e,"pointCircle",i[1],i[0],o);else if(i[1].elementClass==JXG.OBJECT_CLASS_CIRCLE&&JXG.isPoint(i[0]))r=new JXG.Circle(e,"pointCircle",i[0],i[1],o);else if(i[0].elementClass==JXG.OBJECT_CLASS_LINE&&JXG.isPoint(i[1]))r=new JXG.Circle(e,"pointLine",i[1],i[0],o);else if(i[1].elementClass==JXG.OBJECT_CLASS_LINE&&JXG.isPoint(i[0]))r=new JXG.Circle(e,"pointLine",i[0],i[1],o);else{if(!(t.length==3&&JXG.isPoint(i[0])&&JXG.isPoint(i[1])&&JXG.isPoint(i[2])))throw new Error("JSXGraph: Can't create circle with parent types '"+typeof t[0]+"' and '"+typeof t[1]+"'."+"\nPossible parent types: [point,point], [point,number], [point,function], [point,circle], [point,point,point]");r=JXG.createCircumcircle(e,i,n)}r.isDraggable=u,r.parents=[];for(s=0;s<t.length;s++)t[s].id&&r.parents.push(t[s].id);return r.elType="circle",r},JXG.JSXGraph.registerElement("circle",JXG.createCircle),JXG.createEllipse=function(e,t,n){var r=[],i,s,o,u,a=JXG.copyAttributes(n,e.options,"conic","foci"),f=JXG.copyAttributes(n,e.options,"conic");for(o=0;o<2;o++)if(t[o].length>1)r[o]=e.create("point",t[o],a);else if(JXG.isPoint(t[o]))r[o]=JXG.getReference(e,t[o]);else if(typeof t[o]=="function"&&t[o]().elementClass===JXG.OBJECT_CLASS_POINT)r[o]=t[o]();else{if(!JXG.isString(t[o]))throw new Error("JSXGraph: Can't create Ellipse with parent types '"+typeof t[0]+"' and '"+typeof t[1]+"'."+"\nPossible parent types: [point,point,point], [point,point,number|function]");r[o]=JXG.getReference(e,t[o])}if(JXG.isNumber(t[2]))s=JXG.createFunction(t[2],e);else if(typeof t[2]=="function"&&JXG.isNumber(t[2]()))s=t[2];else{if(JXG.isPoint(t[2]))i=JXG.getReference(e,t[2]);else if(t[2].length>1)i=e.create("point",t[2],a);else if(typeof t[2]=="function"&&t[2]().elementClass==JXG.OBJECT_CLASS_POINT)i=t[2]();else{if(!JXG.isString(t[2]))throw new Error("JSXGraph: Can't create Ellipse with parent types '"+typeof t[0]+"' and '"+typeof t[1]+"' and '"+typeof t[2]+"'."+"\nPossible parent types: [point,point,point], [point,point,number|function]");i=JXG.getReference(e,t[2])}s=function(){return i.Dist(r[0])+i.Dist(r[1])}}typeof t[4]=="undefined"&&(t[4]=1.0001*Math.PI),typeof t[3]=="undefined"&&(t[3]=-1.0001*Math.PI);var l=e.create("point",[function(){return(r[0].X()+r[1].X())*.5},function(){return(r[0].Y()+r[1].Y())*.5}],a),c=function(){var e=r[0].X(),t=r[0].Y(),n=r[1].X(),i=r[1].Y(),s,o,u,a=n-e>0?1:-1;Math.abs(n-e)>1e-7?s=Math.atan2(i-t,n-e)+(a<0?Math.PI:0):s=(i-t>0?.5:-0.5)*Math.PI,o=Math.cos(s),u=Math.sin(s);var f=[[1,0,0],[l.X(),o,-u],[l.Y(),u,o]];return f},h=e.create("curve",[function(e){return 0},function(e){return 0},t[3],t[4]],f),p=function(e,t){var n=s()*.5,i=n*n,o=r[1].Dist(r[0])*.5,a=i-o*o,f=Math.sqrt(a),p=[[1,0,0],[0,1,0],[0,0,1]],d,v;return t||(u=c(),d=l.X(),v=l.Y(),p[0][0]=u[0][0],p[0][1]=0,p[0][2]=0,p[1][0]=d*(1-u[1][1])+v*u[1][2],p[1][1]=u[1][1],p[1][2]=u[2][1],p[2][0]=v*(1-u[1][1])-d*u[1][2],p[2][1]=u[1][2],p[2][2]=u[2][2],h.quadraticform=JXG.Math.matMatMult(JXG.Math.transpose(p),JXG.Math.matMatMult([[-1+d*d/(n*n)+v*v/a,-d/i,-d/a],[-d/i,1/i,0],[-v/a,0,1/a]],p))),JXG.Math.matVecMult(u,[1,n*Math.cos(e),f*Math.sin(e)])};h.X=function(e,t){return p(e,t)[1]},h.Y=function(e,t){return p(e,t)[2]},h.midpoint=l,h.type=JXG.OBJECT_TYPE_CONIC,l.addChild(h);for(o=0;o<2;o++)JXG.isPoint(r[o])&&r[o].addChild(h);JXG.isPoint(i)&&i.addChild(h),h.parents=[];for(o=0;o<t.length;o++)t[o].id&&h.parents.push(t[o].id);return h},JXG.createHyperbola=function(e,t,n){var r=[],i,s,o,u,a=JXG.copyAttributes(n,e.options,"conic","foci"),f=JXG.copyAttributes(n,e.options,"conic");for(o=0;o<2;o++)if(t[o].length>1)r[o]=e.create("point",t[o],attr_focu);else if(JXG.isPoint(t[o]))r[o]=JXG.getReference(e,t[o]);else if(typeof t[o]=="function"&&t[o]().elementClass==JXG.OBJECT_CLASS_POINT)r[o]=t[o]();else{if(!JXG.isString(t[o]))throw new Error("JSXGraph: Can't create Hyperbola with parent types '"+typeof t[0]+"' and '"+typeof t[1]+"'."+"\nPossible parent types: [point,point,point], [point,point,number|function]");r[o]=JXG.getReference(e,t[o])}if(JXG.isNumber(t[2]))s=JXG.createFunction(t[2],e);else if(typeof t[2]=="function"&&JXG.isNumber(t[2]()))s=t[2];else{if(JXG.isPoint(t[2]))i=JXG.getReference(e,t[2]);else if(t[2].length>1)i=e.create("point",t[2],a);else if(typeof t[2]=="function"&&t[2]().elementClass==JXG.OBJECT_CLASS_POINT)i=t[2]();else{if(!JXG.isString(t[2]))throw new Error("JSXGraph: Can't create Hyperbola with parent types '"+typeof t[0]+"' and '"+typeof t[1]+"' and '"+typeof t[2]+"'."+"\nPossible parent types: [point,point,point], [point,point,number|function]");i=JXG.getReference(e,t[2])}s=function(){return i.Dist(r[0])-i.Dist(r[1])}}typeof t[4]=="undefined"&&(t[4]=1.0001*Math.PI),typeof t[3]=="undefined"&&(t[3]=-1.0001*Math.PI);var l=e.create("point",[function(){return(r[0].X()+r[1].X())*.5},function(){return(r[0].Y()+r[1].Y())*.5}],a),c=function(){var e=r[0].X(),t=r[0].Y(),n=r[1].X(),i=r[1].Y(),s,o=n-e>0?1:-1;Math.abs(n-e)>1e-7?s=Math.atan2(i-t,n-e)+(o<0?Math.PI:0):s=(i-t>0?.5:-0.5)*Math.PI;var u=[[1,0,0],[l.X(),Math.cos(s),-Math.sin(s)],[l.Y(),Math.sin(s),Math.cos(s)]];return u},h=e.create("curve",[function(e){return 0},function(e){return 0},t[3],t[4]],f),p=function(e,t){var n=s()*.5,i=n*n,o=r[1].Dist(r[0])*.5,a=Math.sqrt(-n*n+o*o),f=a*a,p=[[1,0,0],[0,1,0],[0,0,1]],d,v;return t||(u=c(),d=l.X(),v=l.Y(),p[0][0]=u[0][0],p[0][1]=0,p[0][2]=0,p[1][0]=d*(1-u[1][1])+v*u[1][2],p[1][1]=u[1][1],p[1][2]=u[2][1],p[2][0]=v*(1-u[1][1])-d*u[1][2],p[2][1]=u[1][2],p[2][2]=u[2][2],h.quadraticform=JXG.Math.matMatMult(JXG.Math.transpose(p),JXG.Math.matMatMult([[-1+d*d/i+v*v/f,-d/i,v/f],[-d/i,1/i,0],[v/f,0,-1/f]],p))),JXG.Math.matVecMult(u,[1,n/Math.cos(e),a*Math.tan(e)])};h.X=function(e,t){return p(e,t)[1]},h.Y=function(e,t){return p(e,t)[2]},h.midpoint=l,h.type=JXG.OBJECT_TYPE_CONIC,l.addChild(h);for(o=0;o<2;o++)JXG.isPoint(r[o])&&r[o].addChild(h);JXG.isPoint(i)&&i.addChild(h),h.parents=[];for(o=0;o<t.length;o++)t[o].id&&h.parents.push(t[o].id);return h},JXG.createParabola=function(e,t,n){var r=t[0],s=t[1],o,u=JXG.copyAttributes(n,e.options,"conic","foci"),a=JXG.copyAttributes(n,e.options,"conic");if(t[0].length>1)r=e.create("point",t[0],u);else if(JXG.isPoint(t[0]))r=JXG.getReference(e,t[0]);else if(typeof t[0]=="function"&&t[0]().elementClass==JXG.OBJECT_CLASS_POINT)r=t[0]();else{if(!JXG.isString(t[0]))throw new Error("JSXGraph: Can't create Parabola with parent types '"+typeof t[0]+"' and '"+typeof t[1]+"'."+"\nPossible parent types: [point,line]");r=JXG.getReference(e,t[0])}typeof t[3]=="undefined"&&(t[3]=10),typeof t[2]=="undefined"&&(t[2]=-10);var f=e.create("point",[function(){var t=[0,s.stdform[1],s.stdform[2]];return t=JXG.Math.crossProduct(t,r.coords.usrCoords),JXG.Math.Geometry.meetLineLine(t,s.stdform,0,e).usrCoords}],u),l=function(){var e=Math.atan(s.getSlope()),t=(f.X()+r.X())*.5,n=(f.Y()+r.Y())*.5;e+=r.Y()-f.Y()<0||r.Y()==f.Y()&&r.X()>f.X()?Math.PI:0;var i=[[1,0,0],[t*(1-Math.cos(e))+n*Math.sin(e),Math.cos(e),-Math.sin(e)],[n*(1-Math.cos(e))-t*Math.sin(e),Math.sin(e),Math.cos(e)]];return i},c=e.create("curve",[function(e){return 0},function(e){return 0},t[2],t[3]],a),h=function(e,t){var n=f.Dist(r)*.5,i=[[1,0,0],[0,1,0],[0,0,1]],s=(f.X()+r.X())*.5,u=(f.Y()+r.Y())*.5;return t||(o=l(),i[0][0]=o[0][0],i[0][1]=0,i[0][2]=0,i[1][0]=s*(1-o[1][1])+u*o[1][2],i[1][1]=o[1][1],i[1][2]=o[2][1],i[2][0]=u*(1-o[1][1])-s*o[1][2],i[2][1]=o[1][2],i[2][2]=o[2][2],c.quadraticform=JXG.Math.matMatMult(JXG.Math.transpose(i),JXG.Math.matMatMult([[-u*4*n-s*s,s,2*n],[s,-1,0],[2*n,0,0]],i))),JXG.Math.matVecMult(o,[1,e+s,e*e/(n*4)+u])};c.X=function(e,t){return h(e,t)[1]},c.Y=function(e,t){return h(e,t)[2]},c.type=JXG.OBJECT_TYPE_CONIC,f.addChild(c),JXG.isPoint(F[1])&&F[1].addChild(c),s.addChild(c),c.parents=[];for(i=0;i<t.length;i++)t[i].id&&c.parents.push(t[i].id);return c},JXG.createConic=function(e,t,n){var r=[[1,0,0],[0,1,0],[0,0,1]],i,s,o,u,a=[[1,0,0],[0,1,0],[0,0,1]],f,l,c=[],h,p,d,v=[],m=JXG.copyAttributes(n,e.options,"conic","foci"),g=JXG.copyAttributes(n,e.options,"conic");if(t.length==5)d=!0;else{if(t.length!=6)throw new Error("JSXGraph: Can't create generic Conic with "+parent.length+" parameters.");d=!1}if(d)for(h=0;h<5;h++)if(t[h].length>1)c[h]=e.create("point",t[h],m);else if(JXG.isPoint(t[h]))c[h]=JXG.getReference(e,t[h]);else if(typeof t[h]=="function"&&t[h]().elementClass==JXG.OBJECT_CLASS_POINT)c[h]=t[h]();else{if(!JXG.isString(t[h]))throw new Error("JSXGraph: Can't create Conic section with parent types '"+typeof t[h]+"'."+"\nPossible parent types: [point,point,point,point,point], [a00,a11,a22,a01,a02,a12]");c[h]=JXG.getReference(e,t[h])}else p=[[0,0,0],[0,0,0],[0,0,0]],p[0][0]=JXG.isFunction(t[2])?function(){return t[2]()}:function(){return t[2]},p[0][1]=JXG.isFunction(t[4])?function(){return t[4]()}:function(){return t[4]},p[0][2]=JXG.isFunction(t[5])?function(){return t[5]()}:function(){return t[5]},p[1][1]=JXG.isFunction(t[0])?function(){return t[0]()}:function(){return t[0]},p[1][2]=JXG.isFunction(t[3])?function(){return t[3]()}:function(){return t[3]},p[2][2]=JXG.isFunction(t[1])?function(){return t[1]()}:function(){return t[1]};var y=function(e){var t,n;for(t=0;t<3;t++)for(n=t;n<3;n++)e[t][n]+=e[n][t];for(t=0;t<3;t++)for(n=0;n<t;n++)e[t][n]=e[n][t];return e},b=function(e,t){var n,r,i=[[0,0,0],[0,0,0],[0,0,0]];for(n=0;n<3;n++)for(r=0;r<3;r++)i[n][r]=e[n]*t[r];return y(i)},w=function(e,t,n){var r,i,s,o=[[0,0,0],[0,0,0],[0,0,0]],u,a;s=JXG.Math.matVecMult(t,n),r=JXG.Math.innerProduct(n,s),s=JXG.Math.matVecMult(e,n),i=JXG.Math.innerProduct(n,s);for(u=0;u<3;u++)for(a=0;a<3;a++)o[u][a]=r*e[u][a]-i*t[u][a];return o},E=e.create("curve",[function(e){return 0},function(e){return 0},0,2*Math.PI],g),S=function(e,t){var n,h,m,g;if(!t){if(d){for(n=0;n<5;n++)v[n]=c[n].coords.usrCoords;f=b(JXG.Math.crossProduct(v[0],v[1]),JXG.Math.crossProduct(v[2],v[3])),l=b(JXG.Math.crossProduct(v[0],v[2]),JXG.Math.crossProduct(v[1],v[3])),a=w(f,l,v[4])}else for(n=0;n<3;n++)for(h=n;h<3;h++)a[n][h]=p[n][h](),h>n&&(a[h][n]=a[n][h]);E.quadraticform=a,i=JXG.Math.Numerics.Jacobi(a),i[0][0][0]<0&&(i[0][0][0]*=-1,i[0][1][1]*=-1,i[0][2][2]*=-1);for(n=0;n<3;n++){m=0;for(h=0;h<3;h++)m+=i[1][h][n]*i[1][h][n];m=Math.sqrt(m);for(h=0;h<3;h++);}r=i[1],u=Math.sqrt(Math.abs(i[0][0][0])),s=Math.sqrt(Math.abs(i[0][1][1])),o=Math.sqrt(Math.abs(i[0][2][2]))}return i[0][1][1]<=0&&i[0][2][2]<=0?g=JXG.Math.matVecMult(r,[1/u,Math.cos(e)/s,Math.sin(e)/o]):i[0][1][1]<=0&&i[0][2][2]>0?g=JXG.Math.matVecMult(r,[Math.cos(e)/u,1/s,Math.sin(e)/o]):i[0][2][2]<0&&(g=JXG.Math.matVecMult(r,[Math.sin(e)/u,Math.cos(e)/s,1/o])),g[1]/=g[0],g[2]/=g[0],g[0]=1,g};E.X=function(e,t){return S(e,t)[1]},E.Y=function(e,t){return S(e,t)[2]},E.midpoint=e.create("point",[function(){var e=E.quadraticform;return[e[1][1]*e[2][2]-e[1][2]*e[1][2],e[1][2]*e[0][2]-e[2][2]*e[0][1],e[0][1]*e[1][2]-e[1][1]*e[0][2]]}],m),E.type=JXG.OBJECT_TYPE_CONIC;if(d){for(h=0;h<5;h++)JXG.isPoint(c[h])&&c[h].addChild(E);E.parents=[];for(h=0;h<t.length;h++)t[h].id&&E.parents.push(t[h].id)}return E.addChild(E.midpoint),E},JXG.JSXGraph.registerElement("ellipse",JXG.createEllipse),JXG.JSXGraph.registerElement("hyperbola",JXG.createHyperbola),JXG.JSXGraph.registerElement("parabola",JXG.createParabola),JXG.JSXGraph.registerElement("conic",JXG.createConic),JXG.Polygon=function(e,t,n){this.constructor(e,n,JXG.OBJECT_TYPE_POLYGON,JXG.OBJECT_CLASS_AREA);var r,i,s,o=JXG.copyAttributes(n,e.options,"polygon","borders");this.withLines=n.withlines,this.attr_line=o,this.vertices=[];for(r=0;r<t.length;r++)i=JXG.getRef(this.board,t[r]),this.vertices[r]=i;this.vertices[this.vertices.length-1]!=this.vertices[0]&&this.vertices.push(this.vertices[0]),this.borders=[];if(this.withLines)for(r=0;r<this.vertices.length-1;r++)o.id=o.ids&&o.ids[r],o.strokecolor=JXG.isArray(o.colors)&&o.colors[r%o.colors.length]||o.strokecolor,o.strokecolor===!1&&(o.strokecolor="none"),s=JXG.createSegment(e,[this.vertices[r],this.vertices[r+1]],o),s.dump=!1,this.borders[r]=s,s.parentPolygon=this;for(r=0;r<this.vertices.length-1;r++)i=JXG.getReference(this.board,this.vertices[r]),i.addChild(this);this.id=this.board.setId(this,"Py"),this.board.renderer.drawPolygon(this),this.board.finalizeAdding(this),this.elType="polygon",this.createLabel(),this.methodMap.borders="borders",this.methodMap.vertices="vertices"},JXG.Polygon.prototype=new JXG.GeometryElement,JXG.extend(JXG.Polygon.prototype,{hasPoint:function(e,t){var n,r,i,s=!1;if(this.visProp.hasinnerpoints){i=this.vertices.length;for(n=0,r=i-2;n<i-1;r=n++)this.vertices[n].coords.scrCoords[2]>t!=this.vertices[r].coords.scrCoords[2]>t&&e<(this.vertices[r].coords.scrCoords[1]-this.vertices[n].coords.scrCoords[1])*(t-this.vertices[n].coords.scrCoords[2])/(this.vertices[r].coords.scrCoords[2]-this.vertices[n].coords.scrCoords[2])+this.vertices[n].coords.scrCoords[1]&&(s=!s)}else{i=this.borders.length;for(n=0;n<i;n++)if(this.borders[n].hasPoint(e,t)){s=!0;break}}return s},updateRenderer:function(){this.needsUpdate&&(this.board.renderer.updatePolygon(this),this.needsUpdate=!1),this.hasLabel&&this.label.content.visProp.visible&&(this.label.content.update(),this.board.renderer.updateText(this.label.content))},getTextAnchor:function(){var e=this.vertices[0].X(),t=this.vertices[0].Y(),n=e,r=t,i;for(i=0;i<this.vertices.length;i++)this.vertices[i].X()<e&&(e=this.vertices[i].X()),this.vertices[i].X()>n&&(n=this.vertices[i].X()),this.vertices[i].Y()>t&&(t=this.vertices[i].Y()),this.vertices[i].Y()<r&&(r=this.vertices[i].Y());return new JXG.Coords(JXG.COORDS_BY_USER,[(e+n)*.5,(t+r)*.5],this.board)},getLabelAnchor:JXG.shortcut(JXG.Polygon.prototype,"getTextAnchor"),cloneToBackground:function(){var e={},t;return e.id=this.id+"T"+this.numTraces,this.numTraces++,e.vertices=this.vertices,e.visProp=JXG.deepCopy(this.visProp,this.visProp.traceattributes,!0),e.visProp.layer=this.board.options.layer.trace,e.board=this.board,JXG.clearVisPropOld(e),t=this.board.renderer.enhancedRendering,this.board.renderer.enhancedRendering=!0,this.board.renderer.drawPolygon(e),this.board.renderer.enhancedRendering=t,this.traces[e.id]=e.rendNode,this},hideElement:function(){var e;this.visProp.visible=!1,this.board.renderer.hide(this);for(e=0;e<this.borders.length;e++)this.borders[e].hideElement();this.hasLabel&&JXG.exists(this.label)&&(this.label.hiddenByParent=!0,this.label.content.visProp.visible&&this.board.renderer.hide(this.label.content))},showElement:function(){var e;this.visProp.visible=!0,this.board.renderer.show(this);for(e=0;e<this.borders.length;e++)this.borders[e].showElement();this.hasLabel&&JXG.exists(this.label)&&this.label.content.visProp.visible&&this.board.renderer.show(this.label.content)},Area:function(){var e=0,t;for(t=0;t<this.vertices.length-1;t++)e+=this.vertices[t].X()*this.vertices[t+1].Y()-this.vertices[t+1].X()*this.vertices[t].Y();return e/=2,Math.abs(e)},remove:function(){var e;for(e=0;e<this.borders.length;e++)this.board.removeObject(this.borders[e]);JXG.GeometryElement.prototype.remove.call(this)},findPoint:function(e){var t;if(!JXG.isPoint(e))return-1;for(t=0;t<this.vertices.length;t++)if(this.vertices[t].id===e.id)return t;return-1},addPoints:function(){var e=Array.prototype.slice.call(arguments);return this.insertPoints.apply(this,[this.vertices.length-2].concat(e))},insertPoints:function(){var e,t,n=[],r;if(arguments.length===0)return this;e=arguments[0];if(e<0||e>this.vertices.length-2)return this;for(t=1;t<arguments.length;t++)JXG.isPoint(arguments[t])&&n.push(arguments[t]);r=this.vertices.slice(0,e+1).concat(n),this.vertices=r.concat(this.vertices.slice(e+1));if(this.withLines){r=this.borders.slice(0,e),this.board.removeObject(this.borders[e]);for(t=0;t<n.length;t++)r.push(JXG.createSegment(this.board,[this.vertices[e+t],this.vertices[e+t+1]],this.attr_line));r.push(JXG.createSegment(this.board,[this.vertices[e+n.length],this.vertices[e+n.length+1]],this.attr_line)),this.borders=r.concat(this.borders.slice(e))}return this.board.update(),this},removePoints:function(){var e,t,n,r=[],i=[],s=[],o=[];this.vertices=this.vertices.slice(0,this.vertices.length-1);for(e=0;e<arguments.length;e++)JXG.isPoint(arguments[e])&&(n=this.findPoint(arguments[e])),JXG.isNumber(n)&&n>-1&&n<this.vertices.length&&JXG.indexOf(s,n)===-1&&s.push(n);s=s.sort(),r=this.vertices.slice(),i=this.borders.slice(),this.withLines&&o.push([s[s.length-1]]);for(e=s.length-1;e>-1;e--)r[s[e]]=-1,this.withLines&&s[e]-1>s[e-1]&&(o[o.length-1][1]=s[e],o.push([s[e-1]]));this.withLines&&(o[o.length-1][1]=s[0]),this.vertices=[];for(e=0;e<r.length;e++)JXG.isPoint(r[e])&&this.vertices.push(r[e]);this.vertices[this.vertices.length-1].id!==this.vertices[0].id&&this.vertices.push(this.vertices[0]);if(this.withLines){for(e=0;e<o.length;e++){for(t=o[e][1]-1;t<o[e][0]+1;t++)t<0?(t=0,this.board.removeObject(this.borders[i.length-1]),i[i.length-1]=-1):t>i.length-1&&(t=i.length-1),this.board.removeObject(this.borders[t]),i[t]=-1;o[e][1]!==0&&o[e][0]!==r.length-1&&(i[o[e][0]-1]=JXG.createSegment(this.board,[r[Math.max(o[e][1]-1,0)],r[Math.min(o[e][0]+1,this.vertices.length-1)]],this.attr_line))}this.borders=[];for(e=0;e<i.length;e++)i[e]!==-1&&this.borders.push(i[e]);(o[0][1]===5||o[o.length-1][1]===0)&&this.borders.push(JXG.createSegment(this.board,[this.vertices[0],this.vertices[this.vertices.length-2]],this.attr_line))}return this.board.update(),this},getParents:function(){var e=[],t;for(t=0;t<this.vertices.length;t++)e.push(this.vertices[t].id);return e},getAttributes:function(){var e=JXG.GeometryElement.prototype.getAttributes.call(this),t;if(this.withLines){e.lines=e.lines||{},e.lines.ids=[],e.lines.colors=[];for(t=0;t<this.borders.length;t++)e.lines.ids.push(this.borders[t].id),e.lines.colors.push(this.borders[t].visProp.strokecolor)}return e},setPositionDirectly:function(e,t,n){var r,i,s,o,u=new JXG.Coords(e,t,this.board),a=new JXG.Coords(e,n,this.board);o=this.vertices.length-1;for(s=0;s<o;s++)if(!this.vertices[s].draggable())return this;return r=JXG.Math.Statistics.subtract(u.usrCoords,a.usrCoords),i=this.board.create("transform",r.slice(1),{type:"translate"}),i.applyOnce(this.vertices.slice(0,-1)),this}}),JXG.createPolygon=function(e,t,n){var r,i,s=JXG.copyAttributes(n,e.options,"polygon");for(i=0;i<t.length;i++){t[i]=JXG.getReference(e,t[i]);if(!JXG.isPoint(t[i]))throw new Error("JSXGraph: Can't create polygon with parent types other than 'point'.")}return r=new JXG.Polygon(e,t,s),r.isDraggable=!0,r},JXG.createRegularPolygon=function(e,t,n){var r,i,s,o=[],u,a,f,l,c;if(JXG.isNumber(t[t.length-1])&&t.length!=3)throw new Error("JSXGraph: A regular polygon needs two points and a number as input.");f=t.length,s=t[f-1];if(!JXG.isNumber(s)&&!JXG.isPoint(JXG.getReference(e,s))||s<3)throw new Error("JSXGraph: The third parameter has to be number greater than 2 or a point.");JXG.isPoint(JXG.getReference(e,s))?(s=f,l=!0):(f--,l=!1);for(i=0;i<f;i++){t[i]=JXG.getReference(e,t[i]);if(!JXG.isPoint(t[i]))throw new Error("JSXGraph: Can't create regular polygon if the first two parameters aren't points.")}o[0]=t[0],o[1]=t[1],c=JXG.copyAttributes(n,e.options,"polygon","vertices");for(i=2;i<s;i++)u=e.create("transform",[Math.PI*(2-(s-2)/s),o[i-1]],{type:"rotate"}),l?(o[i]=t[i],o[i].addTransform(t[i-2],u)):(JXG.isArray(c.ids)&&c.ids.length>=s-2&&(c.id=c.ids[i-2]),o[i]=e.create("point",[o[i-2],u],c),o[i].type=JXG.OBJECT_TYPE_CAS,o[i].isDraggable=!0,o[i].visProp.fixed=!1);return c=JXG.copyAttributes(n,e.options,"polygon"),r=e.create("polygon",o,c),r.elType="regularpolygon",r},JXG.JSXGraph.registerElement("polygon",JXG.createPolygon),JXG.JSXGraph.registerElement("regularpolygon",JXG.createRegularPolygon),JXG.Curve=function(e,t,n){this.constructor(e,n,JXG.OBJECT_TYPE_CURVE,JXG.OBJECT_CLASS_CURVE),this.points=[],this.numberPoints=this.visProp.numberpointshigh,this.bezierDegree=1,this.dataX=null,this.dataY=null,t[0]!=null?this.varname=t[0]:this.varname="x",this.xterm=t[1],this.yterm=t[2],this.generateTerm(this.varname,this.xterm,this.yterm,t[3],t[4]),this.updateCurve(),this.id=this.board.setId(this,"G"),this.board.renderer.drawCurve(this),this.board.finalizeAdding(this),this.createGradient(),this.elType="curve",this.createLabel(),typeof this.xterm=="string"&&this.notifyParents(this.xterm),typeof this.yterm=="string"&&this.notifyParents(this.yterm)},JXG.Curve.prototype=new JXG.GeometryElement,JXG.extend(JXG.Curve.prototype,{minX:function(){if(this.visProp.curvetype=="polar")return 0;var e=new JXG.Coords(JXG.COORDS_BY_SCREEN,[0,0],this.board);return e.usrCoords[1]},maxX:function(){var e;return this.visProp.curvetype=="polar"?2*Math.PI:(e=new JXG.Coords(JXG.COORDS_BY_SCREEN,[this.board.canvasWidth,0],this.board),e.usrCoords[1])},Z:function(e){return 1},hasPoint:function(e,t,n){var r,i=Infinity,s,o,u,a,f,l,c,h,p,d,v,m,g=this.visProp.numberpointslow,y=(this.maxX()-this.minX())/g,b=this.board.options.precision.hasPoint/this.board.unitX,w,E,S=!0,x,T;b*=b,w=new JXG.Coords(JXG.COORDS_BY_SCREEN,[e,t],this.board),e=w.usrCoords[1],t=w.usrCoords[2],this.transformations.length>0&&(this.updateTransformMatrix(),x=JXG.Math.inverse(this.transformMat),T=JXG.Math.matVecMult(x,[1,e,t]),e=T[1],t=T[2]);if(this.visProp.curvetype=="parameter"||this.visProp.curvetype=="polar"||this.visProp.curvetype=="functiongraph")for(s=0,r=this.minX();s<g;s++){o=this.X(r,S),u=this.Y(r,S),i=(e-o)*(e-o)+(t-u)*(t-u);if(i<b)return!0;r+=y}else if(this.visProp.curvetype=="plot"){if(!JXG.exists(n)||n<0)n=0;E=this.numberPoints;for(s=n;s<E-1;s++){a=this.X(s),f=this.Y(s),l=e-a,c=t-f,h=this.X(s+1)-a,p=this.Y(s+1)-f,v=h*h+p*p,i=l*l+c*c,v>=JXG.Math.eps?(d=l*h+c*p,m=d/v,i-=m*d):m=0;if(m>=0&&m<=1&&i<b)return!0}return!1}return i<b},allocatePoints:function(){var e,t;t=this.numberPoints;if(this.points.length<this.numberPoints)for(e=this.points.length;e<t;e++)this.points[e]=new JXG.Coords(JXG.COORDS_BY_USER,[0,0],this.board)},update:function(){return this.needsUpdate&&(this.visProp.trace&&this.cloneToBackground(!0),this.updateCurve()),this},updateRenderer:function(){return this.needsUpdate&&this.visProp.visible&&(this.board.renderer.updateCurve(this),this.needsUpdate=!1,this.hasLabel&&this.label.content.visProp.visible&&(this.label.content.update(),this.board.renderer.updateText(this.label.content))),this},updateDataArray:function(){},updateCurve:function(){var e,t,n,r,i,s,o=!1;this.updateTransformMatrix(),this.updateDataArray(),t=this.minX(),n=this.maxX();if(this.dataX!=null){this.numberPoints=this.dataX.length,e=this.numberPoints,this.allocatePoints();for(s=0;s<e;s++)r=s,this.dataY!=null?(i=s,this.points[s].setCoordinates(JXG.COORDS_BY_USER,[this.dataX[s],this.dataY[s]],!1)):(i=this.X(r),this.points[s].setCoordinates(JXG.COORDS_BY_USER,[this.dataX[s],this.Y(i,o)],!1)),this.updateTransform(this.points[s]),o=!0}else{this.visProp.doadvancedplot?this.updateParametricCurve(t,n,e):(this.board.updateQuality==this.board.BOARD_QUALITY_HIGH?this.numberPoints=this.visProp.numberpointshigh:this.numberPoints=this.visProp.numberpointslow,this.allocatePoints(),this.updateParametricCurveNaive(t,n,this.numberPoints)),e=this.numberPoints;for(s=0;s<e;s++)this.updateTransform(this.points[s])}return this},updateTransformMatrix:function(){var e,t,n,r=this.transformations.length;this.transformMat=[[1,0,0],[0,1,0],[0,0,1]];for(n=0;n<r;n++)e=this.transformations[n],e.update(),this.transformMat=JXG.Math.matMatMult(e.matrix,this.transformMat);return this},updateParametricCurveNaive:function(e,t,n){var r,i,s=!1,o=(t-e)/n;for(r=0;r<n;r++)i=e+r*o,this.points[r].setCoordinates(JXG.COORDS_BY_USER,[this.X(i,s),this.Y(i,s)],!1),s=!0;return this},updateParametricCurve:function(e,t){var n,r,i,s=!1,o=new JXG.Coords(JXG.COORDS_BY_USER,[0,0],this.board),u,a,f,l,c,h,p,d,v,m=[],g=[],y=[],b=[],w=!1,E=0,S,x=function(e,t,n){var r=n[1]-e[1],i=n[2]-e[2],s=t[0]-e[1],o=t[1]-e[2],u=s*s+o*o,a,f;return u>=JXG.Math.eps&&(a=(r*s+i*o)/u,a>0&&(a<=1?(r-=a*s,i-=a*o):(r-=s,i-=o))),f=r*r+i*i,Math.sqrt(f)};this.board.updateQuality==this.board.BOARD_QUALITY_LOW?(p=15,d=10,v=10):(p=21,d=.7,v=.7),b[0]=t-e;for(n=1;n<p;n++)b[n]=b[n-1]*.5;n=1,m[0]=1,g[0]=0,r=e,o.setCoordinates(JXG.COORDS_BY_USER,[this.X(r,s),this.Y(r,s)],!1),s=!0,f=o.scrCoords[1],l=o.scrCoords[2],i=r,r=t,o.setCoordinates(JXG.COORDS_BY_USER,[this.X(r,s),this.Y(r,s)],!1),u=o.scrCoords[1],a=o.scrCoords[2],y[0]=[u,a],c=1,h=0,this.points=[],this.points[E++]=new JXG.Coords(JXG.COORDS_BY_SCREEN,[f,l],this.board);do{w=this.isDistOK(u-f,a-l,d,v)||this.isSegmentOutside(f,l,u,a);while(h<p&&(!w||h<6)&&(h<=7||this.isSegmentDefined(f,l,u,a)))m[c]=n,g[c]=h,y[c]=[u,a],c++,n=2*n-1,h++,r=e+n*b[h],o.setCoordinates(JXG.COORDS_BY_USER,[this.X(r,s),this.Y(r,s)],!1),u=o.scrCoords[1],a=o.scrCoords[2],w=this.isDistOK(u-f,a-l,d,v)||this.isSegmentOutside(f,l,u,a);E>1&&(S=x(this.points[E-2].scrCoords,[u,a],this.points[E-1].scrCoords),S<.015&&E--),this.points[E]=new JXG.Coords(JXG.COORDS_BY_SCREEN,[u,a],this.board),E++,f=u,l=a,i=r,c--,u=y[c][0],a=y[c][1],h=g[c]+1,n=m[c]*2}while(c>0&&E<5e5);return this.numberPoints=this.points.length,this},isSegmentOutside:function(e,t,n,r){return t<0&&r<0||t>this.board.canvasHeight&&r>this.board.canvasHeight||e<0&&n<0||e>this.board.canvasWidth&&n>this.board.canvasWidth},isDistOK:function(e,t,n,r){return Math.abs(e)<n&&Math.abs(t)<r&&!isNaN(e+t)},isSegmentDefined:function(e,t,n,r){return!isNaN(e+t)||!isNaN(n+r)},updateTransform:function(e){var t,n=this.transformations.length;return n>0&&(t=JXG.Math.matVecMult(this.transformMat,e.usrCoords),e.setCoordinates(JXG.COORDS_BY_USER,[t[1],t[2]])),e},addTransform:function(e){var t,n=JXG.isArray(e)?e:[e],r=n.length;for(t=0;t<r;t++)this.transformations.push(n[t]);return this},setPosition:function(e,t){var n,r,i=0,s;JXG.exists(this.parents)&&(i=this.parents.length);for(s=0;s<i;s++){r=JXG.getRef(this.board,this.parents[s]);if(!r.draggable())return this}t=new JXG.Coords(e,t,this.board),n=this.board.create("transform",t.usrCoords.slice(1),{type:"translate"});if(i>0)for(s=0;s<i;s++)r=JXG.getRef(this.board,this.parents[s]),n.applyOnce(r);else this.transformations.length>0&&this.transformations[this.transformations.length-1].isNumericMatrix?this.transformations[this.transformations.length-1].melt(n):this.addTransform(n);return this},setPositionDirectly:function(e,t,n){var r=new JXG.Coords(e,t,this.board),i=new JXG.Coords(e,n,this.board),s=JXG.Math.Statistics.subtract(r.usrCoords,i.usrCoords);return this.setPosition(JXG.COORDS_BY_USER,s),this},interpolationFunctionFromArray:function(e){var t="data"+e;return function(e,n){var r,i,s,o=this[t],u=o.length,a,f,l,c=[],h;if(isNaN(e))return NaN;if(e<0)return JXG.isFunction(o[0])?o[0]():o[0];if(this.bezierDegree==3){u/=3;if(e>=u)return JXG.isFunction(o[o.length-1])?o[o.length-1]():o[o.length-1];r=Math.floor(e)*3,f=e%1,l=1-f;for(h=0;h<4;h++)JXG.isFunction(o[r+h])?c[h]=o[r+h]():c[h]=o[r+h];return l*l*(l*c[0]+3*f*c[1])+(3*l*c[2]+f*c[3])*f*f}e>u-2?r=u-2:r=parseInt(Math.floor(e));if(r==e)return JXG.isFunction(o[r])?o[r]():o[r];for(h=0;h<2;h++)JXG.isFunction(o[r+h])?c[h]=o[r+h]():c[h]=o[r+h];return c[0]+(c[1]-c[0])*(e-r)}},generateTerm:function(e,t,n,r,i){var s,o;if(JXG.isArray(t))this.dataX=t,this.numberPoints=this.dataX.length,this.X=this.interpolationFunctionFromArray("X"),this.visProp.curvetype="plot",this.isDraggable=!0;else{this.X=JXG.createFunction(t,this.board,e);if(JXG.isString(t))this.visProp.curvetype="functiongraph";else if(JXG.isFunction(t)||JXG.isNumber(t))this.visProp.curvetype="parameter";this.isDraggable=!0}JXG.isArray(n)?(this.dataY=n,this.Y=this.interpolationFunctionFromArray("Y")):this.Y=JXG.createFunction(n,this.board,e),JXG.isFunction(t)&&JXG.isArray(n)&&(s=JXG.createFunction(n[0],this.board,""),o=JXG.createFunction(n[1],this.board,""),this.X=function(e){return t(e)*Math.cos(e)+s()},this.Y=function(e){return t(e)*Math.sin(e)+o()},this.visProp.curvetype="polar"),r!=null&&(this.minX=JXG.createFunction(r,this.board,"")),i!=null&&(this.maxX=JXG.createFunction(i,this.board,""))},notifyParents:function(e){JXG.GeonextParser.findDependencies(this,e,this.board)},getLabelAnchor:function(){var e,t,n,r=.05*this.board.canvasWidth,i=.05*this.board.canvasHeight,s=.95*this.board.canvasWidth,o=.95*this.board.canvasHeight;switch(this.visProp.label.position){case"ulft":t=r,n=i;break;case"llft":t=r,n=o;break;case"rt":t=s,n=.5*o;break;case"lrt":t=s,n=o;break;case"urt":t=s,n=i;break;case"top":t=.5*s,n=i;break;case"bot":t=.5*s,n=o;break;case"lft":default:t=r,n=.5*o}return e=new JXG.Coords(JXG.COORDS_BY_SCREEN,[t,n],this.board),JXG.Math.Geometry.projectCoordsToCurve(e.usrCoords[1],e.usrCoords[2],0,this,this.board)[0]},cloneToBackground:function(){var e={},t;return e.id=this.id+"T"+this.numTraces,e.elementClass=JXG.OBJECT_CLASS_CURVE,this.numTraces++,e.points=this.points.slice(0),e.numberPoints=this.numberPoints,e.board=this.board,e.visProp=JXG.deepCopy(this.visProp,this.visProp.traceattributes,!0),e.visProp.layer=this.board.options.layer.trace,e.visProp.curvetype=this.visProp.curvetype,JXG.clearVisPropOld(e),t=this.board.renderer.enhancedRendering,this.board.renderer.enhancedRendering=!0,this.board.renderer.drawCurve(e),this.board.renderer.enhancedRendering=t,this.traces[e.id]=e.rendNode,this},bounds:function(){var e=Infinity,t=-Infinity,n=Infinity,r=-Infinity,i=this.points.length,s;for(s=0;s<i;s++)e>this.points[s].usrCoords[1]&&(e=this.points[s].usrCoords[1]),t<this.points[s].usrCoords[1]&&(t=this.points[s].usrCoords[1]),n>this.points[s].usrCoords[2]&&(n=this.points[s].usrCoords[2]),r<this.points[s].usrCoords[2]&&(r=this.points[s].usrCoords[2]);return[e,r,t,n]}}),JXG.createCurve=function(e,t,n){var r=JXG.copyAttributes(n,e.options,"curve");return new JXG.Curve(e,["x"].concat(t),r)},JXG.JSXGraph.registerElement("curve",JXG.createCurve),JXG.createFunctiongraph=function(e,t,n){var r,i=["x","x"].concat(t);return r=JXG.copyAttributes(n,e.options,"curve"),r.curvetype="functiongraph",new JXG.Curve(e,i,r)},JXG.JSXGraph.registerElement("functiongraph",JXG.createFunctiongraph),JXG.JSXGraph.registerElement("plot",JXG.createFunctiongraph),JXG.createSpline=function(e,t,n){var r;return r=function(){var e,n=[],r=[],i=function(i,s){var o,u;if(!s){n=[],r=[];if(t.length==2&&JXG.isArray(t[0])&&JXG.isArray(t[1])&&t[0].length==t[1].length)for(o=0;o<t[0].length;o++)typeof t[0][o]=="function"?n.push(t[0][o]()):n.push(t[0][o]),typeof t[1][o]=="function"?r.push(t[1][o]()):r.push(t[1][o]);else for(o=0;o<t.length;o++)if(JXG.isPoint(t[o]))n.push(t[o].X()),r.push(t[o].Y());else if(JXG.isArray(t[o])&&t[o].length==2)for(o=0;o<t.length;o++)typeof t[o][0]=="function"?n.push(t[o][0]()):n.push(t[o][0]),typeof t[o][1]=="function"?r.push(t[o][1]()):r.push(t[o][1]);e=JXG.Math.Numerics.splineDef(n,r)}return JXG.Math.Numerics.splineEval(i,n,r,e)};return i},e.create("curve",["x",r()],n)},JXG.JSXGraph.registerElement("spline",JXG.createSpline),JXG.createRiemannsum=function(e,t,n){var r,i,s,o,u,a;a=JXG.copyAttributes(n,e.options,"riemannsum"),a.curvetype="plot",s=t[0],r=JXG.createFunction(t[1],e,"");if(r==null)throw new Error("JSXGraph: JXG.createRiemannsum: argument '2' n has to be number or function.\nPossible parent types: [function,n:number|function,type,start:number|function,end:number|function]");i=JXG.createFunction(t[2],e,"",!1);if(i==null)throw new Error("JSXGraph: JXG.createRiemannsum: argument 3 'type' has to be string or function.\nPossible parent types: [function,n:number|function,type,start:number|function,end:number|function]");return o=[[0],[0]].concat(t.slice(3)),u=e.create("curve",o,a),u.sum=0,u.Value=function(){return this.sum},u.updateDataArray=function(){var e=JXG.Math.Numerics.riemann(s,r(),i(),this.minX(),this.maxX());this.dataX=e[0],this.dataY=e[1],this.sum=e[2]},u},JXG.JSXGraph.registerElement("riemannsum",JXG.createRiemannsum),JXG.createTracecurve=function(e,t,n){var r,i,s,o;if(t.length!=2)throw new Error("JSXGraph: Can't create trace curve with given parent'\nPossible parent types: [glider, point]");i=JXG.getRef(this.board,t[0]),s=JXG.getRef(this.board,t[1]);if(i.type!=JXG.OBJECT_TYPE_GLIDER||!JXG.isPoint(s))throw new Error("JSXGraph: Can't create trace curve with parent types '"+typeof t[0]+"' and '"+typeof t[1]+"'."+"\nPossible parent types: [glider, point]");return o=JXG.copyAttributes(n,e.options,"tracecurve"),o.curvetype="plot",r=e.create("curve",[[0],[0]],o),r.updateDataArray=function(){var e,t,n,r,u,a,f,l,c=o.numberpoints,h,p=i.position,d=i.slideObject,v=d.minX(),m=d.maxX(),g;t=(m-v)/c,this.dataX=[],this.dataY=[],d.elementClass!=JXG.OBJECT_CLASS_CURVE&&c++;for(e=0;e<c;e++){n=v+e*t,a=d.X(n)/d.Z(n),f=d.Y(n)/d.Z(n),i.setPositionDirectly(JXG.COORDS_BY_USER,[a,f]),h=!1;for(r in this.board.objects){u=this.board.objects[r],u==i&&(h=!0);if(!h)continue;if(!u.needsRegularUpdate)continue;g=u.visProp.trace,u.visProp.trace=!1,u.needsUpdate=!0,u.update(!0),u.visProp.trace=g;if(u==s)break}this.dataX[e]=s.X(),this.dataY[e]=s.Y()}i.position=p,h=!1;for(r in this.board.objects){u=this.board.objects[r],u==i&&(h=!0);if(!h)continue;if(!u.needsRegularUpdate)continue;g=u.visProp.trace,u.visProp.trace=!1,u.needsUpdate=!0,u.update(!0),u.visProp.trace=g;if(u==s)break}},r},JXG.JSXGraph.registerElement("tracecurve",JXG.createTracecurve),JXG.createArc=function(e,t,n){var r,i,s;if(!(t=JXG.checkParents("arc",t,[[JXG.OBJECT_CLASS_POINT,JXG.OBJECT_CLASS_POINT,JXG.OBJECT_CLASS_POINT],[JXG.OBJECT_CLASS_POINT,JXG.OBJECT_CLASS_POINT,JXG.OBJECT_CLASS_POINT,JXG.OBJECT_CLASS_POINT]])))throw new Error("JSXGraph: Can't create Arc with parent types '"+typeof t[0]+"' and '"+typeof t[1]+"' and '"+typeof t[2]+"'."+"\nPossible parent types: [point,point,point]");i=JXG.copyAttributes(n,e.options,"arc"),r=e.create("curve",[[0],[0]],i),r.elType="arc",r.parents=[];for(s=0;s<t.length;s++)t[s].id&&r.parents.push(t[s].id);return r.type=JXG.OBJECT_TYPE_ARC,r.center=JXG.getReference(e,t[0]),r.radiuspoint=JXG.getReference(e,t[1]),r.point2=r.radiuspoint,r.anglepoint=JXG.getReference(e,t[2]),r.point3=r.anglepoint,r.center.addChild(r),r.radiuspoint.addChild(r),r.anglepoint.addChild(r),r.useDirection=i.usedirection,r.updateDataArray=function(){var e=this.radiuspoint,n=this.center,r=this.anglepoint,i,s,o,u,a,f,l=n.X(),c=n.Y(),h=n.Z(),p,d,v,m,g,y,b,w,E,S,x,T,N,C,k,L,A=1,O=Math.PI*.5;a=JXG.Math.Geometry.rad(e,n,r);if(this.visProp.type=="minor"&&a>Math.PI||this.visProp.type=="major"&&a<Math.PI)a=2*Math.PI-a,A=-1;this.useDirection&&(v=t[1].coords.usrCoords,m=t[3].coords.usrCoords,g=t[2].coords.usrCoords,d=(v[1]-g[1])*(v[2]-m[2])-(v[2]-g[2])*(v[1]-m[1]),d<0?(this.radiuspoint=t[1],this.anglepoint=t[2]):(this.radiuspoint=t[2],this.anglepoint=t[1])),y=[e.Z(),e.X(),e.Y()],E=y.slice(0),L=n.Dist(e),l/=h,c/=h,this.dataX=[y[1]/y[0]],this.dataY=[y[2]/y[0]];while(a>JXG.Math.eps)a>=O?(i=O,a-=O):(i=a,a=0),s=Math.cos(A*i),o=Math.sin(A*i),u=[[1,0,0],[l*(1-s)+c*o,s,-o],[c*(1-s)-l*o,o,s]],p=JXG.Math.matVecMult(u,y),E=[p[0]/p[0],p[1]/p[0],p[2]/p[0]],x=y[1]-l,T=y[2]-c,N=E[1]-l,C=E[2]-c,k=Math.sqrt((x+N)*(x+N)+(T+C)*(T+C)),Math.abs(C-T)>JXG.Math.eps?S=(x+N)*(L/k-.5)/(C-T)*8/3:S=(T+C)*(L/k-.5)/(x-N)*8/3,b=[1,y[1]-S*T,y[2]+S*x],w=[1,E[1]+S*C,E[2]-S*N],this.dataX=this.dataX.concat([b[1],w[1],E[1]]),this.dataY=this.dataY.concat([b[2],w[2],E[2]]),y=E.slice(0);this.bezierDegree=3,this.updateStdform(),this.updateQuadraticform()},r.Radius=function(){return this.radiuspoint.Dist(this.center)},r.getRadius=function(){return this.Radius()},r.hasPoint=function(e,t){var n=this.board.options.precision.hasPoint/this.board.unitX,r=this.Radius(),i,s,o,u,a,f,l,c;s=new JXG.Coords(JXG.COORDS_BY_SCREEN,[e,t],this.board),this.transformations.length>0&&(this.updateTransformMatrix(),l=JXG.Math.inverse(this.transformMat),c=JXG.Math.matVecMult(l,s.usrCoords),s=new JXG.Coords(JXG.COORDS_BY_USER,c,this.board)),i=this.center.coords.distance(JXG.COORDS_BY_USER,s),o=Math.abs(i-r)<n;if(o){u=JXG.Math.Geometry.rad(this.radiuspoint,this.center,s.usrCoords.slice(1)),a=0,f=JXG.Math.Geometry.rad(this.radiuspoint,this.center,this.anglepoint);if(this.visProp.type=="minor"&&f>Math.PI||this.visProp.type=="major"&&f<Math.PI)a=f,f=2*Math.PI;if(u<a||u>f)o=!1}return o},r.hasPointSector=function(e,t){var n=new JXG.Coords(JXG.COORDS_BY_SCREEN,[e,t],this.board),r=this.Radius(),i=this.center.coords.distance(JXG.COORDS_BY_USER,n),s=i<r,o,u,a;if(s){o=JXG.Math.Geometry.rad(this.radiuspoint,this.center,n.usrCoords.slice(1)),u=0,a=JXG.Math.Geometry.rad(this.radiuspoint,this.center,this.anglepoint);if(this.visProp.type=="minor"&&a>Math.PI||this.visProp.type=="major"&&a<Math.PI)u=a,a=2*Math.PI;if(o<u||o>a)s=!1}return s},r.getTextAnchor=function(){return this.center.coords},r.getLabelAnchor=function(){var e,t=10/this.board.unitX,n=10/this.board.unitY,r=this.point2.coords.usrCoords,i=this.center.coords.usrCoords,s=r[1]-i[1],o=r[2]-i[2],u,a,f,l;this.label.content!=null&&(this.label.content.relativeCoords=new JXG.Coords(JXG.COORDS_BY_SCREEN,[0,0],this.board)),e=JXG.Math.Geometry.rad(this.radiuspoint,this.center,this.anglepoint);if(this.visProp.type=="minor"&&e>Math.PI||this.visProp.type=="major"&&e<Math.PI)e=-(2*Math.PI-e);return u=new JXG.Coords(JXG.COORDS_BY_USER,[i[1]+Math.cos(e*.5)*s-Math.sin(e*.5)*o,i[2]+Math.sin(e*.5)*s+Math.cos(e*.5)*o],this.board),a=u.usrCoords[1]-i[1],f=u.usrCoords[2]-i[2],l=Math.sqrt(a*a+f*f),a=a*(l+t)/l,f=f*(l+n)/l,new JXG.Coords(JXG.COORDS_BY_USER,[i[1]+a,i[2]+f],this.board)},r.updateQuadraticform=function(){var e=this.center,t=e.X(),n=e.Y(),r=this.Radius();this.quadraticform=[[t*t+n*n-r*r,-t,-n],[-t,1,0],[-n,0,1]]},r.updateStdform=function(){this.stdform[3]=.5,this.stdform[4]=this.Radius(),this.stdform[1]=-this.center.coords.usrCoords[1],this.stdform[2]=-this.center.coords.usrCoords[2],this.normalize()},r.prepareUpdate().update(),r},JXG.JSXGraph.registerElement("arc",JXG.createArc),JXG.createSemicircle=function(e,t,n){var r,i,s;if(!JXG.isPoint(t[0])||!JXG.isPoint(t[1]))throw new Error("JSXGraph: Can't create Semicircle with parent types '"+typeof t[0]+"' and '"+typeof t[1]+"'."+"\nPossible parent types: [point,point]");return s=JXG.copyAttributes(n,e.options,"semicircle","midpoint"),i=e.create("midpoint",[t[0],t[1]],s),i.dump=!1,s=JXG.copyAttributes(n,e.options,"semicircle"),r=e.create("arc",[i,t[1],t[0]],s),r.elType="semicircle",r.parents=[t[0].id,t[1].id],r.subs={midpoint:i},r.midpoint=r.center=i,r},JXG.JSXGraph.registerElement("semicircle",JXG.createSemicircle),JXG.createCircumcircleArc=function(e,t,n){var r,i,s;if(!(JXG.isPoint(t[0])&&JXG.isPoint(t[1])&&JXG.isPoint(t[2])))throw new Error("JSXGraph: create Circumcircle Arc with parent types '"+typeof t[0]+"' and '"+typeof t[1]+"' and '"+typeof t[2]+"'."+"\nPossible parent types: [point,point,point]");return s=JXG.copyAttributes(n,e.options,"circumcirclearc","center"),i=e.create("circumcenter",[t[0],t[1],t[2]],s),i.dump=!1,s=JXG.copyAttributes(n,e.options,"circumcirclearc"),s.usedirection=!0,r=e.create("arc",[i,t[0],t[2],t[1]],s),r.elType="circumcirclearc",r.parents=[t[0].id,t[1].id,t[2].id],r.subs={center:i},r.center=i,r},JXG.JSXGraph.registerElement("circumcirclearc",JXG.createCircumcircleArc),JXG.createMinorArc=function(e,t,n){return n.type="minor",JXG.createArc(e,t,n)},JXG.JSXGraph.registerElement("minorarc",JXG.createMinorArc),JXG.createMajorArc=function(e,t,n){return n.type="major",JXG.createArc(e,t,n)},JXG.JSXGraph.registerElement("majorarc",JXG.createMajorArc),JXG.createSector=function(e,t,n){var r,i;if(!(JXG.isPoint(t[0])&&JXG.isPoint(t[1])&&JXG.isPoint(t[2])))throw new Error("JSXGraph: Can't create Sector with parent types '"+typeof t[0]+"' and '"+typeof t[1]+"' and '"+typeof t[2]+"'.");return i=JXG.copyAttributes(n,e.options,"sector"),r=e.create("curve",[[0],[0]],i),r.type=JXG.OBJECT_TYPE_SECTOR,r.elType="sector",r.parents=[t[0].id,t[1].id,t[2].id],r.point1=JXG.getReference(e,t[0]),r.center=r.point1,r.point2=JXG.getReference(e,t[1]),r.radiuspoint=r.point2,r.point3=JXG.getReference(e,t[2]),r.anglepoint=r.point3,r.point1.addChild(r),r.point2.addChild(r),r.point3.addChild(r),r.useDirection=n.usedirection,r.updateDataArray=function(){var e=this.point2,n=this.point1,r=this.point3,i,s,o,u,a=JXG.Math.Geometry.rad(e,n,r),f,l=n.X(),c=n.Y(),h=n.Z(),p,d,v,m,g,y,b,w,E,S,x,T,N,C,k,L,A=Math.PI*.5;this.useDirection&&(v=t[1].coords.usrCoords,m=t[3].coords.usrCoords,g=t[2].coords.usrCoords,d=(v[1]-g[1])*(v[2]-m[2])-(v[2]-g[2])*(v[1]-m[1]),d<0?(this.point2=t[1],this.point3=t[2]):(this.point2=t[2],this.point3=t[1])),L=n.Dist(e),y=[e.Z(),e.X(),e.Y()],y[1]/=y[0],y[2]/=y[0],y[0]/=y[0],E=y.slice(0),l/=h,c/=h,this.dataX=[l,l+.333*(y[1]-l),l+.666*(y[1]-l),y[1]],this.dataY=[c,c+.333*(y[2]-c),c+.666*(y[2]-c),y[2]];while(a>JXG.Math.eps)a>=A?(i=A,a-=A):(i=a,a=0),s=Math.cos(i),o=Math.sin(i),u=[[1,0,0],[l*(1-s)+c*o,s,-o],[c*(1-s)-l*o,o,s]],p=JXG.Math.matVecMult(u,y),E=[p[0]/p[0],p[1]/p[0],p[2]/p[0]],x=y[1]-l,T=y[2]-c,N=E[1]-l,C=E[2]-c,k=Math.sqrt((x+N)*(x+N)+(T+C)*(T+C)),Math.abs(C-T)>JXG.Math.eps?S=(x+N)*(L/k-.5)/(C-T)*8/3:S=(T+C)*(L/k-.5)/(x-N)*8/3,b=[1,y[1]-S*T,y[2]+S*x],w=[1,E[1]+S*C,E[2]-S*N],this.dataX=this.dataX.concat([b[1],w[1],E[1]]),this.dataY=this.dataY.concat([b[2],w[2],E[2]]),y=E.slice(0);this.dataX=this.dataX.concat([E[1]+.333*(l-E[1]),E[1]+.666*(l-E[1]),l]),this.dataY=this.dataY.concat([E[2]+.333*(c-E[2]),E[2]+.666*(c-E[2]),c]),this.bezierDegree=3},r.Radius=function(){return this.point2.Dist(this.point1)},r.getRadius=function(){return this.Radius()},r.hasPoint=function(e,t){var n=this.board.options.precision.hasPoint/this.board.unitX,r=new JXG.Coords(JXG.COORDS_BY_SCREEN,[e,t],this.board),i=this.Radius(),s=this.center.coords.distance(JXG.COORDS_BY_USER,r),o=Math.abs(s-i)<n,u,a,f;if(o){u=JXG.Math.Geometry.rad(this.point2,this.center,r.usrCoords.slice(1)),a=0,f=JXG.Math.Geometry.rad(this.point2,this.center,this.point3);if(u<a||u>f)o=!1}return o},r.hasPointSector=function(e,t){var n=new JXG.Coords(JXG.COORDS_BY_SCREEN,[e,t],this.board),r=this.Radius(),i=this.point1.coords.distance(JXG.COORDS_BY_USER,n),s=i<r,o;return s&&(o=JXG.Math.Geometry.rad(this.point2,this.point1,n.usrCoords.slice(1)),o>JXG.Math.Geometry.rad(this.point2,this.point1,this.point3)&&(s=!1)),s},r.getTextAnchor=function(){return this.point1.coords},r.getLabelAnchor=function(){var e=JXG.Math.Geometry.rad(this.point2,this.point1,this.point3),t=13/this.board.unitX,n=13/this.board.unitY,r=this.point2.coords.usrCoords,i=this.point1.coords.usrCoords,s=r[1]-i[1],o=r[2]-i[2],u,a,f,l;return this.label.content!=null&&(this.label.content.relativeCoords=new JXG.Coords(JXG.COORDS_BY_SCREEN,[0,0],this.board)),u=new JXG.Coords(JXG.COORDS_BY_USER,[i[1]+Math.cos(e*.5)*s-Math.sin(e*.5)*o,i[2]+Math.sin(e*.5)*s+Math.cos(e*.5)*o],this.board),a=u.usrCoords[1]-i[1],f=u.usrCoords[2]-i[2],l=Math.sqrt(a*a+f*f),a=a*(l+t)/l,f=f*(l+n)/l,new JXG.Coords(JXG.COORDS_BY_USER,[i[1]+a,i[2]+f],this.board)},r.prepareUpdate().update(),r},JXG.JSXGraph.registerElement("sector",JXG.createSector),JXG.createCircumcircleSector=function(e,t,n){var r,i,s;if(!(JXG.isPoint(t[0])&&JXG.isPoint(t[1])&&JXG.isPoint(t[2])))throw new Error("JSXGraph: Can't create circumcircle sector with parent types '"+typeof t[0]+"' and '"+typeof t[1]+"' and '"+typeof t[2]+"'.");return s=JXG.copyAttributes(n,e.options,"circumcirclesector","center"),i=e.create("circumcenter",[t[0],t[1],t[2]],s),i.dump=!1,s=JXG.copyAttributes(n,e.options,"circumcirclesector"),r=e.create("sector",[i,t[0],t[2],t[1]],s),r.elType="circumcirclesector",r.parents=[t[0].id,t[1].id,t[2].id],r.center=i,r.subs={center:i},r},JXG.JSXGraph.registerElement("circumcirclesector",JXG.createCircumcircleSector),JXG.createAngle=function(e,t,n){var r,i,s,o,u,a,f,l;if(!(JXG.isPoint(t[0])&&JXG.isPoint(t[1])&&JXG.isPoint(t[2])))throw new Error("JSXGraph: Can't create angle with parent types '"+typeof t[0]+"' and '"+typeof t[1]+"' and '"+typeof t[2]+"'.");u=JXG.copyAttributes(n,e.options,"angle"),o=u.name;if(typeof o=="undefined"||o=="")o=e.generateName({type:JXG.OBJECT_TYPE_ANGLE}),u.name=o;a=JXG.copyAttributes(n,e.options,"angle","radiuspoint"),i=e.create("point",[0,1,0],a),i.dump=!1,a=JXG.copyAttributes(n,e.options,"angle","pointsquare"),s=e.create("point",[0,1,1],a),s.dump=!1,r=e.create("sector",[t[1],i,t[2]],u),r.elType="angle",r.parents=[t[0].id,t[1].id,t[2].id],r.subs={point:i,pointsquare:s},r.updateDataArraySquare=function(){var e=t[1],n,r,o,u;n=JXG.Math.crossProduct(s.coords.usrCoords,e.coords.usrCoords),r=[-i.X()*n[1]-i.Y()*n[2],i.Z()*n[1],i.Z()*n[2]],n=JXG.Math.crossProduct(i.coords.usrCoords,e.coords.usrCoords),o=[-s.X()*n[1]-s.Y()*n[2],s.Z()*n[1],s.Z()*n[2]],u=JXG.Math.crossProduct(r,o),u[1]/=u[0],u[2]/=u[0],this.dataX=[e.X(),i.X(),u[1],s.X(),e.X()],this.dataY=[e.Y(),i.Y(),u[2],s.Y(),e.Y()],this.bezierDegree=1},r.updateDataArrayNone=function(){this.dataX=[NaN],this.dataY=[NaN],this.bezierDegree=1},r.updateDataArraySector=r.updateDataArray,r.updateDataArray=function(){var e=this.visProp.type,n=JXG.Math.Geometry.trueAngle(t[0],t[1],t[2]);Math.abs(n-90)<this.visProp.orthosensitivity&&(e=this.visProp.orthotype),e=="none"?this.updateDataArrayNone():e==="square"?this.updateDataArraySquare():e==="sector"?this.updateDataArraySector():e==="sectordot"&&(this.updateDataArraySector(),this.dot.visProp.visible===!1&&this.dot.setProperty({visible:!0})),e!=="sectordot"&&this.dot.visProp.visible===!0&&this.dot.setProperty({visible:!1})},i.addConstraint([function(){var e=t[0],n=t[1],i=JXG.evaluate(r.visProp.radius),s=n.Dist(e);return[n.X()+(e.X()-n.X())*i/s,n.Y()+(e.Y()-n.Y())*i/s]}]),s.addConstraint([function(){var e=t[2],n=t[1],i=JXG.evaluate(r.visProp.radius),s=n.Dist(e);return[n.X()+(e.X()-n.X())*i/s,n.Y()+(e.Y()-n.Y())*i/s]}]),r.radiuspoint=i,r.point=i,r.pointsquare=s,l=JXG.copyAttributes(n,e.options,"angle","dot"),r.dot=e.create("point",[function(){if(JXG.exists(r.dot)&&r.dot.visProp.visible===!1)return[0,0];var e=i.coords.usrCoords,n=JXG.Math.Geometry.rad(t[0],t[1],t[2])*.5,s=t[1].X(),o=t[1].Y(),u=[[1,0,0],[s-.5*s*Math.cos(n)+.5*o*Math.sin(n),Math.cos(n)*.5,-Math.sin(n)*.5],[o-.5*s*Math.sin(n)-.5*o*Math.cos(n),Math.sin(n)*.5,Math.cos(n)*.5]];return JXG.Math.matVecMult(u,e)}],l),r.dot.dump=!1,r.subs.dot=r.dot;for(f=0;f<3;f++)JXG.getRef(e,t[f]).addChild(i),JXG.getRef(e,t[f]).addChild(r.dot);return r.type=JXG.OBJECT_TYPE_ANGLE,JXG.getRef(e,t[0]).addChild(r),r.rot=e.create("transform",[function(){return.5*JXG.Math.Geometry.rad(r.point2,r.point1,r.point3)},r.point1],{type:"rotate"}),r.getLabelAnchor=function(){var e=12,t=12,n=this.point1.coords.usrCoords,r,i,s,o;return this.label.content!=null&&(this.label.content.relativeCoords=new JXG.Coords(JXG.COORDS_BY_SCREEN,[0,0],this.board)),JXG.exists(this.visProp.label.fontSize)&&(e=this.visProp.label.fontSize,t=this.visProp.label.fontSize),e/=this.board.unitX,t/=this.board.unitY,this.rot.update(),o=JXG.Math.matVecMult(this.rot.matrix,this.point2.coords.usrCoords),r=o[1]-n[1],i=o[2]-n[2],s=Math.sqrt(r*r+i*i),r=r*(s+e)/s,i=i*(s+t)/s,new JXG.Coords(JXG.COORDS_BY_USER,[n[1]+r,n[2]+i],this.board)},r.Value=function(){return JXG.Math.Geometry.rad(this.point2,this.point1,this.point3)},r.methodMap=JXG.deepCopy(r.methodMap,{Value:"Value"}),r.setAngle=function(e){var t,n,r;return t=this.anglepoint,n=this.radiuspoint,t.draggable()&&(r=this.board.create("transform",[e,this.center],{type:"rotate"}),t.addTransform(n,r),t.isDraggable=!1,t.parents=[n]),this},r.free=function(){var e=this.anglepoint;return e.transformations.length>0&&(e.transformations.pop(),e.isDraggable=!0,e.parents=[]),this},r},JXG.JSXGraph.registerElement("angle",JXG.createAngle),JXG.Composition=function(e){var t=["setProperty","prepareUpdate","updateRenderer","update","highlight","noHighlight"],n=function(e){return function(){var t;for(t in r.elements)JXG.exists(r.elements[t][e])&&r.elements[t][e].apply(r.elements[t],arguments);return r}},r=this,i;for(i=0;i<t.length;i++)this[t[i]]=n(t[i]);this.elements={};for(i in e)e.hasOwnProperty(i)&&this.add(i,e[i]);this.dump=!0,this.subs={}},JXG.extend(JXG.Composition.prototype,{add:function(e,t){return!JXG.exists(this[e])&&JXG.exists(t)?(JXG.exists(t.id)?this.elements[t.id]=t:this.elements[e]=t,this[e]=t,!0):!1},remove:function(e){var t=!1,n;for(n in this.elements)if(this.elements[n].id===this[e].id){t=!0;break}return t&&(delete this.elements[this[e].id],delete this[e]),t},getParents:function(){return this.parents},getType:function(){return this.elType},getAttributes:function(){var e={},t;for(t in this.subs)e[t]=this.subs[t].visProp;return this.attr}}),JXG.createOrthogonalProjection=function(e,t,n){var r,i,s,o;if(JXG.isPoint(t[0])&&t[1].elementClass==JXG.OBJECT_CLASS_LINE)i=t[0],r=t[1];else{if(!JXG.isPoint(t[1])||t[0].elementClass!=JXG.OBJECT_CLASS_LINE)throw new Error("JSXGraph: Can't create perpendicular point with parent types '"+typeof t[0]+"' and '"+typeof t[1]+"'."+"\nPossible parent types: [point,line]");i=t[1],r=t[0]}return attr=JXG.copyAttributes(n,e.options,"orthogonalprojection"),s=e.create("point",[function(){return JXG.Math.Geometry.projectPointToLine(i,r,e)}],n),i.addChild(s),r.addChild(s),s.elType="orthogonalprojection",s.parents=[i.id,s.id],s.update(),s.generatePolynomial=function(){var e=r.point1.symbolic.x,t=r.point1.symbolic.y,n=r.point2.symbolic.x,o=r.point2.symbolic.y,u=i.symbolic.x,a=i.symbolic.y,f=s.symbolic.x,c=s.symbolic.y,h="("+t+")*("+f+")-("+t+")*("+n+")+("+c+")*("+n+")-("+e+")*("+c+")+("+e+")*("+o+")-("+f+")*("+o+")",d="("+a+")*("+t+")-("+a+")*("+o+")-("+c+")*("+t+")+("+c+")*("+o+")+("+u+")*("+e+")-("+u+")*("+n+")-("+f+")*("+e+")+("+f+")*("+n+")";return[h,d]},s},JXG.createPerpendicular=function(e,t,n){var r,i,s,o;t[0]=JXG.getReference(e,t[0]),t[1]=JXG.getReference(e,t[1]);if(JXG.isPoint(t[0])&&t[1].elementClass==JXG.OBJECT_CLASS_LINE)i=t[1],r=t[0];else{if(!JXG.isPoint(t[1])||t[0].elementClass!=JXG.OBJECT_CLASS_LINE)throw new Error("JSXGraph: Can't create perpendicular with parent types '"+typeof t[0]+"' and '"+typeof t[1]+"'."+"\nPossible parent types: [line,point]");i=t[0],r=t[1]}return o=JXG.copyAttributes(n,e.options,"perpendicular"),s=JXG.createLine(e,[function(){return i.stdform[2]*r.X()-i.stdform[1]*r.Y()},function(){return-i.stdform[2]*r.Z()},function(){return i.stdform[1]*r.Z()}],o),s.elType="perpendicular",s.parents=[i.id,r.id],s},JXG.createPerpendicularPoint=function(e,t,n){var r,i,s;if(JXG.isPoint(t[0])&&t[1].elementClass==JXG.OBJECT_CLASS_LINE)i=t[0],r=t[1];else{if(!JXG.isPoint(t[1])||t[0].elementClass!=JXG.OBJECT_CLASS_LINE)throw new Error("JSXGraph: Can't create perpendicular point with parent types '"+typeof t[0]+"' and '"+typeof t[1]+"'."+"\nPossible parent types: [point,line]");i=t[1],r=t[0]}return s=e.create("point",[function(){return JXG.Math.Geometry.perpendicular(r,i,e)[0]}],n),i.addChild(s),r.addChild(s),s.elType="perpendicularpoint",s.parents=[i.id,r.id],s.update(),s.generatePolynomial=function(){var e=r.point1.symbolic.x,t=r.point1.symbolic.y,n=r.point2.symbolic.x,o=r.point2.symbolic.y,u=i.symbolic.x,a=i.symbolic.y,f=s.symbolic.x,c=s.symbolic.y,h="("+t+")*("+f+")-("+t+")*("+n+")+("+c+")*("+n+")-("+e+")*("+c+")+("+e+")*("+o+")-("+f+")*("+o+")",d="("+a+")*("+t+")-("+a+")*("+o+")-("+c+")*("+t+")+("+c+")*("+o+")+("+u+")*("+e+")-("+u+")*("+n+")-("+f+")*("+e+")+("+f+")*("+n+")";return[h,d]},s},JXG.createPerpendicularSegment=function(e,t,n){var r,i,s,o,u;t[0]=JXG.getReference(e,t[0]),t[1]=JXG.getReference(e,t[1]);if(JXG.isPoint(t[0])&&t[1].elementClass==JXG.OBJECT_CLASS_LINE)i=t[1],r=t[0];else{if(!JXG.isPoint(t[1])||t[0].elementClass!=JXG.OBJECT_CLASS_LINE)throw new Error("JSXGraph: Can't create perpendicular with parent types '"+typeof t[0]+"' and '"+typeof t[1]+"'."+"\nPossible parent types: [line,point]");i=t[0],r=t[1]}return u=JXG.copyAttributes(n,e.options,"perpendicularsegment","point"),o=JXG.createPerpendicularPoint(e,[i,r],u),o.dump=!1,JXG.exists(n.layer)||(n.layer=e.options.layer.line),u=JXG.copyAttributes(n,e.options,"perpendicularsegment"),s=JXG.createLine(e,[function(){return JXG.Math.Geometry.perpendicular(i,r,e)[1]?[o,r]:[r,o]}],u),s.point=o,s.elType="perpendicularsegment",s.parents=[r.id,i.id],s.subs={point:o},s},JXG.createMidpoint=function(e,t,n){var r,i,s;if(t.length==2&&JXG.isPoint(t[0])&&JXG.isPoint(t[1]))r=t[0],i=t[1];else{if(t.length!=1||t[0].elementClass!=JXG.OBJECT_CLASS_LINE)throw new Error("JSXGraph: Can't create midpoint.\nPossible parent types: [point,point], [line]");r=t[0].point1,i=t[0].point2}return s=e.create("point",[function(){var e=r.coords.usrCoords[1]+i.coords.usrCoords[1];return isNaN(e)||Math.abs(r.coords.usrCoords[0])<JXG.Math.eps||Math.abs(i.coords.usrCoords[0])<JXG.Math.eps?NaN:e*.5},function(){var e=r.coords.usrCoords[2]+i.coords.usrCoords[2];return isNaN(e)||Math.abs(r.coords.usrCoords[0])<JXG.Math.eps||Math.abs(i.coords.usrCoords[0])<JXG.Math.eps?NaN:e*.5}],n),r.addChild(s),i.addChild(s),s.elType="midpoint",s.parents=[r.id,i.id],s.prepareUpdate().update(),s.generatePolynomial=function(){var e=r.symbolic.x,t=r.symbolic.y,n=i.symbolic.x,o=i.symbolic.y,u=s.symbolic.x,f=s.symbolic.y,l="("+t+")*("+u+")-("+t+")*("+n+")+("+f+")*("+n+")-("+e+")*("+f+")+("+e+")*("+o+")-("+u+")*("+o+")",c="("+e+")^2 - 2*("+e+")*("+u+")+("+t+")^2-2*("+t+")*("+f+")-("+n+")^2+2*("+n+")*("+u+")-("+o+")^2+2*("+o+")*("+f+")";return[l,c]},s},JXG.createParallelPoint=function(e,t,n){var r,i,s,o;if(t.length==3&&t[0].elementClass==JXG.OBJECT_CLASS_POINT&&t[1].elementClass==JXG.OBJECT_CLASS_POINT&&t[2].elementClass==JXG.OBJECT_CLASS_POINT)r=t[0],i=t[1],s=t[2];else if(t[0].elementClass==JXG.OBJECT_CLASS_POINT&&t[1].elementClass==JXG.OBJECT_CLASS_LINE)s=t[0],r=t[1].point1,i=t[1].point2;else{if(t[1].elementClass!=JXG.OBJECT_CLASS_POINT||t[0].elementClass!=JXG.OBJECT_CLASS_LINE)throw new Error("JSXGraph: Can't create parallel point with parent types '"+typeof t[0]+"', '"+typeof t[1]+"' and '"+typeof t[2]+"'."+"\nPossible parent types: [line,point], [point,point,point]");s=t[1],r=t[0].point1,i=t[0].point2}return o=e.create("point",[function(){return s.coords.usrCoords[1]+i.coords.usrCoords[1]-r.coords.usrCoords[1]},function(){return s.coords.usrCoords[2]+i.coords.usrCoords[2]-r.coords.usrCoords[2]}],n),r.addChild(o),i.addChild(o),s.addChild(o),o.elType="parallelpoint",o.parents=[r.id,i.id,s.id],o.prepareUpdate().update(),o.generatePolynomial=function(){var e=r.symbolic.x,t=r.symbolic.y,n=i.symbolic.x,u=i.symbolic.y,f=s.symbolic.x,l=s.symbolic.y,h=o.symbolic.x,d=o.symbolic.y,v="("+u+")*("+h+")-("+u+")*("+f+")-("+t+")*("+h+")+("+t+")*("+f+")-("+d+")*("+n+")+("+d+")*("+e+")+("+l+")*("+n+")-("+l+")*("+e+")",m="("+d+")*("+e+")-("+d+")*("+f+")-("+u+")*("+e+")+("+u+")*("+f+")-("+h+")*("+t+")+("+h+")*("+l+")+("+n+")*("+t+")-("+n+")*("+l+")";return[v,m]},o},JXG.createParallel=function(e,t,n){var r,i,s,o,u;return r=null,t.length==3?(r=t[2],o=function(){return JXG.Math.crossProduct(t[0].coords.usrCoords,t[1].coords.usrCoords)}):t[0].elementClass==JXG.OBJECT_CLASS_POINT?(r=t[0],o=function(){return t[1].stdform}):t[1].elementClass==JXG.OBJECT_CLASS_POINT&&(r=t[1],o=function(){return t[0].stdform}),JXG.exists(n.layer)||(n.layer=e.options.layer.line),u=JXG.copyAttributes(n,e.options,"parallel","point"),i=e.create("point",[function(){return JXG.Math.crossProduct([1,0,0],o())}],u),i.isDraggable=!0,u=JXG.copyAttributes(n,e.options,"parallel"),s=e.create("line",[r,i],u),s.elType="parallel",s.parents=[t[0].id,t[1].id],t.length===3&&s.parents.push(t[2].id),s.point=i,s},JXG.createArrowParallel=function(e,t,n){var r;try{return n.firstArrow=!1,n.lastArrow=!0,r=JXG.createParallel(e,t,n).setStraight(!1,!1),r.elType="arrowparallel",r}catch(i){throw new Error("JSXGraph: Can't create arrowparallel with parent types '"+typeof t[0]+"' and '"+typeof t[1]+"'."+"\nPossible parent types: [line,point], [point,point,point]")}},JXG.createNormal=function(e,t,n){var r,i,s,o,u,a,f;if(t.length==1)r=t[0],i=r.slideObject;else{if(t.length!=2)throw new Error("JSXGraph: Can't create normal with parent types '"+typeof t[0]+"' and '"+typeof t[1]+"'."+"\nPossible parent types: [point,line], [point,circle], [glider]");if(JXG.isPoint(t[0]))r=t[0],i=t[1];else{if(!JXG.isPoint(t[1]))throw new Error("JSXGraph: Can't create normal with parent types '"+typeof t[0]+"' and '"+typeof t[1]+"'."+"\nPossible parent types: [point,line], [point,circle], [glider]");i=t[0],r=t[1]}}u=JXG.copyAttributes(n,e.options,"normal");if(i.elementClass==JXG.OBJECT_CLASS_LINE)f=JXG.copyAttributes(n,e.options,"normal","point"),a=e.create("point",[function(){var e=JXG.Math.crossProduct([1,0,0],i.stdform);return[e[0],-e[2],e[1]]}],f),a.isDraggable=!0,s=e.create("line",[r,a],u),s.point=a;else if(i.elementClass==JXG.OBJECT_CLASS_CIRCLE)s=e.create("line",[i.midpoint,r],u);else if(i.elementClass==JXG.OBJECT_CLASS_CURVE)if(i.visProp.curvetype!="plot"){var l=i.X,c=i.Y;s=e.create("line",[function(){return-r.X()*e.D(l)(r.position)-r.Y()*e.D(c)(r.position)},function(){return e.D(l)(r.position)},function(){return e.D(c)(r.position)}],u)}else s=e.create("line",[function(){var e=Math.floor(r.position),t=r.position-e;return e==i.numberPoints-1&&(e--,t=1),e<0?1:(i.Y(e)+t*(i.Y(e+1)-i.Y(e)))*(i.Y(e)-i.Y(e+1))-(i.X(e)+t*(i.X(e+1)-i.X(e)))*(i.X(e+1)-i.X(e))},function(){var e=Math.floor(r.position);return e==i.numberPoints-1&&e--,e<0?0:i.X(e+1)-i.X(e)},function(){var e=Math.floor(r.position);return e==i.numberPoints-1&&e--,e<0?0:i.Y(e+1)-i.Y(e)}],u);else{if(i.type!=JXG.OBJECT_TYPE_TURTLE)throw new Error("JSXGraph: Can't create normal with parent types '"+typeof t[0]+"' and '"+typeof t[1]+"'."+"\nPossible parent types: [point,line], [point,circle], [glider]");s=e.create("line",[function(){var e=Math.floor(r.position),t=r.position-e,n,s;for(s=0;s<i.objects.length;s++){n=i.objects[s];if(n.type==JXG.OBJECT_TYPE_CURVE){if(e<n.numberPoints)break;e-=n.numberPoints}}return e==n.numberPoints-1&&(e--,t=1),e<0?1:(n.Y(e)+t*(n.Y(e+1)-n.Y(e)))*(n.Y(e)-n.Y(e+1))-(n.X(e)+t*(n.X(e+1)-n.X(e)))*(n.X(e+1)-n.X(e))},function(){var e=Math.floor(r.position),t,n;for(n=0;n<i.objects.length;n++){t=i.objects[n];if(t.type==JXG.OBJECT_TYPE_CURVE){if(e<t.numberPoints)break;e-=t.numberPoints}}return e==t.numberPoints-1&&e--,e<0?0:t.X(e+1)-t.X(e)},function(){var e=Math.floor(r.position),t,n;for(n=0;n<i.objects.length;n++){t=i.objects[n];if(t.type==JXG.OBJECT_TYPE_CURVE){if(e<t.numberPoints)break;e-=t.numberPoints}}return e==t.numberPoints-1&&e--,e<0?0:t.Y(e+1)-t.Y(e)}],u)}s.parents=[];for(o=0;o<t.length;o++)s.parents.push(t[o].id);return s.elType="normal",s},JXG.createBisector=function(e,t,n){var r,i,s,o;if(t[0].elementClass==JXG.OBJECT_CLASS_POINT&&t[1].elementClass==JXG.OBJECT_CLASS_POINT&&t[2].elementClass==JXG.OBJECT_CLASS_POINT){o=JXG.copyAttributes(n,e.options,"bisector","point"),r=e.create("point",[function(){return JXG.Math.Geometry.angleBisector(t[0],t[1],t[2],e)}],o),r.dump=!1;for(s=0;s<3;s++)t[s].addChild(r);return JXG.exists(n.layer)||(n.layer=e.options.layer.line),o=JXG.copyAttributes(n,e.options,"bisector"),i=JXG.createLine(e,[t[1],r],o),i.point=r,i.elType="bisector",i.parents=[t[0].id,t[1].id,t[2].id],i.subs={point:r},i}throw new Error("JSXGraph: Can't create angle bisector with parent types '"+typeof t[0]+"' and '"+typeof t[1]+"'."+"\nPossible parent types: [point,point,point]")},JXG.createAngularBisectorsOfTwoLines=function(e,t,n){var r=JXG.getReference(e,t[0]),i=JXG.getReference(e,t[1]),s,o,u,a;if(r.elementClass!=JXG.OBJECT_CLASS_LINE||i.elementClass!=JXG.OBJECT_CLASS_LINE)throw new Error("JSXGraph: Can't create angle bisectors of two lines with parent types '"+typeof t[0]+"' and '"+typeof t[1]+"'."+"\nPossible parent types: [line,line]");return JXG.exists(n.layer)||(n.layer=e.options.layer.line),u=JXG.copyAttributes(n,e.options,"bisectorlines","line1"),s=e.create("line",[function(){var e=Math.sqrt(r.stdform[1]*r.stdform[1]+r.stdform[2]*r.stdform[2]),t=Math.sqrt(i.stdform[1]*i.stdform[1]+i.stdform[2]*i.stdform[2]);return r.stdform[0]/e-i.stdform[0]/t},function(){var e=Math.sqrt(r.stdform[1]*r.stdform[1]+r.stdform[2]*r.stdform[2]),t=Math.sqrt(i.stdform[1]*i.stdform[1]+i.stdform[2]*i.stdform[2]);return r.stdform[1]/e-i.stdform[1]/t},function(){var e=Math.sqrt(r.stdform[1]*r.stdform[1]+r.stdform[2]*r.stdform[2]),t=Math.sqrt(i.stdform[1]*i.stdform[1]+i.stdform[2]*i.stdform[2]);return r.stdform[2]/e-i.stdform[2]/t}],u),JXG.exists(n.layer)||(n.layer=e.options.layer.line),u=JXG.copyAttributes(n,e.options,"bisectorlines","line2"),o=e.create("line",[function(){var e=Math.sqrt(r.stdform[1]*r.stdform[1]+r.stdform[2]*r.stdform[2]),t=Math.sqrt(i.stdform[1]*i.stdform[1]+i.stdform[2]*i.stdform[2]);return r.stdform[0]/e+i.stdform[0]/t},function(){var e=Math.sqrt(r.stdform[1]*r.stdform[1]+r.stdform[2]*r.stdform[2]),t=Math.sqrt(i.stdform[1]*i.stdform[1]+i.stdform[2]*i.stdform[2]);return r.stdform[1]/e+i.stdform[1]/t},function(){var e=Math.sqrt(r.stdform[1]*r.stdform[1]+r.stdform[2]*r.stdform[2]),t=Math.sqrt(i.stdform[1]*i.stdform[1]+i.stdform[2]*i.stdform[2]);return r.stdform[2]/e+i.stdform[2]/t}],u),a=new JXG.Composition({line1:s,line2:o}),s.dump=!1,o.dump=!1,a.elType="bisectorlines",a.parents=[r.id,i.id],a.subs={line1:s,line2:o},a},JXG.createCircumcircleMidpoint=function(e,t,n){var r,i;if(t[0].elementClass==JXG.OBJECT_CLASS_POINT&&t[1].elementClass==JXG.OBJECT_CLASS_POINT&&t[2].elementClass==JXG.OBJECT_CLASS_POINT){r=JXG.createPoint(e,[function(){return JXG.Math.Geometry.circumcenterMidpoint(t[0],t[1],t[2],e)}],n);for(i=0;i<3;i++)t[i].addChild(r);return r.elType="circumcenter",r.parents=[t[0].id,t[1].id,t[2].id],r.generatePolynomial=function(){var e=a.symbolic.x,t=a.symbolic.y,n=b.symbolic.x,i=b.symbolic.y,s=c.symbolic.x,o=c.symbolic.y,u=r.symbolic.x,f=r.symbolic.y,l=["((",u,")-(",e,"))^2+((",f,")-(",t,"))^2-((",u,")-(",n,"))^2-((",f,")-(",i,"))^2"].join(""),h=["((",u,")-(",e,"))^2+((",f,")-(",t,"))^2-((",u,")-(",s,"))^2-((",f,")-(",o,"))^2"].join("");return[l,h]},r}throw new Error("JSXGraph: Can't create circumcircle midpoint with parent types '"+typeof t[0]+"', '"+typeof t[1]+"' and '"+typeof t[2]+"'."+"\nPossible parent types: [point,point,point]")},JXG.createIncenter=function(e,t,n){var r,i,s,o,u;if(!(t.length>=3&&JXG.isPoint(t[0])&&JXG.isPoint(t[1])&&JXG.isPoint(t[2])))throw new Error("JSXGraph: Can't create incenter with parent types '"+typeof t[0]+"', '"+typeof t[1]+"' and '"+typeof t[2]+"'."+"\nPossible parent types: [point,point,point]");return s=t[0],o=t[1],u=t[2],r=e.create("point",[function(){var t,n,r;return t=Math.sqrt((o.X()-u.X())*(o.X()-u.X())+(o.Y()-u.Y())*(o.Y()-u.Y())),n=Math.sqrt((s.X()-u.X())*(s.X()-u.X())+(s.Y()-u.Y())*(s.Y()-u.Y())),r=Math.sqrt((o.X()-s.X())*(o.X()-s.X())+(o.Y()-s.Y())*(o.Y()-s.Y())),new JXG.Coords(JXG.COORDS_BY_USER,[(t*s.X()+n*o.X()+r*u.X())/(t+n+r),(t*s.Y()+n*o.Y()+r*u.Y())/(t+n+r)],e)}],n),r.elType="incenter",r.parents=[t[0].id,t[1].id,t[2].id],r},JXG.createCircumcircle=function(e,t,n){var r,i,s;try{s=JXG.copyAttributes(n,e.options,"circumcircle","center"),r=JXG.createCircumcircleMidpoint(e,t,s),r.dump=!1,JXG.exists(n.layer)||(n.layer=e.options.layer.circle),s=JXG.copyAttributes(n,e.options,"circumcircle"),i=JXG.createCircle(e,[r,t[0]],s),i.elType="circumcircle",i.parents=[t[0].id,t[1].id,t[2].id],i.subs={center:r}}catch(o){throw new Error("JSXGraph: Can't create circumcircle with parent types '"+typeof t[0]+"', '"+typeof t[1]+"' and '"+typeof t[2]+"'."+"\nPossible parent types: [point,point,point]")}return i},JXG.createIncircle=function(e,t,n){var r,i,s,o;try{s=JXG.copyAttributes(n,e.options,"incircle","center"),r=JXG.createIncenter(e,t,s),r.dump=!1,JXG.exists(n.layer)||(n.layer=e.options.layer.circle),s=JXG.copyAttributes(n,e.options,"incircle"),i=JXG.createCircle(e,[r,function(){var e=Math.sqrt((t[1].X()-t[2].X())*(t[1].X()-t[2].X())+(t[1].Y()-t[2].Y())*(t[1].Y()-t[2].Y())),n=Math.sqrt((t[0].X()-t[2].X())*(t[0].X()-t[2].X())+(t[0].Y()-t[2].Y())*(t[0].Y()-t[2].Y())),r=Math.sqrt((t[1].X()-t[0].X())*(t[1].X()-t[0].X())+(t[1].Y()-t[0].Y())*(t[1].Y()-t[0].Y())),i=(e+n+r)/2;return Math.sqrt((i-e)*(i-n)*(i-r)/i)}],s),i.elType="incircle",i.parents=[t[0].id,t[1].id,t[2].id],i.center=r,i.subs={center:r}}catch(u){throw new Error("JSXGraph: Can't create circumcircle with parent types '"+typeof t[0]+"', '"+typeof t[1]+"' and '"+typeof t[2]+"'."+"\nPossible parent types: [point,point,point]")}return i},JXG.createReflection=function(e,t,n){var r,i,s,o;if(t[0].elementClass==JXG.OBJECT_CLASS_POINT&&t[1].elementClass==JXG.OBJECT_CLASS_LINE)i=t[0],r=t[1];else{if(t[1].elementClass!=JXG.OBJECT_CLASS_POINT||t[0].elementClass!=JXG.OBJECT_CLASS_LINE)throw new Error("JSXGraph: Can't create reflection point with parent types '"+typeof t[0]+"' and '"+typeof t[1]+"'."+"\nPossible parent types: [line,point]");i=t[1],r=t[0]}return o=JXG.createTransform(e,[r],{type:"reflect"}),s=JXG.createPoint(e,[i,o],n),i.addChild(s),r.addChild(s),s.elType="reflection",s.parents=[t[0].id,t[1].id],s.prepareUpdate().update(),s.generatePolynomial=function(){var e=r.point1.symbolic.x,t=r.point1.symbolic.y,n=r.point2.symbolic.x,o=r.point2.symbolic.y,u=i.symbolic.x,a=i.symbolic.y,f=s.symbolic.x,c=s.symbolic.y,h=["((",c,")-(",a,"))*((",t,")-(",o,"))+((",e,")-(",n,"))*((",f,")-(",u,"))"].join(""),d=["((",f,")-(",e,"))^2+((",c,")-(",t,"))^2-((",u,")-(",e,"))^2-((",a,")-(",t,"))^2"].join("");return[h,d]},s},JXG.createMirrorPoint=function(e,t,n){var r,i;if(!JXG.isPoint(t[0])||!JXG.isPoint(t[1]))throw new Error("JSXGraph: Can't create mirror point with parent types '"+typeof t[0]+"' and '"+typeof t[1]+"'."+"\nPossible parent types: [point,point]");r=JXG.createPoint(e,[function(){return JXG.Math.Geometry.rotation(t[0],t[1],Math.PI,e)}],n);for(i=0;i<2;i++)t[i].addChild(r);return r.elType="mirrorpoint",r.parents=[t[0].id,t[1].id],r.prepareUpdate().update(),r},JXG.createIntegral=function(e,t,n){var r,i,s,o=0,u=0,a,f,l,c,h=1,p,d,v,m,g,y,b;if(JXG.isArray(t[0])&&t[1].elementClass==JXG.OBJECT_CLASS_CURVE)r=t[0],i=t[1];else{if(!JXG.isArray(t[1])||t[0].elementClass!=JXG.OBJECT_CLASS_CURVE)throw new Error("JSXGraph: Can't create integral with parent types '"+typeof t[0]+"' and '"+typeof t[1]+"'."+"\nPossible parent types: [[number|function,number|function],curve]");r=t[1],i=t[0]}return o=r[0],u=r[1],JXG.isFunction(o)?(a=o,f=function(){return i.Y(a())},o=a()):(a=o,f=i.Y(o)),JXG.isFunction(o)?(l=u,c=function(){return i.Y(l())},u=l()):(l=u,c=i.Y(u)),u<o&&(h=-1),s=JXG.copyAttributes(n,e.options,"integral","curveLeft"),p=e.create("glider",[a,f,i],s),JXG.isFunction(a)&&p.hideElement(),s=JXG.copyAttributes(n,e.options,"integral","baseLeft"),d=e.create("point",[function(){return p.X()},0],s),s=JXG.copyAttributes(n,e.options,"integral","curveRight"),v=e.create("glider",[l,c,i],s),JXG.isFunction(l)&&v.hideElement(),s=JXG.copyAttributes(n,e.options,"integral","baseRight"),m=e.create("point",[function(){return v.X()},0],s),s=JXG.copyAttributes(n,e.options,"integral"),s.withLabel!==!1&&(s=JXG.copyAttributes(n,e.options,"integral","label"),y=e.create("text",[function(){return v.X()+.2},function(){return v.Y()-.8},function(){var e=JXG.Math.Numerics.I([d.X(),m.X()],i.Y);return"∫ = "+e.toFixed(4)}],s),y.dump=!1,p.addChild(y),v.addChild(y)),s=JXG.copyAttributes(n,e.options,"integral"),b=e.create("curve",[[0],[0]],s),p.dump=!1,d.dump=!1,v.dump=!1,m.dump=!1,b.elType="integral",b.parents=[i.id,r],b.subs={curveLeft:p,baseLeft:d,curveRight:v,baseRight:m},s.withLabel&&(b.subs.label=y),b.updateDataArray=function(){var e,t,n,r,s;d.X()<m.X()?(r=d.X(),s=m.X()):(r=m.X(),s=d.X()),e=[r,r],t=[0,i.Y(r)];for(n=0;n<i.numberPoints;n++)r<=i.points[n].usrCoords[1]&&i.points[n].usrCoords[1]<=s&&(e.push(i.points[n].usrCoords[1]),t.push(i.points[n].usrCoords[2]));e.push(s),t.push(i.Y(s)),e.push(s),t.push(0),e.push(r),t.push(0),this.dataX=e,this.dataY=t},p.addChild(b),v.addChild(b),b.baseLeft=d,b.baseRight=m,b.curveLeft=p,b.curveRight=v,b.label={content:y},b},JXG.createLocus=function(e,t,n){var r,i;if(!JXG.isArray(t)||t.length!=1||t[0].elementClass!=JXG.OBJECT_CLASS_POINT)throw new Error("JSXGraph: Can't create locus with parent of type other than point.\nPossible parent types: [point]");return i=t[0],r=e.create("curve",[[null],[null]],n),r.dontCallServer=!1,r.elType="locus",r.parents=[i.id],r.updateDataArray=function(){if(r.board.mode>0)return;var t=JXG.Math.Symbolic.generatePolynomials(e,i,!0).join("|");if(t===r.spe)return;r.spe=t;var n=function(e,t,n,i){r.dataX=e,r.dataY=t,r.eq=n,r.ctime=i,r.generatePolynomial=function(e){return function(t){var n="("+t.symbolic.x+")",r="("+t.symbolic.y+")",i=[],s;for(s=0;s<e.length;s++)i[s]=e[s].replace(/\*\*/g,"^").replace(/x/g,n).replace(/y/g,r);return i}}(n)},s=JXG.Math.Symbolic.geometricLocusByGroebnerBase(e,i,n);n(s.datax,s.datay,s.polynomial,s.exectime)},r},JXG.createGrid=function(e,t,n){var r,i;return i=JXG.copyAttributes(n,e.options,"grid"),r=e.create("curve",[[null],[null]],i),r.elType="grid",r.parents=[],r.type=JXG.OBJECT_TYPE_GRID,r.updateDataArray=function(){var t=this.visProp.gridx,n=this.visProp.gridy,i=new JXG.Coords(JXG.COORDS_BY_SCREEN,[0,0],e),s=new JXG.Coords(JXG.COORDS_BY_SCREEN,[e.canvasWidth,e.canvasHeight],e),o;e.options.grid.hasGrid=!0,i.setCoordinates(JXG.COORDS_BY_USER,[Math.floor(i.usrCoords[1]/t)*t,Math.ceil(i.usrCoords[2]/n)*n]),s.setCoordinates(JXG.COORDS_BY_USER,[Math.ceil(s.usrCoords[1]/t)*t,Math.floor(s.usrCoords[2]/n)*n]),r.dataX=[],r.dataY=[];for(o=i.usrCoords[2];o>s.usrCoords[2]-n;o-=n)r.dataX.push(i.usrCoords[1],s.usrCoords[1],NaN),r.dataY.push(o,o,NaN);for(o=i.usrCoords[1];o<s.usrCoords[1]+t;o+=t)r.dataX.push(o,o,NaN),r.dataY.push(i.usrCoords[2],s.usrCoords[2],NaN)},r.hasPoint=function(){return!1},e.grids.push(r),r},JXG.createInequality=function(e,t,n){var r,i,s;s=JXG.copyAttributes(n,e.options,"inequality");if(t[0].elementClass===JXG.OBJECT_CLASS_LINE)i=e.create("curve",[[],[]],s),i.hasPoint=function(){return!1},i.updateDataArray=function(){var n=e.getBoundingBox(),r=s.inverse?-1:1,i=1.5,o=i*Math.max(n[2]-n[0],n[1]-n[3]),u,a={coords:{usrCoords:[1,(n[0]+n[2])/2,s.inverse?n[1]:n[3]]}},f=t[0].stdform.slice(1),l=f,c,h;f[1]>0&&(f=JXG.Math.Statistics.multiply(f,-1),l=f),u=i*Math.max(JXG.Math.Geometry.perpendicular(t[0],a,e)[0].distance(JXG.COORDS_BY_USER,a.coords),o),u*=r,a={coords:{usrCoords:[1,(n[0]+n[2])/2,(n[1]+n[3])/2]}},a=JXG.Math.Geometry.perpendicular(t[0],a,e)[0].usrCoords,c=[1,a[1]+f[1]*o,a[2]-f[0]*o],h=[1,a[1]-l[1]*o,a[2]+l[0]*o],this.dataX=[c[1],c[1]+f[0]*u,h[1]+l[0]*u,h[1],c[1]],this.dataY=[c[2],c[2]+f[1]*u,h[2]+l[1]*u,h[2],c[2]]};else{r=JXG.createFunction(t[0]);if(!JXG.exists(r))throw new Error("JSXGraph: Can't create area with the given parents.\nPossible parent types: [line], [function]")}return i},JXG.JSXGraph.registerElement("arrowparallel",JXG.createArrowParallel),JXG.JSXGraph.registerElement("bisector",JXG.createBisector),JXG.JSXGraph.registerElement("bisectorlines",JXG.createAngularBisectorsOfTwoLines),JXG.JSXGraph.registerElement("circumcircle",JXG.createCircumcircle),JXG.JSXGraph.registerElement("circumcirclemidpoint",JXG.createCircumcircleMidpoint),JXG.JSXGraph.registerElement("circumcenter",JXG.createCircumcircleMidpoint),JXG.JSXGraph.registerElement("incenter",JXG.createIncenter),JXG.JSXGraph.registerElement("incircle",JXG.createIncircle),JXG.JSXGraph.registerElement("integral",JXG.createIntegral),JXG.JSXGraph.registerElement("midpoint",JXG.createMidpoint),JXG.JSXGraph.registerElement("mirrorpoint",JXG.createMirrorPoint),JXG.JSXGraph.registerElement("normal",JXG.createNormal),JXG.JSXGraph.registerElement("orthogonalprojection",JXG.createOrthogonalProjection),JXG.JSXGraph.registerElement("parallel",JXG.createParallel),JXG.JSXGraph.registerElement("parallelpoint",JXG.createParallelPoint),JXG.JSXGraph.registerElement("perpendicular",JXG.createPerpendicular),JXG.JSXGraph.registerElement("perpendicularpoint",JXG.createPerpendicularPoint),JXG.JSXGraph.registerElement("perpendicularsegment",JXG.createPerpendicularSegment),JXG.JSXGraph.registerElement("reflection",JXG.createReflection),JXG.JSXGraph.registerElement("locus",JXG.createLocus),JXG.JSXGraph.registerElement("grid",JXG.createGrid),JXG.JSXGraph.registerElement("inequality",JXG.createInequality),JXG.Text=function(e,t,n,r){this.constructor(e,r,JXG.OBJECT_TYPE_TEXT,JXG.OBJECT_CLASS_OTHER);var i;this.content="",this.plaintext="",this.isDraggable=!1,this.needsSizeUpdate=!1;if(this.element=JXG.getRef(this.board,r.anchor)){var s;this.visProp.islabel?this.relativeCoords=new JXG.Coords(JXG.COORDS_BY_SCREEN,[parseFloat(n[0]),parseFloat(n[1])],this.board):this.relativeCoords=new JXG.Coords(JXG.COORDS_BY_USER,[parseFloat(n[0]),parseFloat(n[1])],this.board),this.element.addChild(this),this.X=function(){var e,t,n;return this.visProp.islabel?(e=parseFloat(this.visProp.offset[0]),n=this.element.getLabelAnchor(),t=new JXG.Coords(JXG.COORDS_BY_SCREEN,[e+this.relativeCoords.scrCoords[1]+n.scrCoords[1],0],this.board),t.usrCoords[1]):(n=this.element.getTextAnchor(),this.relativeCoords.usrCoords[1]+n.usrCoords[1])},this.Y=function(){var e,t,n;return this.visProp.islabel?(e=-parseFloat(this.visProp.offset[1]),n=this.element.getLabelAnchor(),t=new JXG.Coords(JXG.COORDS_BY_SCREEN,[0,e+this.relativeCoords.scrCoords[2]+n.scrCoords[2]],this.board),t.usrCoords[2]):(n=this.element.getTextAnchor(),this.relativeCoords.usrCoords[2]+n.usrCoords[2])},this.coords=new JXG.Coords(JXG.COORDS_BY_SCREEN,[0,0],this.board),this.isDraggable=!0}else JXG.isNumber(n[0])&&JXG.isNumber(n[1])&&(this.isDraggable=!0),this.X=JXG.createFunction(n[0],this.board,null,!0),this.Y=JXG.createFunction(n[1],this.board,null,!0),this.coords=new JXG.Coords(JXG.COORDS_BY_USER,[this.X(),this.Y()],this.board);return this.Z=JXG.createFunction(1,this.board,""),this.size=[1,1],this.id=this.board.setId(this,"T"),this.board.renderer.drawText(this),this.setText(t),this.updateSize(),this.visProp.visible||this.board.renderer.hide(this),typeof this.content=="string"&&this.notifyParents(this.content),this.elType="text",this.methodMap=JXG.deepCopy(this.methodMap,{setText:"setTextJessieCode",free:"free",move:"setCoords"}),this},JXG.Text.prototype=new JXG.GeometryElement,JXG.extend(JXG.Text.prototype,{hasPoint:function(e,t){var n,r,i,s,o=this.board.options.precision.hasPoint;return this.visProp.anchorx==="right"?n=this.coords.scrCoords[1]-this.size[0]:this.visProp.anchorx==="middle"?n=this.coords.scrCoords[1]-.5*this.size[0]:n=this.coords.scrCoords[1],r=n+this.size[0],this.visProp.anchory==="top"?s=this.coords.scrCoords[2]+this.size[1]:this.visProp.anchorx==="middle"?s=this.coords.scrCoords[2]+.5*this.size[1]:s=this.coords.scrCoords[2],i=s-this.size[1],t>=i-o&&t<=s+o&&(e>=n-o&&e<=n+2*o||e>=r-2*o&&e<=r+o)},_setText:function(e){return this.needsSizeUpdate=!1,typeof e=="function"?(this.updateText=function(){this.plaintext=e()},this.needsSizeUpdate=!0):(JXG.isNumber(e)?this.content=e.toFixed(this.visProp.digits):this.visProp.useasciimathml?(this.content="'`"+e+"`'",this.needsSizeUpdate=!0):this.content=this.generateTerm(e),this.updateText=new Function("this.plaintext = "+this.content+"; ")),this.updateText(),this.prepareUpdate().update().updateRenderer(),this},setTextJessieCode:function(e){var t;return this.visProp.castext=e,typeof e=="function"?t=function(){return e().replace(/</g,"<").replace(/>/g,">")}:JXG.isNumber(e)?t=e:t=e.replace(/</g,"<").replace(/>/g,">"),this._setText(t)},setText:function(e){this._setText(e)},updateSize:function(){var e;if(typeof document=="undefined")return this;if(this.visProp.display=="html"&&this.board.renderer.type!=="vml"&&this.board.renderer.type!=="no")this.size=[this.rendNode.offsetWidth,this.rendNode.offsetHeight];else if(this.visProp.display==="internal"&&this.board.renderer.type==="svg")try{e=this.rendNode.getBBox(),this.size=[e.width,e.height]}catch(t){}else if(this.board.renderer.type==="vml"||this.visProp.display==="internal"&&this.board.renderer.type==="canvas")this.size=[parseFloat(this.visProp.fontsize)*this.plaintext.length*.45,parseFloat(this.visProp.fontsize)*.9];return this},getSize:function(){return this.size},setCoords:function(e,t){return JXG.isArray(e)&&e.length>1&&(t=e[1],e=e[0]),this.X=function(){return e},this.Y=function(){return t},this.coords.setCoordinates(JXG.COORDS_BY_USER,[e,t]),this.prepareUpdate().update().updateRenderer(),this},free:function(){this.X=JXG.createFunction(this.X(),this.board,""),this.Y=JXG.createFunction(this.Y(),this.board,""),this.isDraggable=!0},update:function(){var e,t,n;return this.needsUpdate&&(this.updateCoords(),this.updateText(),this.needsSizeUpdate&&this.updateSize(),this.updateTransform()),this},updateCoords:function(){this.coords.setCoordinates(JXG.COORDS_BY_USER,[this.X(),this.Y()])},updateRenderer:function(){return this.needsUpdate&&(this.board.renderer.updateText(this),this.needsUpdate=!1),this},updateTransform:function(){var e;if(this.transformations.length==0)return;for(e=0;e<this.transformations.length;e++)this.transformations[e].update();return this},generateTerm:function(e){var t,n='""',r;e=e||"",e=e.replace(/\r/g,""),e=e.replace(/\n/g,""),e=e.replace(/\"/g,'\\"'),e=e.replace(/\'/g,"\\'"),e=e.replace(/&arc;/g,"&ang;"),e=e.replace(/<arc\s*\/>/g,"&ang;"),e=e.replace(/<sqrt\s*\/>/g,"√");var i;i=e.indexOf("<value>");var s=e.indexOf("</value>");if(i>=0){this.needsSizeUpdate=!0;while(i>=0)n+=' + "'+JXG.GeonextParser.replaceSub(JXG.GeonextParser.replaceSup(e.slice(0,i)))+'"',r=e.slice(i+7,s),t=JXG.GeonextParser.geonext2JS(r,this.board),t=t.replace(/\\"/g,'"'),t=t.replace(/\\'/g,"'"),t.indexOf("toFixed")<0?JXG.isNumber(JXG.bind(new Function("return "+t+";"),this)())?n+="+("+t+").toFixed("+this.visProp.digits+")":n+="+("+t+")":n+="+("+t+")",e=e.slice(s+8),i=e.indexOf("<value>"),s=e.indexOf("</value>")}return n+=' + "'+JXG.GeonextParser.replaceSub(JXG.GeonextParser.replaceSup(e))+'"',n=n.replace(/<overline>/g,""),n=n.replace(/<\/overline>/g,""),n=n.replace(/<arrow>/g,""),n=n.replace(/<\/arrow>/g,""),n=n.replace(/&/g,"&"),n},notifyParents:function(e){var t=null;do{var n=/<value>([\w\s\*\/\^\-\+\[\],<>=!]+)<\/value>/;t=n.exec(e),t!=null&&(JXG.GeonextParser.findDependencies(this,t[1],this.board),e=e.substr(t.index),e=e.replace(n,""))}while(t!=null);return this},bounds:function(){var e=this.coords.usrCoords;return this.visProp.islabel?[0,0,0,0]:[e[1],e[2]+this.size[1],e[1]+this.size[0],e[2]]},setPositionDirectly:function(e,t,n){var r=new JXG.Coords(e,t,this.board),i=new JXG.Coords(e,n,this.board),s,o;return this.relativeCoords?this.visProp.islabel?(s=JXG.Math.Statistics.subtract(r.scrCoords,i.scrCoords),this.relativeCoords.scrCoords[1]+=s[1],this.relativeCoords.scrCoords[2]+=s[2]):(s=JXG.Math.Statistics.subtract(r.usrCoords,i.usrCoords),this.relativeCoords.usrCoords[1]+=s[1],this.relativeCoords.usrCoords[2]+=s[2]):(s=JXG.Math.Statistics.subtract(r.usrCoords,i.usrCoords),o=[this.Z(),this.X(),this.Y()],this.X=JXG.createFunction(o[1]+s[1],this.board,""),this.Y=JXG.createFunction(o[2]+s[2],this.board,"")),this}}),JXG.createText=function(e,t,n){var r,i=JXG.copyAttributes(n,e.options,"text");return i.anchor=i.parent||i.anchor,r=new JXG.Text(e,t[t.length-1],t,i),typeof t[t.length-1]!="function"&&(r.parents=t),JXG.evaluate(i.rotate)!=0&&i.display=="internal"&&r.addRotation(JXG.evaluate(i.rotate)),r},JXG.JSXGraph.registerElement("text",JXG.createText),JXG.Image=function(e,t,n,r,i){this.constructor(e,i,JXG.OBJECT_TYPE_IMAGE,JXG.OBJECT_CLASS_OTHER),this.initialCoords=new JXG.Coords(JXG.COORDS_BY_USER,n,this.board),!JXG.isFunction(n[0])&&!JXG.isFunction(n[1])&&(this.isDraggable=!0),this.X=JXG.createFunction(n[0],this.board,""),this.Y=JXG.createFunction(n[1],this.board,""),this.Z=JXG.createFunction(1,this.board,""),this.W=JXG.createFunction(r[0],this.board,""),this.H=JXG.createFunction(r[1],this.board,""),this.coords=new JXG.Coords(JXG.COORDS_BY_USER,[this.X(),this.Y()],this.board),this.usrSize=[this.W(),this.H()],this.size=[Math.abs(this.usrSize[0]*e.unitX),Math.abs(this.usrSize[1]*e.unitY)],this.url=t,this.elType="image",this.span=[[this.Z(),this.X(),this.Y()],[this.Z(),this.W(),0],[this.Z(),0,this.H()]],this.parent=JXG.getRef(i.anchor),this.id=this.board.setId(this,"Im"),this.board.renderer.drawImage(this),this.visProp.visible||this.board.renderer.hide(this)},JXG.Image.prototype=new JXG.GeometryElement,JXG.extend(JXG.Image.prototype,{hasPoint:function(e,t){var n=this.transformations.length,r,i,s,o,u,a,f;if(n==0)return r=e-this.coords.scrCoords[1],i=this.coords.scrCoords[2]-t,s=this.board.options.precision.hasPoint,r>=-s&&r-this.size[0]<=s&&i>=-s&&i-this.size[1]<=s?!0:!1;o=new JXG.Coords(JXG.COORDS_BY_SCREEN,[e,t],this.board),o=o.usrCoords,u=[o[0]-this.span[0][0],o[1]-this.span[0][1],o[2]-this.span[0][2]],f=JXG.Math.innerProduct,a=f(u,this.span[1]);if(0<=a&&a<=f(this.span[1],this.span[1])){a=f(u,this.span[2]);if(0<=a&&a<=f(this.span[2],this.span[2]))return!0}return!1},update:function(){return this.needsUpdate&&(this.updateCoords(),this.usrSize=[this.W(),this.H()],this.size=[Math.abs(this.usrSize[0]*this.board.unitX),Math.abs(this.usrSize[1]*this.board.unitY)],this.updateTransform(),this.updateSpan()),this},updateRenderer:function(){return this.needsUpdate&&(this.board.renderer.updateImage(this),this.needsUpdate=!1),this},updateTransform:function(){var e,t=this.transformations.length;if(t>0)for(e=0;e<t;e++)this.transformations[e].update();return this},updateCoords:function(){this.coords.setCoordinates(JXG.COORDS_BY_USER,[this.X(),this.Y()])},updateSize:function(){this.coords.setCoordinates(JXG.COORDS_BY_USER,[this.W(),this.H()])},updateSpan:function(){var e,t,n=this.transformations.length,r=[];if(n==0)this.span=[[this.Z(),this.X(),this.Y()],[this.Z(),this.W(),0],[this.Z(),0,this.H()]];else{r[0]=[this.Z(),this.X(),this.Y()],r[1]=[this.Z(),this.X()+this.W(),this.Y()],r[2]=[this.Z(),this.X(),this.Y()+this.H()];for(e=0;e<n;e++)for(t=0;t<3;t++)r[t]=JXG.Math.matVecMult(this.transformations[e].matrix,r[t]);for(t=0;t<3;t++)r[t][1]/=r[t][0],r[t][2]/=r[t][0],r[t][0]/=r[t][0];for(t=1;t<3;t++)r[t][0]-=r[0][0],r[t][1]-=r[0][1],r[t][2]-=r[0][2];this.span=r}return this},addTransform:function(e){if(JXG.isArray(e))for(var t=0;t<e.length;t++)this.transformations.push(e[t]);else this.transformations.push(e)},setPositionDirectly:function(e,t,n){var r=new JXG.Coords(e,t,this.board),i=new JXG.Coords(e,n,this.board),s,o=[this.Z(),this.X(),this.Y()];return s=JXG.Math.Statistics.subtract(r.usrCoords,i.usrCoords),this.X=JXG.createFunction(o[1]+s[1],this.board,""),this.Y=JXG.createFunction(o[2]+s[2],this.board,""),this}}),JXG.createImage=function(e,t,n){var r,i,s;return i=JXG.copyAttributes(n,e.options,"image"),s=new JXG.Image(e,t[0],t[1],t[2],i),JXG.evaluate(i.rotate)!=0&&s.addRotation(JXG.evaluate(i.rotate)),s},JXG.JSXGraph.registerElement("image",JXG.createImage),JXG.createSlider=function(e,t,n){var r,i,s,o,u,a,f,l,c,h,p,d,v,m,g,y,b,w,E,S,x,T;return r=t[0],i=t[1],s=t[2][0],o=t[2][1],u=t[2][2],a=u-s,x=JXG.copyAttributes(n,e.options,"slider"),E=x.withticks,w=x.withlabel,S=x.snapwidth,T=x.precision,x=JXG.copyAttributes(n,e.options,"slider","point1"),f=e.create("point",r,x),x=JXG.copyAttributes(n,e.options,"slider","point2"),l=e.create("point",i,x),e.create("group",[f,l]),x=JXG.copyAttributes(n,e.options,"slider","baseline"),c=e.create("segment",[f,l],x),c.updateStdform(),E&&(x=JXG.copyAttributes(n,e.options,"slider","ticks"),h=2,p=e.create("ticks",[c,l.Dist(f)/h],x)),d=r[0]+(i[0]-r[0])*(o-s)/(u-s),v=r[1]+(i[1]-r[1])*(o-s)/(u-s),x=JXG.copyAttributes(n,e.options,"slider"),x.withLabel=!1,m=e.create("glider",[d,v,c],x),m.setProperty({snapwidth:S}),x=JXG.copyAttributes(n,e.options,"slider","highline"),g=e.create("segment",[f,m],x),m.Value=function(){return m.visProp.snapwidth===-1?this.position*a+s:Math.round((this.position*a+s)/this.visProp.snapwidth)*this.visProp.snapwidth},m.methodMap=JXG.deepCopy(m.methodMap,{Value:"Value"}),m._smax=u,m._smin=s,w&&(n.name&&n["name"]!=""?y=n.name+" = ":y="",x=JXG.copyAttributes(n,e.options,"slider","label"),b=e.create("text",[function(){return(l.X()-f.X())*.05+l.X()},function(){return(l.Y()-f.Y())*.05+l.Y()},function(){return y+m.Value().toFixed(T)}],x),m.label.content=b),m.point1=f,m.point2=l,m.baseline=c,m.highline=g,E&&(m.ticks=p),m.remove=function(){w&&e.removeObject(b),e.removeObject(g),E&&c.removeTicks(p),e.removeObject(c),e.removeObject(l),e.removeObject(f),JXG.Point.prototype.remove.call(m)},f.dump=!1,l.dump=!1,c.dump=!1,g.dump=!1,m.elType="slider",m.parents=t,m.subs={point1:f,point2:l,baseLine:c,highLine:g},E&&(p.dump=!1,m.subs.ticks=p),m},JXG.JSXGraph.registerElement("slider",JXG.createSlider),JXG.Chart=function(e,t,n){this.constructor(e,n);var r,i,s,o,u,a;if(!JXG.isArray(t)||t.length===0)throw new Error("JSXGraph: Can't create a chart without data");this.elements=[];if(JXG.isNumber(t[0])){i=t,r=[];for(s=0;s<i.length;s++)r[s]=s+1}else if(t.length===1&&JXG.isArray(t[0])){i=t[0],r=[],a=JXG.evaluate(i).length;for(s=0;s<a;s++)r[s]=s+1}else t.length===2&&(a=Math.min(t[0].length,t[1].length),r=t[0].slice(0,a),i=t[1].slice(0,a));if(JXG.isArray(i)&&i.length===0)throw new Error("JSXGraph: Can't create charts without data.");u=n.chartstyle.replace(/ /g,"").split(",");for(s=0;s<u.length;s++){switch(u[s]){case"bar":o=this.drawBar(e,r,i,n);break;case"line":o=this.drawLine(e,r,i,n);break;case"fit":o=this.drawFit(e,r,i,n);break;case"spline":o=this.drawSpline(e,r,i,n);break;case"pie":o=this.drawPie(e,i,n);break;case"point":o=this.drawPoints(e,r,i,n);break;case"radar":o=this.drawRadar(e,t,n)}this.elements.push(o)}return this.id=this.board.setId(this,"Chart"),this.elements},JXG.Chart.prototype=new JXG.GeometryElement,JXG.extend(JXG.Chart.prototype,{drawLine:function(e,t,n,r){return r.fillcolor="none",r.highlightfillcolor="none",e.create("curve",[t,n],r)},drawSpline:function(e,t,n,r){return r.fillColor="none",r.highlightfillcolor="none",e.create("spline",[t,n],r)},drawFit:function(e,t,n,r){var i=r.degree;return i=!JXG.exists(i)||parseInt(i)==NaN||parseInt(i)<1?1:parseInt(i),r.fillcolor="none",r.highlightfillcolor="none",e.create("functiongraph",[JXG.Math.Numerics.regressionPolynomial(i,t,n)],r)},drawBar:function(e,t,n,r){var i,s=[],o,u,a,f,l,c,h,p,d,v,m=[],g={fixed:!0,withLabel:!1,visible:!1,name:""};JXG.exists(r.fillopacity)||(r.fillopacity=.6);if(r&&r.width)l=r.width;else{if(t.length<=1)l=1;else{l=t[1]-t[0];for(i=1;i<t.length-1;i++)l=t[i+1]-t[i]<l?t[i+1]-t[i]:l}l*=.8}u=r.fillcolor,a=parseFloat(e.options.text.fontSize);for(i=0;i<t.length;i++)isNaN(JXG.evaluate(t[i]))||isNaN(n[i]),JXG.isFunction(t[i])?(c=function(){return t[i]()-l*.5},h=function(){return t[i]()},p=function(){return t[i]()+l*.5}):(c=t[i]-l*.5,h=t[i],p=t[i]+l*.5),d=n[i],r.dir=="horizontal"?(m[0]=e.create("point",[0,c],g),m[1]=e.create("point",[d,c],g),m[2]=e.create("point",[d,p],g),m[3]=e.create("point",[0,p],g),JXG.exists(r.labels)&&JXG.exists(r.labels[i])&&(o=r.labels[i].toString().length,o=2*o*a/e.unitX,d>=0?d+=a*.5/e.unitX:d-=a*o/e.unitX,h-=a*.2/e.unitY,f=e.create("text",[d,h,r.labels[i]],r))):(m[0]=e.create("point",[c,0],g),m[1]=e.create("point",[c,d],g),m[2]=e.create("point",[p,d],g),m[3]=e.create("point",[p,0],g),JXG.exists(r.labels)&&JXG.exists(r.labels[i])&&(o=r.labels[i].toString().length,o=.6*o*a/e.unitX,d>=0?d+=a*.5/e.unitY:d-=a*1/e.unitY,f=e.create("text",[h-o*.5,d,r.labels[i]],r))),r.withlines=!1,JXG.exists(r.colors)&&JXG.isArray(r.colors)&&(v=r.colors,r.fillcolor=v[i%v.length]),s[i]=e.create("polygon",m,r),JXG.exists(r.labels)&&JXG.exists(r.labels[i])&&(s[i].text=f);return s},drawPoints:function(e,t,n,r){var i,s=[],o=r.infoboxarray;r.fixed=!0,r.name="";for(i=0;i<t.length;i++)r.infoboxtext=o?o[i%o.length]:!1,s[i]=e.create("point",[t[i],n[i]],r);return s},drawPie:function(e,t,n){var r,i=[],s=[],o=JXG.Math.Statistics.sum(t),u=n.colors,a=n.highlightcolors,f=n.labels,l=n.radius||4,c=l,h=n.center||[0,0],p=h[0],d=h[1],v,m={fixed:!0,withLabel:!1,visible:!1,name:""};if(!JXG.isArray(f)){f=[];for(r=0;r<t.length;r++)f[r]=""}JXG.isFunction(l)||(c=function(){return l}),n.highlightonsector=n.highlightonsector||!1,n.straightfirst=!1,n.straightlast=!1,v=e.create("point",[p,d],m),i[0]=e.create("point",[function(){return c()+p},function(){return d}],m);for(r=0;r<t.length;r++)i[r+1]=e.create("point",[function(e){return function(){var n,r=0,i,s;for(i=0;i<=e;i++)r+=parseFloat(JXG.evaluate(t[i]));n=r;for(i=e+1;i<t.length;i++)n+=parseFloat(JXG.evaluate(t[i]));return s=n!=0?2*Math.PI*r/n:0,c()*Math.cos(s)+p}}(r),function(e){return function(){var n,r=0,i,s;for(i=0;i<=e;i++)r+=parseFloat(JXG.evaluate(t[i]));n=r;for(i=e+1;i<t.length;i++)n+=parseFloat(JXG.evaluate(t[i]));return s=n!=0?2*Math.PI*r/n:0,c()*Math.sin(s)+d}}(r)],m),n.name=f[r],n.withlabel=n.name!="",n.fillcolor=u&&u[r%u.length],n.labelcolor=u&&u[r%u.length],n.highlightfillcolor=a&&a[r%a.length],s[r]=e.create("sector",[v,i[r],i[r+1]],n),n.highlightonsector&&(s[r].hasPoint=s[r].hasPointSector),n.highlightbysize&&(s[r].highlight=function(){if(!this.highlighted){this.highlighted=!0,this.board.renderer.highlight(this);var e=-this.point1.coords.usrCoords[1]+this.point2.coords.usrCoords[1],t=-this.point1.coords.usrCoords[2]+this.point2.coords.usrCoords[2];this.label.content!=null&&(this.label.content.rendNode.style.fontSize=2*this.label.content.visProp.fontsize+"px",this.label.content.prepareUpdate().update().updateRenderer()),this.point2.coords=new JXG.Coords(JXG.COORDS_BY_USER,[this.point1.coords.usrCoords[1]+e*1.1,this.point1.coords.usrCoords[2]+t*1.1],this.board),this.prepareUpdate().update().updateRenderer()}},s[r].noHighlight=function(){if(this.highlighted){this.highlighted=!1,this.board.renderer.noHighlight(this);var e=-this.point1.coords.usrCoords[1]+this.point2.coords.usrCoords[1],t=-this.point1.coords.usrCoords[2]+this.point2.coords.usrCoords[2];this.label.content!=null&&(this.label.content.rendNode.style.fontSize=this.label.content.visProp.fontsize*2+"px",this.label.content.prepareUpdate().update().updateRenderer()),this.point2.coords=new JXG.Coords(JXG.COORDS_BY_USER,[this.point1.coords.usrCoords[1]+e/1.1,this.point1.coords.usrCoords[2]+t/1.1],this.board),this.prepareUpdate().update().updateRenderer()}});return{sectors:s,points:i,midpoint:v}},drawRadar:function(e,t,n){var r,i,s,o,u,a,f=t.length,l,c,h,p,d,v,m,g,y,b,w,E,S,x,T,N,C,k,L,A,O,M,_,D,P,H,B,j,F,I,q,R,U,z,W;if(f<=0){JXG.debug("No data");return}s=n.paramarray;if(!JXG.exists(s)){JXG.debug("Need paramArray attribute");return}o=s.length;if(o<=1){JXG.debug("Need more than 1 param");return}for(r=0;r<f;r++)if(o!=t[r].length){JXG.debug("Use data length equal to number of params ("+t[r].length+" != "+o+")");return}u=new Array(o),a=new Array(o);for(i=0;i<o;i++)u[i]=t[0][i],a[i]=u[i];for(r=1;r<f;r++)for(i=0;i<o;i++)t[r][i]>u[i]&&(u[i]=t[r][i]),t[r][i]<a[i]&&(a[i]=t[r][i]);l=new Array(f),c=new Array(f);for(r=0;r<f;r++)l[r]="",c[r]=[];h=new Array(o),p=new Array(o),d=n.startshiftratio||0,v=n.endshiftratio||0;for(r=0;r<o;r++)h[r]=(u[r]-a[r])*d,p[r]=(u[r]-a[r])*v;m=n.startshiftarray||h,g=n.endshiftarray||p,y=n.startarray||a;if(JXG.exists(n.start))for(r=0;r<o;r++)y[r]=n.start;b=n.endarray||u;if(JXG.exists(n.end))for(r=0;r<o;r++)b[r]=n.end;if(m.length!=o){JXG.debug("Start shifts length is not equal to number of parameters");return}if(g.length!=o){JXG.debug("End shifts length is not equal to number of parameters");return}if(y.length!=o){JXG.debug("Starts length is not equal to number of parameters");return}if(b.length!=o){JXG.debug("Ends length is not equal to number of parameters");return}w=n.labelarray||l,E=n.colors,S=n.highlightcolors,x=n.radius||10,T={},JXG.exists(n.highlightonsector)||(n.highlightonsector=!1),T.name=n.name,T.id=n.id,T.strokewidth=n.strokewidth||1,T.polystrokewidth=n.polystrokewidth||2*T.strokewidth,T.strokecolor=n.strokecolor||"black",T.straightfirst=!1,T.straightlast=!1,T.fillcolor=n.fillColor||"#FFFF88",T.fillopacity=n.fillOpacity||.4,T.highlightfillcolor=n.highlightFillColor||"#FF7400",T.highlightstrokecolor=n.highlightStrokeColor||"black",T.gradient=n.gradient||"none",N=n.center||[0,0],C=N[0],k=N[1],L=e.create("point",[C,k],{name:"",fixed:!0,withlabel:!1,visible:!1}),A=Math.PI/2-Math.PI/o;if(n.startangle||n.startangle===0)A=n.startangle;O=A,M=[],_=[];var X=function(){var e,t,n,r,i=this.visProp.label.offset.slice(0);return e=this.point1.X(),t=this.point2.X(),n=this.point1.Y(),r=this.point2.Y(),t<e&&(i[0]=-i[0]),r<n&&(i[1]=-i[1]),this.setLabelRelativeCoords(i),new JXG.Coords(JXG.COORDS_BY_USER,[this.point2.X(),this.point2.Y()],this.board)},V=function(t,n){var r,i,s;return r=e.create("transform",[-(y[n]-m[n]),0],{type:"translate"}),i=e.create("transform",[x/(b[n]+g[n]-(y[n]-m[n])),1],{type:"scale"}),r.melt(i),s=e.create("transform",[t],{type:"rotate"}),r.melt(s),r};for(r=0;r<o;r++){O+=2*Math.PI/o,P=x*Math.cos(O)+C,H=x*Math.sin(O)+k,M[r]=e.create("point",[P,H],{name:"",fixed:!0,withlabel:!1,visible:!1}),_[r]=e.create("line",[L,M[r]],{name:s[r],strokeColor:T.strokecolor,strokeWidth:T.strokewidth,strokeOpacity:1,straightFirst:!1,straightLast:!1,withLabel:!0,highlightStrokeColor:T.highlightstrokecolor}),_[r].getLabelAnchor=X,D=V(O,r);for(i=0;i<t.length;i++){var $=t[i][r];c[i][r]=e.create("point",[$,0],{name:"",fixed:!0,withlabel:!1,visible:!1}),c[i][r].addTransform(c[i][r],D)}}B=new Array(f);for(r=0;r<f;r++){T.labelcolor=E&&E[r%E.length],T.strokecolor=E&&E[r%E.length],T.fillcolor=E&&E[r%E.length],B[r]=e.create("polygon",c[r],{withLines:!0,withLabel:!1,fillColor:T.fillcolor,fillOpacity:T.fillopacity,highlightFillColor:T.highlightfillcolor});for(i=0;i<o;i++)B[r].borders[i].setProperty("strokecolor:"+E[r%E.length]),B[r].borders[i].setProperty("strokewidth:"+T.polystrokewidth)}j=n.legendposition||"none";switch(j){case"right":var J=n.legendleftoffset||2,K=n.legendtopoffset||1;this.legend=e.create("legend",[C+x+J,k+x-K],{labels:w,colors:E});break;case"none":break;default:JXG.debug("Unknown legend position")}F=[];if(n["showcircles"]!=0){I=[];for(r=0;r<6;r++)I[r]=20*r;I[0]="0",q=n.circlelabelarray||I,R=q.length;if(R<2){alert("Too less circles");return}U=[],z=A+Math.PI/o,D=V(z,0),T.fillcolor="none",T.highlightfillcolor="none",T.strokecolor=n.strokecolor||"black",T.strokewidth=n.circlestrokewidth||.5,T.layer=0,W=(b[0]-y[0])/(R-1);for(r=0;r<R;r++)U[r]=e.create("point",[y[0]+r*W,0],{name:q[r],size:0,fixed:!0,withLabel:!0,visible:!0}),U[r].addTransform(U[r],D),F[r]=e.create("circle",[L,U[r]],T)}return this.rendNode=B[0].rendNode,{circles:F,lines:_,points:c,midpoint:L,polygons:B}},updateRenderer:function(){return this},update:function(){return this.needsUpdate&&this.updateDataArray(),this},updateDataArray:function(){}}),JXG.createChart=function(e,t,n){if(t.length==1&&typeof t[0]=="string"){var r=document.getElementById(t[0]),i,s,o,u,a,f=[],l,c,h,p,d,v,m,g,y,b,w;if(JXG.exists(r)){w=JXG.copyAttributes(n,e.options,"chart"),r=(new JXG.DataSource).loadFromTable(t[0],w.withheaders,w.withheaders),i=r.data,a=r.columnHeaders,s=r.rowHeaders,p=w.width,d=w.name,v=w.strokecolor,m=w.fillcolor,g=w.highlightstrokecolor,y=w.highlightfillcolor,e.suspendUpdate(),b=i.length,h=[];if(w.rows&&JXG.isArray(w.rows)){for(o=0;o<b;o++)for(u=0;u<w.rows.length;u++)if(w.rows[u]==o||w.withheaders&&w.rows[u]==s[o]){h.push(i[o]);break}}else h=i;b=h.length;for(o=0;o<b;o++){c=[];if(w.chartstyle&&w.chartstyle.indexOf("bar")!=-1){p?l=p:l=.8,c.push(1-l/2+(o+.5)*l/(1*b));for(u=1;u<h[o].length;u++)c.push(c[u-1]+1);w.width=l/(1*b)}d&&d.length==b?w.name=d[o]:w.withheaders&&(w.name=a[o]),v&&v.length==b?w.strokecolor=v[o]:w.strokecolor=JXG.hsv2rgb((o+1)/(1*b)*360,.9,.6),m&&m.length==b?w.fillcolor=m[o]:w.fillcolor=JXG.hsv2rgb((o+1)/(1*b)*360,.9,1),g&&g.length==b?w.highlightstrokecolor=g[o]:w.highlightstrokecolor=JXG.hsv2rgb((o+1)/(1*b)*360,.9,1),y&&y.length==b?w.highlightfillcolor=y[o]:w.highlightfillcolor=JXG.hsv2rgb((o+1)/(1*b)*360,.9,.6),w.chartstyle&&w.chartstyle.indexOf("bar")!=-1?f.push(new JXG.Chart(e,[c,h[o]],w)):f.push(new JXG.Chart(e,[h[o]],w))}e.unsuspendUpdate()}return f}return w=JXG.copyAttributes(n,e.options,"chart"),new JXG.Chart(e,t,w)},JXG.JSXGraph.registerElement("chart",JXG.createChart),JXG.Legend=function(e,t,n){var r;this.constructor(),r=JXG.copyAttributes(n,e.options,"legend"),this.board=e,this.coords=new JXG.Coords(JXG.COORDS_BY_USER,t,this.board),this.myAtts={},this.label_array=r.labelarray||r.labels,this.color_array=r.colorarray||r.colors,this.lines=[],this.myAtts.strokewidth=r.strokewidth||5,this.myAtts.straightfirst=!1,this.myAtts.straightlast=!1,this.myAtts.withlabel=!0,this.myAtts.fixed=!0,this.style=r.legendstyle||r.style;switch(this.style){case"vertical":this.drawVerticalLegend(e,r);break;default:throw new Error("JSXGraph: Unknown legend style: "+this.style)}},JXG.Legend.prototype=new JXG.GeometryElement,JXG.Legend.prototype.drawVerticalLegend=function(e,t){var n=t.linelength||1,r=(t.rowheight||20)/this.board.unitY,i;for(i=0;i<this.label_array.length;i++)this.myAtts.strokecolor=this.color_array[i],this.myAtts.highlightstrokecolor=this.color_array[i],this.myAtts.name=this.label_array[i],this.myAtts.label={offset:[10,0],strokeColor:this.color_array[i],strokeWidth:this.myAtts.strokewidth},this.lines[i]=e.create("line",[[this.coords.usrCoords[1],this.coords.usrCoords[2]-i*r],[this.coords.usrCoords[1]+n,this.coords.usrCoords[2]-i*r]],this.myAtts),this.lines[i].getLabelAnchor=function(){return this.setLabelRelativeCoords(this.visProp.label.offset),new JXG.Coords(JXG.COORDS_BY_USER,[this.point2.X(),this.point2.Y()],this.board)}},JXG.createLegend=function(e,t,n){var r=[0,0];return JXG.exists(t)&&t.length==2&&(r=t),new JXG.Legend(e,r,n)},JXG.JSXGraph.registerElement("legend",JXG.createLegend),JXG.Transformation=function(e,t,n){this.elementClass=JXG.OBJECT_CLASS_OTHER,this.matrix=[[1,0,0],[0,1,0],[0,0,1]],this.board=e,this.isNumericMatrix=!1,this.setMatrix(e,t,n)},JXG.Transformation.prototype={},JXG.extend(JXG.Transformation.prototype,{update:function(){return this},setMatrix:function(e,t,n){var r;this.isNumericMatrix=!0;for(r=0;r<n.length;r++)if(typeof n[r]!="number"){this.isNumericMatrix=!1;break}t=="translate"?(this.evalParam=JXG.createEvalFunction(e,n,2),this.update=function(){this.matrix[1][0]=this.evalParam(0),this.matrix[2][0]=this.evalParam(1)}):t=="scale"?(this.evalParam=JXG.createEvalFunction(e,n,2),this.update=function(){this.matrix[1][1]=this.evalParam(0),this.matrix[2][2]=this.evalParam(1)}):t=="reflect"?(n.length<4&&(n[0]=JXG.getReference(e,n[0])),n.length==2&&(n[1]=JXG.getReference(e,n[1])),n.length==4&&(this.evalParam=JXG.createEvalFunction(e,n,4)),this.update=function(){var e,t,r,i,s,o,u,a;n.length==1?u=n[0].stdform:n.length==2?u=JXG.Math.crossProduct(n[1].coords.usrCoords,n[0].coords.usrCoords):n.length==4&&(u=JXG.Math.crossProduct([1,this.evalParam(2),this.evalParam(3)],[1,this.evalParam(0),this.evalParam(1)])),e=u[1],t=u[2],r=u[0],a=[-r*e,-r*t,e*e+t*t],o=a[2],i=a[0]/a[2],s=a[1]/a[2],e=-u[2],t=u[1],this.matrix[1][1]=(e*e-t*t)/o,this.matrix[1][2]=2*e*t/o,this.matrix[2][1]=this.matrix[1][2],this.matrix[2][2]=-this.matrix[1][1],this.matrix[1][0]=i*(1-this.matrix[1][1])-s*this.matrix[1][2],this.matrix[2][0]=s*(1-this.matrix[2][2])-i*this.matrix[2][1]}):t=="rotate"?(n.length==3?this.evalParam=JXG.createEvalFunction(e,n,3):n.length<=2&&(this.evalParam=JXG.createEvalFunction(e,n,1),n.length==2&&(n[1]=JXG.getReference(e,n[1]))),this.update=function(){var e=this.evalParam(0),t,r,i=Math.cos(e),s=Math.sin(e);this.matrix[1][1]=i,this.matrix[1][2]=-s,this.matrix[2][1]=s,this.matrix[2][2]=i,n.length>1&&(n.length==3?(t=this.evalParam(1),r=this.evalParam(2)):(t=n[1].X(),r=n[1].Y()),this.matrix[1][0]=t*(1-i)+r*s,this.matrix[2][0]=r*(1-i)-t*s)}):t=="shear"?(this.evalParam=JXG.createEvalFunction(e,n,1),this.update=function(){var e=this.evalParam(0);this.matrix[1][1]=Math.tan(e)}):t=="generic"&&(this.evalParam=JXG.createEvalFunction(e,n,9),this.update=function(){this.matrix[0][0]=this.evalParam(0),this.matrix[0][1]=this.evalParam(1),this.matrix[0][2]=this.evalParam(2),this.matrix[1][0]=this.evalParam(3),this.matrix[1][1]=this.evalParam(4),this.matrix[1][2]=this.evalParam(5),this.matrix[2][0]=this.evalParam(6),this.matrix[2][1]=this.evalParam(7),this.matrix[2][2]=this.evalParam(8)})},apply:function(e){return this.update(),arguments[1]!=null?JXG.Math.matVecMult(this.matrix,e.initialCoords.usrCoords):JXG.Math.matVecMult(this.matrix,e.coords.usrCoords)},applyOnce:function(e){var t,n,r;JXG.isArray(e)||(e=[e]),n=e.length;for(r=0;r<n;r++)this.update(),t=JXG.Math.matVecMult(this.matrix,e[r].coords.usrCoords),e[r].coords.setCoordinates(JXG.COORDS_BY_USER,t)},bindTo:function(e){var t,n;if(JXG.isArray(e)){n=e.length;for(t=0;t<n;t++)e[t].transformations.push(this)}else e.transformations.push(this)},setProperty:function(e){},melt:function(e){var t=[],n,r,i,s,o,u;r=e.matrix.length,i=this.matrix[0].length;for(n=0;n<r;n++)t[n]=[];this.update(),e.update();for(n=0;n<r;n++)for(u=0;u<i;u++){o=0;for(s=0;s<r;s++)o+=e.matrix[n][s]*this.matrix[s][u];t[n][u]=o}return this.update=function(){var e=this.matrix.length,r=this.matrix[0].length;for(n=0;n<e;n++)for(u=0;u<r;u++)this.matrix[n][u]=t[n][u]},this}}),JXG.createTransform=function(e,t,n){return new JXG.Transformation(e,n.type,t)},JXG.JSXGraph.registerElement("transform",JXG.createTransform),JXG.Turtle=function(e,t,n){this.constructor(e,n,JXG.OBJECT_TYPE_TURTLE,JXG.OBJECT_CLASS_OTHER);var r,i,s;return this.turtleIsHidden=!1,this.board=e,this.visProp.curveType="plot",this._attributes=JXG.copyAttributes(this.visProp,e.options,"turtle"),delete this._attributes.id,r=0,i=0,s=90,t.length!=0&&(t.length==3?(r=t[0],i=t[1],s=t[2]):t.length==2?JXG.isArray(t[0])?(r=t[0][0],i=t[0][1],s=t[1]):(r=t[0],i=t[1]):(r=t[0][0],i=t[0][1])),this.init(r,i,s),this},JXG.Turtle.prototype=new JXG.GeometryElement,JXG.extend(JXG.Turtle.prototype,{init:function(e,t,n){this.arrowLen=20/Math.sqrt(this.board.unitX*this.board.unitX+this.board.unitY*this.board.unitY),this.pos=[e,t],this.isPenDown=!0,this.dir=90,this.stack=[],this.objects=[],this.curve=this.board.create("curve",[[this.pos[0]],[this.pos[1]]],this._attributes),this.objects.push(this.curve),this.turtle=this.board.create("point",this.pos,{fixed:!0,name:" ",visible:!1,withLabel:!1}),this.objects.push(this.turtle),this.turtle2=this.board.create("point",[this.pos[0],this.pos[1]+this.arrowLen],{fixed:!0,name:" ",visible:!1,withLabel:!1}),this.objects.push(this.turtle2),this.visProp.arrow.lastArrow=!0,this.visProp.arrow.straightFirst=!1,this.visProp.arrow.straightLast=!1,this.arrow=this.board.create("line",[this.turtle,this.turtle2],this.visProp.arrow),this.objects.push(this.arrow),this.right(90-n),this.board.update()},forward:function(e){if(e===0)return this;var t=e*Math.cos(this.dir*Math.PI/180),n=e*Math.sin(this.dir*Math.PI/180);if(!this.turtleIsHidden){var r=this.board.create("transform",[t,n],{type:"translate"});r.applyOnce(this.turtle),r.applyOnce(this.turtle2)}return this.isPenDown&&this.curve.dataX.length>=8192&&(this.curve=this.board.create("curve",[[this.pos[0]],[this.pos[1]]],this._attributes),this.objects.push(this.curve)),this.pos[0]+=t,this.pos[1]+=n,this.isPenDown&&(this.curve.dataX.push(this.pos[0]),this.curve.dataY.push(this.pos[1])),this.board.update(),this},back:function(e){return this.forward(-e)},right:function(e){this.dir-=e,this.dir%=360;if(!this.turtleIsHidden){var t=this.board.create("transform",[-e*Math.PI/180,this.turtle],{type:"rotate"});t.applyOnce(this.turtle2)}return this.board.update(),this},left:function(e){return this.right(-e)},penUp:function(){return this.isPenDown=!1,this},penDown:function(){return this.isPenDown=!0,this.curve=this.board.create("curve",[[this.pos[0]],[this.pos[1]]],this._attributes),this.objects.push(this.curve),this},clean:function(){for(var e=0;e<this.objects.length;e++){var t=this.objects[e];t.type==JXG.OBJECT_TYPE_CURVE&&(this.board.removeObject(t),this.objects.splice(e,1))}return this.curve=this.board.create("curve",[[this.pos[0]],[this.pos[1]]],this._attributes),this.objects.push(this.curve),this.board.update(),this},clearScreen:function(){var e,t,n=this.objects.length;for(e=0;e<n;e++)t=this.objects[e],this.board.removeObject(t);return this.init(0,0,90),this},setPos:function(e,t){JXG.isArray(e)?this.pos=e:this.pos=[e,t];if(!this.turtleIsHidden){this.turtle.setPositionDirectly(JXG.COORDS_BY_USER,[e,t]),this.turtle2.setPositionDirectly(JXG.COORDS_BY_USER,[e,t+this.arrowLen]);var n=this.board.create("transform",[-(this.dir-90)*Math.PI/180,this.turtle],{type:"rotate"});n.applyOnce(this.turtle2)}return this.curve=this.board.create("curve",[[this.pos[0]],[this.pos[1]]],this._attributes),this.objects.push(this.curve),this.board.update(),this},setPenSize:function(e){return this.curve=this.board.create("curve",[[this.pos[0]],[this.pos[1]]],this.copyAttr("strokeWidth",e)),this.objects.push(this.curve),this},setPenColor:function(e){return this.curve=this.board.create("curve",[[this.pos[0]],[this.pos[1]]],this.copyAttr("strokeColor",e)),this.objects.push(this.curve),this},setHighlightPenColor:function(e){return this.curve=this.board.create("curve",[[this.pos[0]],[this.pos[1]]],this.copyAttr("highlightStrokeColor",e)),this.objects.push(this.curve),this},setProperty:function(e){var t,n,r=this.objects.length,i;for(t=0;t<r;t++)n=this.objects[t],n.type==JXG.OBJECT_TYPE_CURVE&&n.setProperty(e);return i=this.visProp.id,this.visProp=JXG.deepCopy(this.curve.visProp),this.visProp.id=i,this._attributes=JXG.deepCopy(this.visProp),delete this._attributes.id,this},copyAttr:function(e,t){return this._attributes[e.toLowerCase()]=t,this._attributes},showTurtle:function(){return this.turtleIsHidden=!1,this.arrow.setProperty({visible:!0}),this.visProp.arrow.visible=!1,this.setPos(this.pos[0],this.pos[1]),this.board.update(),this},hideTurtle:function(){return this.turtleIsHidden=!0,this.arrow.setProperty({visible:!1}),this.visProp.arrow.visible=!1,this.board.update(),this},home:function(){return this.pos=[0,0],this.setPos(this.pos[0],this.pos[1]),this},pushTurtle:function(){return this.stack.push([this.pos[0],this.pos[1],this.dir]),this},popTurtle:function(){var e=this.stack.pop();return this.pos[0]=e[0],this.pos[1]=e[1],this.dir=e[2],this.setPos(this.pos[0],this.pos[1]),this},lookTo:function(e){if(JXG.isArray(e)){var t=this.pos[0],n=this.pos[1],r=e[0],i=e[1],s;s=Math.atan2(i-n,r-t),this.right(this.dir-s*180/Math.PI)}else JXG.isNumber(e)&&this.right(this.dir-e);return this},moveTo:function(e){if(JXG.isArray(e)){var t=e[0]-this.pos[0],n=e[1]-this.pos[1];if(!this.turtleIsHidden){var r=this.board.create("transform",[t,n],{type:"translate"});r.applyOnce(this.turtle),r.applyOnce(this.turtle2)}this.isPenDown&&this.curve.dataX.length>=8192&&(this.curve=this.board.create("curve",[[this.pos[0]],[this.pos[1]]],this._attributes),this.objects.push(this.curve)),this.pos[0]=e[0],this.pos[1]=e[1],this.isPenDown&&(this.curve.dataX.push(this.pos[0]),this.curve.dataY.push(this.pos[1])),this.board.update()}return this},fd:function(e){return this.forward(e)},bk:function(e){return this.back(e)},lt:function(e){return this.left(e)},rt:function(e){return this.right(e)},pu:function(){return this.penUp()},pd:function(){return this.penDown()},ht:function(){return this.hideTurtle()},st:function(){return this.showTurtle()},cs:function(){return this.clearScreen()},push:function(){return this.pushTurtle()},pop:function(){return this.popTurtle()},evalAt:function(e,t){var n,r,i,s,o=this.objects.length;for(n=0,r=0;n<o;n++){i=this.objects[n];if(i.elementClass==JXG.OBJECT_CLASS_CURVE){if(r<=e&&e<r+i.numberPoints)return s=e-r,i[t](s);r+=i.numberPoints}}return this[t]()},X:function(e){return typeof e=="undefined"?this.pos[0]:this.evalAt(e,"X")},Y:function(e){return typeof e=="undefined"?this.pos[1]:this.evalAt(e,"Y")},Z:function(e){return 1},minX:function(){return 0},maxX:function(){var e=0,t,n=this.objects.length,r;for(t=0;t<n;t++)r=this.objects[t],r.elementClass==JXG.OBJECT_CLASS_CURVE&&(e+=this.objects[t].numberPoints);return e},hasPoint:function(e,t){var n,r;for(n=0;n<this.objects.length;n++){r=this.objects[n];if(r.type==JXG.OBJECT_TYPE_CURVE&&r.hasPoint(e,t))return!0}return!1}}),JXG.createTurtle=function(e,t,n){var r;return t=t||[],r=JXG.copyAttributes(n,e.options,"turtle"),new JXG.Turtle(e,t,r)},JXG.JSXGraph.registerElement("turtle",JXG.createTurtle),JXG.rgbParser=function(){var e,t=!1,n,r,i,s;if(arguments.length===0)return[];arguments.length>=3&&(arguments[0]=[arguments[0],arguments[1],arguments[2]],arguments.length=1),e=arguments[0];if(JXG.isArray(e)){for(n=0;n<3;n++)t|=/\./.test(arguments[0][n].toString());for(n=0;n<3;n++)t&=arguments[0][n]>=0&arguments[0][n]<=1;return t?[Math.ceil(arguments[0][0]*255),Math.ceil(arguments[0][1]*255),Math.ceil(arguments[0][2]*255)]:(arguments[0].length=3,arguments[0])}typeof arguments[0]=="string"&&(e=arguments[0]),e.charAt(0)=="#"&&(e=e.substr(1,6)),e=e.replace(/ /g,"").toLowerCase();var o={aliceblue:"f0f8ff",antiquewhite:"faebd7",aqua:"00ffff",aquamarine:"7fffd4",azure:"f0ffff",beige:"f5f5dc",bisque:"ffe4c4",black:"000000",blanchedalmond:"ffebcd",blue:"0000ff",blueviolet:"8a2be2",brown:"a52a2a",burlywood:"deb887",cadetblue:"5f9ea0",chartreuse:"7fff00",chocolate:"d2691e",coral:"ff7f50",cornflowerblue:"6495ed",cornsilk:"fff8dc",crimson:"dc143c",cyan:"00ffff",darkblue:"00008b",darkcyan:"008b8b",darkgoldenrod:"b8860b",darkgray:"a9a9a9",darkgreen:"006400",darkkhaki:"bdb76b",darkmagenta:"8b008b",darkolivegreen:"556b2f",darkorange:"ff8c00",darkorchid:"9932cc",darkred:"8b0000",darksalmon:"e9967a",darkseagreen:"8fbc8f",darkslateblue:"483d8b",darkslategray:"2f4f4f",darkturquoise:"00ced1",darkviolet:"9400d3",deeppink:"ff1493",deepskyblue:"00bfff",dimgray:"696969",dodgerblue:"1e90ff",feldspar:"d19275",firebrick:"b22222",floralwhite:"fffaf0",forestgreen:"228b22",fuchsia:"ff00ff",gainsboro:"dcdcdc",ghostwhite:"f8f8ff",gold:"ffd700",goldenrod:"daa520",gray:"808080",green:"008000",greenyellow:"adff2f",honeydew:"f0fff0",hotpink:"ff69b4",indianred:"cd5c5c",indigo:"4b0082",ivory:"fffff0",khaki:"f0e68c",lavender:"e6e6fa",lavenderblush:"fff0f5",lawngreen:"7cfc00",lemonchiffon:"fffacd",lightblue:"add8e6",lightcoral:"f08080",lightcyan:"e0ffff",lightgoldenrodyellow:"fafad2",lightgrey:"d3d3d3",lightgreen:"90ee90",lightpink:"ffb6c1",lightsalmon:"ffa07a",lightseagreen:"20b2aa",lightskyblue:"87cefa",lightslateblue:"8470ff",lightslategray:"778899",lightsteelblue:"b0c4de",lightyellow:"ffffe0",lime:"00ff00",limegreen:"32cd32",linen:"faf0e6",magenta:"ff00ff",maroon:"800000",mediumaquamarine:"66cdaa",mediumblue:"0000cd",mediumorchid:"ba55d3",mediumpurple:"9370d8",mediumseagreen:"3cb371",mediumslateblue:"7b68ee",mediumspringgreen:"00fa9a",mediumturquoise:"48d1cc",mediumvioletred:"c71585",midnightblue:"191970",mintcream:"f5fffa",mistyrose:"ffe4e1",moccasin:"ffe4b5",navajowhite:"ffdead",navy:"000080",oldlace:"fdf5e6",olive:"808000",olivedrab:"6b8e23",orange:"ffa500",orangered:"ff4500",orchid:"da70d6",palegoldenrod:"eee8aa",palegreen:"98fb98",paleturquoise:"afeeee",palevioletred:"d87093",papayawhip:"ffefd5",peachpuff:"ffdab9",peru:"cd853f",pink:"ffc0cb",plum:"dda0dd",powderblue:"b0e0e6",purple:"800080",red:"ff0000",rosybrown:"bc8f8f",royalblue:"4169e1",saddlebrown:"8b4513",salmon:"fa8072",sandybrown:"f4a460",seagreen:"2e8b57",seashell:"fff5ee",sienna:"a0522d",silver:"c0c0c0",skyblue:"87ceeb",slateblue:"6a5acd",slategray:"708090",snow:"fffafa",springgreen:"00ff7f",steelblue:"4682b4",tan:"d2b48c",teal:"008080",thistle:"d8bfd8",tomato:"ff6347",turquoise:"40e0d0",violet:"ee82ee",violetred:"d02090",wheat:"f5deb3",white:"ffffff",whitesmoke:"f5f5f5",yellow:"ffff00",yellowgreen:"9acd32"};e=o[e]||e;var u=[{re:/^\s*rgba$\s*(\d{1,3})\s*,\s*(\d{1,3})\s*,\s*(\d{1,3})\s*,\s*([\d\.]{1,3})\s*$\s*$/,example:["rgba(123, 234, 45, 0.5)","rgba(255,234,245,1.0)"],process:function(e){return[parseInt(e[1]),parseInt(e[2]),parseInt(e[3])]}},{re:/^\s*rgb$\s*(\d{1,3})\s*,\s*(\d{1,3})\s*,\s*(\d{1,3})\s*$\s*$/,example:["rgb(123, 234, 45)","rgb(255,234,245)"],process:function(e){return[parseInt(e[1]),parseInt(e[2]),parseInt(e[3])]}},{re:/^(\w{2})(\w{2})(\w{2})$/,example:["#00ff00","336699"],process:function(e){return[parseInt(e[1],16),parseInt(e[2],16),parseInt(e[3],16)]}},{re:/^(\w{1})(\w{1})(\w{1})$/,example:["#fb0","f0f"],process:function(e){return[parseInt(e[1]+e[1],16),parseInt(e[2]+e[2],16),parseInt(e[3]+e[3],16)]}}];for(n=0;n<u.length;n++){var a=u[n].re,f=u[n].process,l=a.exec(e),c;l&&(c=f(l),r=c[0],i=c[1],s=c[2])}return isNaN(r)||isNaN(i)||isNaN(s)?[]:(r=r<0||isNaN(r)?0:r>255?255:r,i=i<0||isNaN(i)?0:i>255?255:i,s=s<0||isNaN(s)?0:s>255?255:s,[r,i,s])},JXG.rgb2css=function(){var e,t,n;return e=JXG.rgbParser.apply(JXG.rgbParser,arguments),t=e[1],n=e[2],e=e[0],"rgb("+e+", "+t+", "+n+")"},JXG.rgb2hex=function(){var e,t,n;return e=JXG.rgbParser.apply(JXG.rgbParser,arguments),t=e[1],n=e[2],e=e[0],e=e.toString(16),t=t.toString(16),n=n.toString(16),e.length==1&&(e="0"+e),t.length==1&&(t="0"+t),n.length==1&&(n="0"+n),"#"+e+t+n},JXG.hex2rgb=function(e){var t,n,r;return e.charAt(0)=="#"&&(e=e.slice(1)),t=parseInt(e.substr(0,2),16),n=parseInt(e.substr(2,2),16),r=parseInt(e.substr(4,2),16),"rgb("+t+", "+n+", "+r+")"},JXG.hsv2rgb=function(e,t,n){var r,i,s,o,u,a,f,l,c;e=(e%360+360)%360;if(t==0){if(!(isNaN(e)||e<JXG.Math.eps))return"#ffffff";r=n,i=n,s=n}else{e>=360?a=0:a=e,a/=60,u=Math.floor(a),o=a-u,f=n*(1-t),l=n*(1-t*o),c=n*(1-t*(1-o));switch(u){case 0:r=n,i=c,s=f;break;case 1:r=l,i=n,s=f;break;case 2:r=f,i=n,s=c;break;case 3:r=f,i=l,s=n;break;case 4:r=c,i=f,s=n;break;case 5:r=n,i=f,s=l}}return r=Math.round(r*255).toString(16),r=r.length==2?r:r.length==1?"0"+r:"00",i=Math.round(i*255).toString(16),i=i.length==2?i:i.length==1?"0"+i:"00",s=Math.round(s*255).toString(16),s=s.length==2?s:s.length==1?"0"+s:"00",["#",r,i,s].join("")},JXG.rgb2hsv=function(){var e,t,n,r,i,s,o,u,a,f,l,c,h,p;return e=JXG.rgbParser.apply(JXG.rgbParser,arguments),t=e[1],n=e[2],e=e[0],p=JXG.Math.Statistics,r=e/255,i=t/255,s=n/255,c=p.max([e,t,n]),h=p.min([e,t,n]),o=c/255,u=h/255,l=o,f=0,l>0&&(f=(l-u)/(l*1)),a=1/(o-u),f>0&&(c==e?a=(i-s)*a:c==t?a=2+(s-r)*a:a=4+(r-i)*a),a*=60,a<0&&(a+=360),c==h&&(a=0),[a,f,l]},JXG.rgb2LMS=function(){var e,t,n,r,i,s,o,u=[[.05059983,.08585369,.0095242],[.01893033,.08925308,.01370054],[.00292202,.00975732,.07145979]];return e=JXG.rgbParser.apply(JXG.rgbParser,arguments),t=e[1],n=e[2],e=e[0],e=Math.pow(e,.476190476),t=Math.pow(t,.476190476),n=Math.pow(n,.476190476),r=e*u[0][0]+t*u[0][1]+n*u[0][2],i=e*u[1][0]+t*u[1][1]+n*u[1][2],s=e*u[2][0]+t*u[2][1]+n*u[2][2],o=[r,i,s],o.l=r,o.m=i,o.s=s,o},JXG.LMS2rgb=function(e,t,n){var r,i,s,o,u=[[30.830854,-29.832659,1.610474],[-6.481468,17.715578,-2.532642],[-0.37569,-1.199062,14.273846]];r=e*u[0][0]+t*u[0][1]+n*u[0][2],i=e*u[1][0]+t*u[1][1]+n*u[1][2],s=e*u[2][0]+t*u[2][1]+n*u[2][2];var a=function(e){var t=127,n=64;while(n>0){if(Math.pow(t,.476190476)>e)t-=n;else{if(Math.pow(t+1,.476190476)>e)return t;t+=n}n/=2}return t==254&&13.994955247<e?255:t};return r=a(r),i=a(i),s=a(s),o=[r,i,s],o.r=r,o.g=i,o.b=s,o},JXG.rgba2rgbo=function(e){var t;return e.length==9&&e.charAt(0)=="#"?(t=parseInt(e.substr(7,2).toUpperCase(),16)/255,e=e.substr(0,7)):t=1,[e,t]},JXG.rgbo2rgba=function(e,t){var n;return e=="none"?e:(n=Math.round(t*255).toString(16),n.length==1&&(n="0"+n),e+n)},JXG.rgb2bw=function(e){if(e=="none")return e;var t,n="0123456789ABCDEF",r,i;return i=JXG.rgbParser(e),t=.3*i[0]+.59*i[1]+.11*i[2],r=n.charAt(t>>4&15)+n.charAt(t&15),e="#"+r+""+r+""+r,e},JXG.rgb2cb=function(e,t){if(e=="none")return e;var n,r,i,s,o,u,a,f,l,c,h,p,d;o=JXG.rgb2LMS(e),r=o.l,i=o.m,s=o.s,t=t.toLowerCase();switch(t){case"protanopia":a=-0.06150039994295001,f=.08277001656812001,l=-0.013200141220000003,c=.05858939668799999,h=-0.07934519995360001,p=.013289415272000003,d=.6903216543277437,u=s/i,u<d?r=-(f*i+l*s)/a:r=-(h*i+p*s)/c;break;case"tritanopia":a=-0.00058973116217,f=.007690316482,l=-0.01011703519052,c=.025495080838999994,h=-0.0422740347,p=.017005316784,d=.8349489908460004,u=i/r,u<d?s=-(a*r+f*i)/l:s=-(c*r+h*i)/p;break;default:a=-0.06150039994295001,f=.08277001656812001,l=-0.013200141220000003,c=.05858939668799999,h=-0.07934519995360001,p=.013289415272000003,d=.5763833686400911,u=s/r,u<d?i=-(a*r+l*s)/f:i=-(c*r+p*s)/h}n=JXG.LMS2rgb(r,i,s);var v="0123456789ABCDEF";return u=v.charAt(n.r>>4&15)+v.charAt(n.r&15),e="#"+u,u=v.charAt(n.g>>4&15)+v.charAt(n.g&15),e+=u,u=v.charAt(n.b>>4&15)+v.charAt(n.b&15),e+=u,e},JXG.extend(JXG.Board.prototype,{intersection:function(e,t,n,r,i){var s;return e=JXG.getReference(this,e),t=JXG.getReference(this,t),i!=null&&(s=i.point),e.elementClass!=JXG.OBJECT_CLASS_CURVE||t.elementClass!=JXG.OBJECT_CLASS_CURVE||e.type==JXG.OBJECT_TYPE_ARC&&t.type==JXG.OBJECT_TYPE_ARC?e.type==JXG.OBJECT_TYPE_ARC&&t.elementClass==JXG.OBJECT_CLASS_LINE||t.type==JXG.OBJECT_TYPE_ARC&&e.elementClass==JXG.OBJECT_CLASS_LINE?function(){return JXG.Math.Geometry.meet(e.stdform,t.stdform,n,e.board)}:e.elementClass==JXG.OBJECT_CLASS_CURVE&&t.elementClass==JXG.OBJECT_CLASS_LINE||t.elementClass==JXG.OBJECT_CLASS_CURVE&&e.elementClass==JXG.OBJECT_CLASS_LINE?function(){return JXG.Math.Geometry.meetCurveLine(e,t,n,e.board,i)}:e.elementClass==JXG.OBJECT_CLASS_LINE&&t.elementClass==JXG.OBJECT_CLASS_LINE?function(){var r,i,o=e.visProp.straightfirst;return first2=t.visProp.straightfirst,last1=e.visProp.straightlast,last2=t.visProp.straightlast,JXG.exists(s)&&!s.visProp.alwaysintersect&&(o==0||last1==0||first2==0||last2==0)?(r=JXG.Math.Geometry.meetSegmentSegment(e.point1.coords.usrCoords,e.point2.coords.usrCoords,t.point1.coords.usrCoords,t.point2.coords.usrCoords,e.board),!o&&r[1]<0||!last1&&r[1]>1||!first2&&r[2]<0||!last2&&r[2]>1?i=[0,NaN,NaN]:i=r[0],new JXG.Coords(JXG.COORDS_BY_USER,i,e.board)):JXG.Math.Geometry.meet(e.stdform,t.stdform,n,e.board)}:function(){return JXG.Math.Geometry.meet(e.stdform,t.stdform,n,e.board)}:function(){return JXG.Math.Geometry.meetCurveCurve(e,t,n,r,e.board)}},intersectionFunc:function(e,t,n,r){return this.intersection(e,t,n,r)},otherIntersection:function(e,t,n){return e=JXG.getReference(this,e),t=JXG.getReference(this,t),function(){var r=JXG.Math.Geometry.meet(e.stdform,t.stdform,0,e.board);return Math.abs(n.X()-r.usrCoords[1])>JXG.Math.eps||Math.abs(n.Y()-r.usrCoords[2])>JXG.Math.eps||Math.abs(n.Z()-r.usrCoords[0])>JXG.Math.eps?r:JXG.Math.Geometry.meet(e.stdform,t.stdform,1,e.board)}}}),JXG.extend(JXG.Board.prototype,{angle:function(e,t,n){return JXG.Math.Geometry.angle(e,t,n)},rad:function(e,t,n){return JXG.Math.Geometry.rad(e,t,n)},distance:function(e,t){return JXG.Math.Geometry.distance(e,t)},pow:function(e,t){return JXG.Math.pow(e,t)},round:function(e,t){return e.toFixed(t)},cosh:function(e){return JXG.Math.cosh(e)},sinh:function(e){return JXG.Math.sinh(e)},sgn:function(e){return e==0?0:e/Math.abs(e)},D:function(e,t){return JXG.Math.Numerics.D(e,t)},I:function(e,t){return JXG.Math.Numerics.I(e,t)},root:function(e,t,n){return JXG.Math.Numerics.root(e,t,n)},lagrangePolynomial:function(e){return JXG.Math.Numerics.lagrangePolynomial(e)},neville:function(e){return JXG.Math.Numerics.Neville(e)},riemannsum:function(e,t,n,r,i){return JXG.Math.Numerics.riemannsum(e,t,n,r,i)},abs:Math.abs,acos:Math.acos,asin:Math.asin,atan:Math.atan,ceil:Math.ceil,cos:Math.cos,exp:Math.exp,floor:Math.floor,log:Math.log,max:Math.max,min:Math.min,random:Math.random,sin:Math.sin,sqrt:Math.sqrt,tan:Math.tan,trunc:Math.ceil,factorial:function(e){return JXG.Math.factorial(e)},binomial:function(e,t){return JXG.Math.binomial(e,t)},getElement:function(e){return JXG.getReference(this,e)},intersectionOptions:["point",[[JXG.OBJECT_CLASS_LINE,JXG.OBJECT_CLASS_LINE],[JXG.OBJECT_CLASS_LINE,JXG.OBJECT_CLASS_CIRCLE],[JXG.OBJECT_CLASS_CIRCLE,JXG.OBJECT_CLASS_CIRCLE]]],pointFunc:function(){return[null]},pointOptions:["point",[[JXG.OBJECT_CLASS_POINT]]],lineFunc:function(){return arguments},lineOptions:["line",[[JXG.OBJECT_CLASS_POINT,JXG.OBJECT_CLASS_POINT]]],linesegmentFunc:function(){return arguments},linesegmentOptions:["line",[[JXG.OBJECT_CLASS_POINT,JXG.OBJECT_CLASS_POINT]]],linesegmentAtts:{straightFirst:!1,straightLast:!1},arrowFunc:function(){return arguments},arrowOptions:["arrow",[[JXG.OBJECT_CLASS_POINT,JXG.OBJECT_CLASS_POINT]]],circleFunc:function(){return arguments},circleOptions:["circle",[[JXG.OBJECT_CLASS_POINT,JXG.OBJECT_CLASS_POINT],[JXG.OBJECT_CLASS_POINT,JXG.OBJECT_CLASS_LINE],[JXG.OBJECT_CLASS_POINT,JXG.OBJECT_CLASS_CIRCLE]]],arrowparallelOptions:["arrowparallel",[[JXG.OBJECT_CLASS_POINT,JXG.OBJECT_CLASS_LINE]]],arrowparallelFunc:function(){return arguments},bisectorOptions:["bisector",[[JXG.OBJECT_CLASS_POINT,JXG.OBJECT_CLASS_POINT,JXG.OBJECT_CLASS_POINT]]],bisectorFunc:function(){return arguments},circumcircleOptions:["circumcircle",[[JXG.OBJECT_CLASS_POINT,JXG.OBJECT_CLASS_POINT,JXG.OBJECT_CLASS_POINT]]],circumcircleFunc:function(){return arguments},circumcirclemidpointOptions:["circumcirclemidpoint",[[JXG.OBJECT_CLASS_POINT,JXG.OBJECT_CLASS_POINT,JXG.OBJECT_CLASS_POINT]]],circumcirclemidpointFunc:function(){return arguments},integralOptions:["integral",[[]]],integralFunc:function(){return arguments},midpointOptions:["midpoint",[[JXG.OBJECT_CLASS_POINT,JXG.OBJECT_CLASS_POINT],[JXG.OBJECT_CLASS_LINE]]],midpointFunc:function(){return arguments},mirrorpointOptions:["mirrorpoint",[[JXG.OBJECT_CLASS_POINT,JXG.OBJECT_CLASS_POINT]]],mirrorpointFunc:function(){return arguments},normalOptions:["normal",[[JXG.OBJECT_CLASS_POINT,JXG.OBJECT_CLASS_LINE]]],normalFunc:function(){return arguments},parallelOptions:["parallel",[[JXG.OBJECT_CLASS_POINT,JXG.OBJECT_CLASS_LINE]]],parallelFunc:function(){return arguments},parallelpointOptions:["parallelpoint",[[JXG.OBJECT_CLASS_POINT,JXG.OBJECT_CLASS_POINT,JXG.OBJECT_CLASS_POINT]]],parallelpointFunc:function(){return arguments},perpendicularOptions:["perpendicular",[[JXG.OBJECT_CLASS_POINT,JXG.OBJECT_CLASS_LINE]]],perpendicularFunc:function(){return arguments},perpendicularpointOptions:["perpendicularpoint",[[JXG.OBJECT_CLASS_POINT,JXG.OBJECT_CLASS_LINE]]],perpendicularpointFunc:function(){return arguments},reflectionOptions:["reflection",[[JXG.OBJECT_CLASS_POINT,JXG.OBJECT_CLASS_LINE]]],reflectionFunc:function(){return arguments}}),JXG.Point.prototype.setPositionX=function(e,t){var n=e==JXG.COORDS_BY_USER?this.coords.usrCoords[2]:this.coords.scrCoords[2];this.setPosition(e,[t,n])},JXG.Point.prototype.setPositionY=function(e,t){var n=e==JXG.COORDS_BY_USER?this.coords.usrCoords[1]:this.coords.scrCoords[1];this.setPosition(e,[n,t])},JXG.Ticks=function(e,t,n){this.constructor(e.board,n,JXG.OBJECT_TYPE_TICKS,JXG.OBJECT_CLASS_OTHER),this.line=e,this.board=this.line.board,this.ticksFunction=null,this.fixedTicks=null,this.equidistant=!1;if(JXG.isFunction(t))throw this.ticksFunction=t,new Error("Function arguments are no longer supported.");JXG.isArray(t)?this.fixedTicks=t:(Math.abs(t)<JXG.Math.eps&&(t=n.defaultdistance),this.ticksFunction=function(e){return t},this.equidistant=!0),this.minTicksDistance=n.minticksdistance,this.maxTicksDistance=n.maxticksdistance,this.labels=[],this.id=this.line.addTicks(this),this.board.setId(this,"Ti")},JXG.Ticks.prototype=new JXG.GeometryElement,JXG.extend(JXG.Ticks.prototype,{hasPoint:function(e,t){var n,r,i=this.ticks.length,s=this.board.options.precision.hasPoint;if(!this.line.visProp.scalable)return!1;if(this.line.stdform[1]!=0&&this.line.stdform[2]!=0&&this.line.type!=JXG.OBJECT_TYPE_AXIS)return!1;for(n=0;n<i;n++){r=this.ticks[n];if(!r[2])continue;if(this.line.stdform[1]==0&&Math.abs(r[0][0]-this.line.point1.coords.scrCoords[1])<JXG.Math.eps)continue;if(this.line.stdform[2]==0&&Math.abs(r[1][0]-this.line.point1.coords.scrCoords[2])<JXG.Math.eps)continue;if(Math.abs(r[0][0]-r[0][1])>=1||Math.abs(r[1][0]-r[1][1])>=1)if(this.line.stdform[1]==0){if(Math.abs(t-(r[1][0]+r[1][1])*.5)<2*s&&r[0][0]-s<e&&e<r[0][1]+s)return!0}else if(this.line.stdform[2]==0&&Math.abs(e-(r[0][0]+r[0][1])*.5)<2*s&&r[1][0]-s<t&&t<r[1][1]+s)return!0}return!1},setPositionDirectly:function(e,t,n){var r,i,s,o=new JXG.Coords(e,t,this.board),u=new JXG.Coords(e,n,this.board),a=this.board.getBoundingBox();return this.line.visProp.scalable?(Math.abs(this.line.stdform[1])<JXG.Math.eps&&Math.abs(o.usrCoords[1]*u.usrCoords[1])>JXG.Math.eps?(r=u.usrCoords[1]/o.usrCoords[1],a[0]*=r,a[2]*=r,this.board.setBoundingBox(a,!1)):Math.abs(this.line.stdform[2])<JXG.Math.eps&&Math.abs(o.usrCoords[2]*u.usrCoords[2])>JXG.Math.eps&&(i=u.usrCoords[2]/o.usrCoords[2],a[3]*=i,a[1]*=i,this.board.setBoundingBox(a,!1)),this):this},calculateTicksCoordinates:function(){var e=this.line.point1,t=this.line.point2,n=e.Dist(t),r=(t.coords.usrCoords[1]-e.coords.usrCoords[1])/n,i=(t.coords.usrCoords[2]-e.coords.usrCoords[2])/n,s=e.coords.distance(JXG.COORDS_BY_SCREEN,new JXG.Coords(JXG.COORDS_BY_USER,[e.coords.usrCoords[1]+r,e.coords.usrCoords[2]+i],this.board)),o=this.equidistant?this.ticksFunction(1):1,u,a,f=5,l,c,h,p,d,v,m,g,y=0,b=0,w,E=2,S=-1,x,T,N,C,k=JXG.Math.eps,L,A,O,M=this.visProp.majorheight*.5,_=this.visProp.minorheight*.5,D,P,H,B,j,F;if(this.board.canvasWidth===0||this.board.canvasHeight===0)return;this.visProp.minorheight<0?this.minStyle="infinite":this.minStyle="finite",this.visProp.majorheight<0?this.majStyle="infinite":this.majStyle="finite",this.line.visProp.straightfirst?A=Number.NEGATIVE_INFINITY:A=0+k,this.line.visProp.straightlast?O=Number.POSITIVE_INFINITY:O=n-k,D=this.line.stdform[1],P=this.line.stdform[2],H=D,B=P,j=D,F=P,T=Math.sqrt(D*D*this.board.unitX*this.board.unitX+P*P*this.board.unitY*this.board.unitY),D*=M/T*this.board.unitX,P*=M/T*this.board.unitY,H*=_/T*this.board.unitX,B*=_/T*this.board.unitY,this.removeTickLabels();if(Math.abs(j)<JXG.Math.eps&&Math.abs(F)<JXG.Math.eps)return;this.ticks=[],this.labels=[];if(!this.equidistant){for(p=0;p<this.fixedTicks.length;p++)y=e.coords.usrCoords[1]+this.fixedTicks[p]*r,b=e.coords.usrCoords[2]+this.fixedTicks[p]*i,l=new JXG.Coords(JXG.COORDS_BY_USER,[y,b],this.board),w=this._tickEndings(l,j,F,D,P,H,B,!0),w.length==2&&this.fixedTicks[p]>=A&&this.fixedTicks[p]<O&&this.ticks.push(w),this.labels.push(this._makeLabel(this.visProp.labels[p]||this.fixedTicks[p],l,this.board,this.visProp.drawlabels,this.id,p));return}u=o,o*=this.visProp.scale,this.visProp.insertticks&&this.minTicksDistance>JXG.Math.eps&&(a=this._adjustTickDistance(o,s,f,e.coords,r,i),o*=a,u*=a),this.visProp.insertticks||(o/=this.visProp.minorticks+1,u/=this.visProp.minorticks+1),this.ticksDelta=o,this.symbTicksDelta=u,N=this.board.getBoundingBox(),y=(N[0]+N[2])*.5,b=(N[1]+N[3])*.5,C=[y*this.line.stdform[2]-b*this.line.stdform[1],-this.line.stdform[2],this.line.stdform[1]],x=JXG.Math.crossProduct(this.line.stdform,C),x[1]/=x[0],x[2]/=x[0],x[0]=1,l=new JXG.Coords(JXG.COORDS_BY_USER,x.slice(1),this.board),T=e.coords.distance(JXG.COORDS_BY_USER,l);if((t.X()-e.X())*(x[1]-e.X())<0||(t.Y()-e.Y())*(x[2]-e.Y())<0)T*=-1;v=Math.round(T/o)*o,Math.abs(v)>JXG.Math.eps&&(S=Math.abs(v)/v),x[1]=e.coords.usrCoords[1]+r*v,x[2]=e.coords.usrCoords[2]+i*v,c=v,v=0,m=0,h=c/this.visProp.scale,y=x[1],b=x[2],p=0,d=0;do{l=new JXG.Coords(JXG.COORDS_BY_USER,[y,b],this.board),l.major=Math.round((S*v+c)/o)%(this.visProp.minorticks+1)===0,w=this._tickEndings(l,j,F,D,P,H,B,l.major);if(w.length===3){L=S*m+h,(Math.abs(L)>=k||this.visProp.drawzero)&&L>A&&L<O&&(this.ticks.push(w),l.major?this.labels.push(this._makeLabel(L,l,this.board,this.visProp.drawlabels,this.id,p)):this.labels.push(null),p++),E==2&&(S*=-1);if(d%2===0||E===1)v+=o,m+=u}else S*=-1,E--;d++,y=x[1]+S*r*v,b=x[2]+S*i*v}while(E>0);this.needsUpdate=!0,this.updateRenderer()},_adjustTickDistance:function(e,t,n,r,i,s){var o,u,a=1;while(t>4*this.minTicksDistance)a/=10,o=r.usrCoords[1]+i*e*a,u=r.usrCoords[2]+s*e*a,t=r.distance(JXG.COORDS_BY_SCREEN,new JXG.Coords(JXG.COORDS_BY_USER,[o,u],this.board));while(t<this.minTicksDistance)a*=n,n=n==5?2:5,o=r.usrCoords[1]+i*e*a,u=r.usrCoords[2]+s*e*a,t=r.distance(JXG.COORDS_BY_SCREEN,new JXG.Coords(JXG.COORDS_BY_USER,[o,u],this.board));return a},_tickEndings:function(e,t,n,r,i,s,o,u){var a,f,l=this.board.canvasWidth,c=this.board.canvasHeight,h=[-1e3*l,-1e3*c],p=[-1e3*l,-1e3*c],d,v,m,g,y=0,b=!1;return f=e.scrCoords,u?(d=r,v=i,g=this.majStyle):(d=s,v=o,g=this.minStyle),Math.abs(t)<JXG.Math.eps?(h[0]=f[1],h[1]=f[1],p[0]=0,p[1]=c):Math.abs(n)<JXG.Math.eps?(h[0]=0,h[1]=l,p[0]=f[2],p[1]=f[2]):(y=0,m=JXG.Math.crossProduct([0,0,1],[-v*f[1]-d*f[2],v,d]),m[1]/=m[0],m[1]>=0&&m[1]<=l&&(h[y]=m[1],p[y]=0,y++),m=JXG.Math.crossProduct([0,1,0],[-v*f[1]-d*f[2],v,d]),m[2]/=m[0],m[2]>=0&&m[2]<=c&&(h[y]=0,p[y]=m[2],y++),y<2&&(m=JXG.Math.crossProduct([c*c,0,-c],[-v*f[1]-d*f[2],v,d]),m[1]/=m[0],m[1]>=0&&m[1]<=l&&(h[y]=m[1],p[y]=c,y++)),y<2&&(m=JXG.Math.crossProduct([l*l,-l,0],[-v*f[1]-d*f[2],v,d]),m[2]/=m[0],m[2]>=0&&m[2]<=c&&(h[y]=l,p[y]=m[2]))),h[0]>=0&&h[0]<=l&&p[0]>=0&&p[0]<=c||h[1]>=0&&h[1]<=l&&p[1]>=0&&p[1]<=c?b=!0:b=!1,g=="finite"&&(h[0]=f[1]+d,p[0]=f[2]-v,h[1]=f[1]-d,p[1]=f[2]+v),b?[h,p,u]:[]},_makeLabel:function(e,t,n,r,i,s){var o,u,a,f=typeof e=="number";return r?(o=e.toString(),Math.abs(e)<JXG.Math.eps&&(o="0"),f&&(o.length>5||o.indexOf("e")!=-1)&&(o=e.toPrecision(3).toString()),f&&o.indexOf(".")>-1&&(o=o.replace(/0+$/,""),o=o.replace(/\.$/,"")),this.visProp.scalesymbol.length>0&&o==="1"?o=this.visProp.scalesymbol:this.visProp.scalesymbol.length>0&&o==="0"?o="0":o+=this.visProp.scalesymbol,a={id:i+s+"Label",isLabel:!0,layer:n.options.layer.line,highlightStrokeColor:n.options.text.strokeColor,highlightStrokeWidth:n.options.text.strokeWidth,highlightStrokeOpacity:n.options.text.strokeOpacity,visible:this.visProp.visible,priv:this.visProp.priv},a=JXG.deepCopy(a,this.visProp.label),u=JXG.createText(n,[t.usrCoords[1],t.usrCoords[2],o],a),u.isDraggable=!1,u.dump=!1,u.distanceX=this.visProp.label.offset[0],u.distanceY=this.visProp.label.offset[1],u.setCoords(t.usrCoords[1]+u.distanceX/n.unitX,t.usrCoords[2]+u.distanceY/n.unitY),u.visProp.visible=r,u):null},removeTickLabels:function(){var e;if(this.labels!=null&&(this.board.needsFullUpdate||this.needsRegularUpdate)&&(this.board.options.renderer!="canvas"||this.board.options.text.display!="internal"))for(e=0;e<this.labels.length;e++)this.labels[e]!=null&&this.board.removeObject(this.labels[e])},update:function(){return this.needsUpdate&&this.calculateTicksCoordinates(),this},updateRenderer:function(){return this.needsUpdate&&(this.ticks&&this.board.renderer.updateTicks(this,this.dxMaj,this.dyMaj,this.dxMin,this.dyMin,this.minStyle,this.majStyle),this.needsUpdate=!1),this},hideElement:function(){var e;this.visProp.visible=!1,this.board.renderer.hide(this);for(e=0;e<this.labels.length;e++)JXG.exists(this.labels[e])&&this.labels[e].hideElement();return this},showElement:function(){var e;this.visProp.visible=!0,this.board.renderer.show(this);for(e=0;e<this.labels.length;e++)JXG.exists(this.labels[e])&&this.labels[e].showElement();return this}}),JXG.createTicks=function(e,t,n){var r,i,s=JXG.copyAttributes(n,e.options,"ticks");t.length<2?i=n.ticksDistance:i=t[1];if(t[0].elementClass!=JXG.OBJECT_CLASS_LINE||!(JXG.isFunction(t[1])||JXG.isArray(t[1])||JXG.isNumber(t[1])))throw new Error("JSXGraph: Can't create Ticks with parent types '"+typeof t[0]+"' and '"+typeof t[1]+"'.");return r=new JXG.Ticks(t[0],i,s),r.isDraggable=!0,r},JXG.JSXGraph.registerElement("ticks",JXG.createTicks),JXG.Util={},JXG.Util.Unzip=function(e){function k(){return x+=8,w<b.length?b[w++]:-1}function L(){S=1}function A(){var e;return x++,e=S&1,S>>=1,S==0&&(S=k(),e=S&1,S=S>>1|128),e}function O(e){var t=0,n=e;while(n--)t=t<<1|A();return e&&(t=p[t]>>8-e),t}function M(){f=0}function _(e){h++,a[f++]=e,t.push(String.fromCharCode(e)),f==32768&&(f=0)}function D(){this.b0=0,this.b1=0,this.jump=null,this.jumppos=-1}function V(){for(;;){if(z[U]>=X)return-1;if(W[z[U]]==U)return z[U]++;z[U]++}}function $(){var e=F[j],t;r&&document.write(" len:"+U+" treepos:"+j);if(U==17)return-1;j++,U++,t=V(),r&&document.write(" IsPat "+t);if(t>=0)e.b0=t,r&&document.write(" b0 "+e.b0);else{e.b0=32768,r&&document.write(" b0 "+e.b0);if($())return-1}t=V();if(t>=0)e.b1=t,r&&document.write(" b1 "+e.b1),e.jump=null;else{e.b1=32768,r&&document.write(" b1 "+e.b1),e.jump=F[j],e.jumppos=j;if($())return-1}return U--,0}function J(e,t,n,i){var s;r&&document.write("currentTree "+e+" numval "+t+" lengths "+n+" show "+i),F=e,j=0,W=n,X=t;for(s=0;s<17;s++)z[s]=0;U=0;if($())return r&&alert("invalid huffman tree\n"),-1;if(r){document.write(" Tree: "+F.length);for(var o=0;o<32;o++)document.write("Places["+o+"].b0="+F[o].b0+" "),document.write("Places["+o+"].b1="+F[o].b1+" ")}return 0}function K(e){var t,n,i=0,s=e[i],o;for(;;){o=A(),r&&document.write("b="+o);if(o){if(!(s.b1&32768))return r&&document.write("ret1"),s.b1;s=s.jump,t=e.length;for(n=0;n<t;n++)if(e[n]===s){i=n;break}}else{if(!(s.b0&32768))return r&&document.write("ret2"),s.b0;i++,s=e[i]}}return r&&document.write("ret3"),-1}function Q(){var e,t,n,i,s;do{e=A(),n=O(2);switch(n){case 0:r&&alert("Stored\n");break;case 1:r&&alert("Fixed Huffman codes\n");break;case 2:r&&alert("Dynamic Huffman codes\n");break;case 3:r&&alert("Reserved block type!!\n");break;default:r&&alert("Unexpected value %d!\n",n)}if(n==0){var o,u;L(),o=k(),o|=k()<<8,u=k(),u|=k()<<8,(o^~u)&65535&&document.write("BlockLen checksum mismatch\n");while(o--)t=k(),_(t)}else if(n==1){var l;for(;;){l=p[O(7)]>>1,l>23?(l=l<<1|A(),l>199?(l-=128,l=l<<1|A()):(l-=48,l>143&&(l+=136))):l+=256;if(l<256)_(l);else{if(l==256)break;var s,c;l-=257,s=O(v[l])+d[l],l=p[O(5)]>>3,g[l]>8?(c=O(8),c|=O(g[l]-8)<<8):c=O(g[l]),c+=m[l];for(l=0;l<s;l++){var t=a[f-c&32767];_(t)}}}}else if(n==2){var l,h,b,w,E,S=new Array(320);b=257+O(5),w=1+O(5),E=4+O(4);for(l=0;l<19;l++)S[l]=0;for(l=0;l<E;l++)S[y[l]]=O(3);s=B.length;for(i=0;i<s;i++)B[i]=new D;if(J(B,19,S,0))return M(),1;if(r){document.write(" distanceTree");for(var T=0;T<B.length;T++)document.write(" "+B[T].b0+" "+B[T].b1+" "+B[T].jump+" "+B[T].jumppos)}h=b+w,i=0;var N=-1;r&&document.write(" n="+h+" bits: "+x+" ");while(i<h){N++,l=K(B),r&&document.write(" "+N+" i:"+i+" decode: "+l+" bits "+x+" ");if(l<16)S[i++]=l;else if(l==16){var C;l=3+O(2);if(i+l>h)return M(),1;C=i?S[i-1]:0;while(l--)S[i++]=C}else{l==17?l=3+O(3):l=11+O(7);if(i+l>h)return M(),1;while(l--)S[i++]=0}}s=H.length;for(i=0;i<s;i++)H[i]=new D;if(J(H,b,S,0))return M(),1;s=H.length;for(i=0;i<s;i++)B[i]=new D;var P=new Array;for(i=b;i<S.length;i++)P[i-b]=S[i];if(J(B,w,P,0))return M(),1;r&&document.write(" literalTree");for(;;){l=K(H);if(l>=256){var s,c;l-=256;if(l==0)break;l--,s=O(v[l])+d[l],l=K(B),g[l]>8?(c=O(8),c|=O(g[l]-8)<<8):c=O(g[l]),c+=m[l];while(s--){var t=a[f-c&32767];_(t)}}else _(l)}}}while(!e);return M(),L(),0}function G(){r&&alert("NEXTFILE"),t=[];var e=[];l=!1,e[0]=k(),e[1]=k(),r&&alert("type: "+e[0]+" "+e[1]),e[0]==parseInt("78",16)&&e[1]==parseInt("da",16)&&(r&&alert("GEONExT-GZIP"),Q(),r&&alert(t.join("")),o[s]=new Array(2),o[s][0]=t.join(""),o[s][1]="geonext.gxt",s++),e[0]==parseInt("1f",16)&&e[1]==parseInt("8b",16)&&(r&&alert("GZIP"),Y(),r&&alert(t.join("")),o[s]=new Array(2),o[s][0]=t.join(""),o[s][1]="file",s++);if(e[0]==parseInt("50",16)&&e[1]==parseInt("4b",16)){l=!0,e[2]=k(),e[3]=k();if(e[2]==parseInt("3",16)&&e[3]==parseInt("4",16)){e[0]=k(),e[1]=k(),r&&alert("ZIP-Version: "+e[1]+" "+e[0]/10+"."+e[0]%10),i=k(),i|=k()<<8,r&&alert("gpflags: "+i);var n=k();n|=k()<<8,r&&alert("method: "+n),k(),k(),k(),k();var u=k();u|=k()<<8,u|=k()<<16,u|=k()<<24;var a=k();a|=k()<<8,a|=k()<<16,a|=k()<<24;var f=k();f|=k()<<8,f|=k()<<16,f|=k()<<24,r&&alert("local CRC: "+u+"\nlocal Size: "+f+"\nlocal CompSize: "+a);var p=k();p|=k()<<8;var d=k();d|=k()<<8,r&&alert("filelen "+p),m=0,N=[];while(p--){var v=k();v=="/"|v==":"?m=0:m<T-1&&(N[m++]=String.fromCharCode(v))}r&&alert("nameBuf: "+N),C||(C=N);var m=0;while(m<d)v=k(),m++;c=4294967295,h=0,(f=0)&&r&&alert("skipdir"),n==8&&(Q(),r&&alert(t.join("")),o[s]=new Array(2),o[s][0]=t.join(""),o[s][1]=N.join(""),s++),Y()}}}function Y(){var e,t=[],n,s,o,u,a;i&8&&(t[0]=k(),t[1]=k(),t[2]=k(),t[3]=k(),t[0]==parseInt("50",16)&&t[1]==parseInt("4b",16)&&t[2]==parseInt("07",16)&&t[3]==parseInt("08",16)?(e=k(),e|=k()<<8,e|=k()<<16,e|=k()<<24):e=t[0]|t[1]<<8|t[2]<<16|t[3]<<24,n=k(),n|=k()<<8,n|=k()<<16,n|=k()<<24,s=k(),s|=k()<<8,s|=k()<<16,s|=k()<<24,r&&alert("CRC:")),l&&G(),t[0]=k();if(t[0]!=8)return r&&alert("Unknown compression method!"),0;i=k(),r&&i&~parseInt("1f",16)&&alert("Unknown flags set!"),k(),k(),k(),k(),k(),o=k();if(i&4){t[0]=k(),t[2]=k(),U=t[0]+256*t[1],r&&alert("Extra field size: "+U);for(u=0;u<U;u++)k()}if(i&8){u=0,N=[];while(a=k()){if(a=="7"||a==":")u=0;u<T-1&&(N[u++]=a)}r&&alert("original file name: "+N)}if(i&16)while(a=k());i&2&&(k(),k()),Q(),e=k(),e|=k()<<8,e|=k()<<16,e|=k()<<24,s=k(),s|=k()<<8,s|=k()<<16,s|=k()<<24,l&&G()}var t=[],n="",r=!1,i,s=0,o=[],u,a=new Array(32768),f=0,l=!1,c,h,p=[0,128,64,192,32,160,96,224,16,144,80,208,48,176,112,240,8,136,72,200,40,168,104,232,24,152,88,216,56,184,120,248,4,132,68,196,36,164,100,228,20,148,84,212,52,180,116,244,12,140,76,204,44,172,108,236,28,156,92,220,60,188,124,252,2,130,66,194,34,162,98,226,18,146,82,210,50,178,114,242,10,138,74,202,42,170,106,234,26,154,90,218,58,186,122,250,6,134,70,198,38,166,102,230,22,150,86,214,54,182,118,246,14,142,78,206,46,174,110,238,30,158,94,222,62,190,126,254,1,129,65,193,33,161,97,225,17,145,81,209,49,177,113,241,9,137,73,201,41,169,105,233,25,153,89,217,57,185,121,249,5,133,69,197,37,165,101,229,21,149,85,213,53,181,117,245,13,141,77,205,45,173,109,237,29,157,93,221,61,189,125,253,3,131,67,195,35,163,99,227,19,147,83,211,51,179,115,243,11,139,75,203,43,171,107,235,27,155,91,219,59,187,123,251,7,135,71,199,39,167,103,231,23,151,87,215,55,183,119,247,15,143,79,207,47,175,111,239,31,159,95,223,63,191,127,255],d=[3,4,5,6,7,8,9,10,11,13,15,17,19,23,27,31,35,43,51,59,67,83,99,115,131,163,195,227,258,0,0],v=[0,0,0,0,0,0,0,0,1,1,1,1,2,2,2,2,3,3,3,3,4,4,4,4,5,5,5,5,0,99,99],m=[1,2,3,4,5,7,9,13,17,25,33,49,65,97,129,193,257,385,513,769,1025,1537,2049,3073,4097,6145,8193,12289,16385,24577],g=[0,0,0,0,1,1,2,2,3,3,4,4,5,5,6,6,7,7,8,8,9,9,10,10,11,11,12,12,13,13],y=[16,17,18,0,8,7,9,6,10,5,11,4,12,3,13,2,14,1,15],b=e,w=0,E=0,S=1,x=0,T=256,N=[],C,P=288,H=new Array(P),B=new Array(32),j=0,F=null,I=null,q=new Array(64),R=new Array(64),U=0,z=new Array(17);z[0]=0;var W,X;JXG.Util.Unzip.prototype.unzipFile=function(e){var t;this.unzip();for(t=0;t<o.length;t++)if(o[t][1]==e)return o[t][0]},JXG.Util.Unzip.prototype.unzip=function(){return r&&alert(b),G(),o}},JXG.Util.Base64={_keyStr:"ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789+/=",encode:function(e){var t=[],n,r,i,s,o,u,a,f=0;e=JXG.Util.Base64._utf8_encode(e);while(f<e.length)n=e.charCodeAt(f++),r=e.charCodeAt(f++),i=e.charCodeAt(f++),s=n>>2,o=(n&3)<<4|r>>4,u=(r&15)<<2|i>>6,a=i&63,isNaN(r)?u=a=64:isNaN(i)&&(a=64),t.push([this._keyStr.charAt(s),this._keyStr.charAt(o),this._keyStr.charAt(u),this._keyStr.charAt(a)].join(""));return t.join("")},decode:function(e,t){var n=[],r,i,s,o,u,a,f,l=0;e=e.replace(/[^A-Za-z0-9\+\/\=]/g,"");while(l<e.length)o=this._keyStr.indexOf(e.charAt(l++)),u=this._keyStr.indexOf(e.charAt(l++)),a=this._keyStr.indexOf(e.charAt(l++)),f=this._keyStr.indexOf(e.charAt(l++)),r=o<<2|u>>4,i=(u&15)<<4|a>>2,s=(a&3)<<6|f,n.push(String.fromCharCode(r)),a!=64&&n.push(String.fromCharCode(i)),f!=64&&n.push(String.fromCharCode(s));return n=n.join(""),t&&(n=JXG.Util.Base64._utf8_decode(n)),n},_utf8_encode:function(e){e=e.replace(/\r\n/g,"\n");var t="";for(var n=0;n<e.length;n++){var r=e.charCodeAt(n);r<128?t+=String.fromCharCode(r):r>127&&r<2048?(t+=String.fromCharCode(r>>6|192),t+=String.fromCharCode(r&63|128)):(t+=String.fromCharCode(r>>12|224),t+=String.fromCharCode(r>>6&63|128),t+=String.fromCharCode(r&63|128))}return t},_utf8_decode:function(e){var t=[],n=0,r=0,i=0,s=0;while(n<e.length)r=e.charCodeAt(n),r<128?(t.push(String.fromCharCode(r)),n++):r>191&&r<224?(i=e.charCodeAt(n+1),t.push(String.fromCharCode((r&31)<<6|i&63)),n+=2):(i=e.charCodeAt(n+1),s=e.charCodeAt(n+2),t.push(String.fromCharCode((r&15)<<12|(i&63)<<6|s&63)),n+=3);return t.join("")},_destrip:function(e,t){var n=[],r,i,s=[];t==null&&(t=76),e.replace(/ /g,""),r=e.length/t;for(i=0;i<r;i++)n[i]=e.substr(i*t,t);r!=e.length/t&&(n[n.length]=e.substr(r*t,e.length-r*t));for(i=0;i<n.length;i++)s.push(n[i]);return s.join("\n")},decodeAsArray:function(e){var t=this.decode(e),n=[],r;for(r=0;r<t.length;r++)n[r]=t.charCodeAt(r);return n},decodeGEONExT:function(e){return decodeAsArray(destrip(e),!1)}},JXG.Util.asciiCharCodeAt=function(e,t){var n=e.charCodeAt(t);if(n>255)switch(n){case 8364:n=128;break;case 8218:n=130;break;case 402:n=131;break;case 8222:n=132;break;case 8230:n=133;break;case 8224:n=134;break;case 8225:n=135;break;case 710:n=136;break;case 8240:n=137;break;case 352:n=138;break;case 8249:n=139;break;case 338:n=140;break;case 381:n=142;break;case 8216:n=145;break;case 8217:n=146;break;case 8220:n=147;break;case 8221:n=148;break;case 8226:n=149;break;case 8211:n=150;break;case 8212:n=151;break;case 732:n=152;break;case 8482:n=153;break;case 353:n=154;break;case 8250:n=155;break;case 339:n=156;break;case 382:n=158;break;case 376:n=159;break;default:}return n},JXG.Util.utf8Decode=function(e){var t=[],n=0,r=0,i=0,s=0,o;if(!JXG.exists(e))return"";while(n<e.length)r=e.charCodeAt(n),r<128?(t.push(String.fromCharCode(r)),n++):r>191&&r<224?(s=e.charCodeAt(n+1),t.push(String.fromCharCode((r&31)<<6|s&63)),n+=2):(s=e.charCodeAt(n+1),o=e.charCodeAt(n+2),t.push(String.fromCharCode((r&15)<<12|(s&63)<<6|o&63)),n+=3);return t.join("")},JXG.Util.genUUID=function(){var e="0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz".split(""),t=new Array(36),n=0,r;for(var i=0;i<36;i++)i==8||i==13||i==18||i==23?t[i]="-":i==14?t[i]="4":(n<=2&&(n=33554432+Math.random()*16777216|0),r=n&15,n>>=4,t[i]=e[i==19?r&3|8:r]);return t.join("")},JXG.PsTricks={convert:function(e){var t=new JXG.Coords(JXG.COORDS_BY_SCREEN,[0,0],e),n=new JXG.Coords(JXG.COORDS_BY_SCREEN,[e.canvasWidth,e.canvasHeight],e),r,i,s=[];s.push("\\begin{pspicture*}("+t.usrCoords[1]+","+n.usrCoords[2]+")("+n.usrCoords[1]+","+t.usrCoords[2]+")\n");for(r in e.objects){i=e.objects[r];if(i.visProp.visible)switch(i.elementClass){case JXG.OBJECT_CLASS_CIRCLE:s.push(this.addCircle(i));break;case JXG.OBJECT_CLASS_LINE:s.push(this.addLine(i));break;case JXG.OBJECT_CLASS_POINT:s.push(this.addPoint(i));break;default:switch(i.type){case JXG.OBJECT_TYPE_ARC:s.push(this.addArc(i));break;case JXG.OBJECT_TYPE_SECTOR:s.push(this.addArc(i)),s.push(this.addSector(i));break;case JXG.OBJECT_TYPE_POLYGON:s.push(this.addPolygon(i));break;case JXG.OBJECT_TYPE_ANGLE:s.push(this.addAngle(i))}}}return s.push("\\end{pspicture*}"),s.join("\n")},setArrows:function(e){var t="";return e.visProp.firstarrow&&e.visProp.lastarrow?t="{<->}":e.visProp.firstarrow?t="{<-}":e.visProp.lastarrow&&(t="{->}"),t},drawWedge:function(e,t,n,r,i,s){var o="";return e!="none"&&t>0&&(o+="\\pswedge[linestyle=none, fillstyle=solid, fillcolor="+this.parseColor(e)+", opacity="+t.toFixed(5)+"]",o+="("+n.join(",")+"){"+r+"}{"+i+"}{"+s+"}\n"),o},addPoint:function(e){var t="\\psdot[linecolor="+this.parseColor(e.visProp.strokecolor)+",dotstyle=",n=e.normalizeFace(e.visProp.face)||"o",r=e.visProp.size>4?4:e.visProp.size,i=[0,0,"2pt 2","5pt 2","5pt 3"];return n=="x"?t+="x, dotsize="+i[r]:n=="o"?(t+="*, dotsize=",r==1?t+="2pt 2":r==2?t+="4pt 2":r==3?t+="6pt 2":r==4&&(t+="6pt 3")):n=="[]"?t+="square*, dotsize="+i[r]:n=="+"&&(t+="+, dotsize="+i[r]),t+="]("+e.coords.usrCoords.slice(1).join(",")+")\n",t+="\\rput("+(e.coords.usrCoords[1]+15/e.board.unitY)+","+(e.coords.usrCoords[2]+15/e.board.unitY)+"){\\small $"+e.name+"$}\n",t},addLine:function(e){var t=new JXG.Coords(JXG.COORDS_BY_USER,e.point1.coords.usrCoords,e.board),n=new JXG.Coords(JXG.COORDS_BY_USER,e.point2.coords.usrCoords,e.board),r="\\psline[linecolor="+this.parseColor(e.visProp.strokecolor)+", linewidth="+e.visProp.strokewidth+"px]";return(e.visProp.straightfirst||e.visProp.straightlast)&&JXG.Math.Geometry.calcStraight(e,t,n),r+=this.setArrows(e),r+="("+t.usrCoords.slice(1).join(",")+")("+n.usrCoords.slice(2).join(",")+")\n",r},addCircle:function(e){var t=e.Radius(),n="\\pscircle[linecolor="+this.parseColor(e.visProp.strokecolor)+", linewidth="+e.visProp.strokewidth+"px";return e.visProp.fillcolor!="none"&&e.visProp.fillopacity!=0&&(n+=", fillstyle=solid, fillcolor="+this.parseColor(e.visProp.fillcolor)+", opacity="+e.visProp.fillopacity.toFixed(5)),n+="]("+e.center.coords.usrCoords.slice(1).join("1")+"){"+t+"}\n",n},addPolygon:function(e){var t="\\pspolygon[linestyle=none, fillstyle=solid, fillcolor="+this.parseColor(e.visProp.fillcolor)+", opacity="+e.visProp.fillopacity.toFixed(5)+"]",n;for(n=0;n<e.vertices.length;n++)t+="("+e.vertices[n].coords.usrCoords.slice(1).join(",")+")";return t+="\n",t},addArc:function(e){var t=e.Radius(),n={coords:new JXG.Coords(JXG.COORDS_BY_USER,[e.board.canvasWidth/e.board.unitY,e.center.coords.usrCoords[2]],e.board)},r=JXG.Math.Geometry.trueAngle(n,e.center,e.point2).toFixed(4),i=JXG.Math.Geometry.trueAngle(n,e.center,e.point3).toFixed(4),s="\\psarc[linecolor="+this.parseColor(e.visProp.strokecolor)+", linewidth="+e.visProp.strokewidth+"px]";return s+=this.setArrows(e),s+="("+e.center.coords.usrCoords.slice(1).join(",")+"){"+t+"}{"+r+"}{"+i+"}\n",s},addSector:function(e){var t=e.Radius(),n={coords:new JXG.Coords(JXG.COORDS_BY_USER,[e.board.canvasWidth/e.board.unitY,e.point1.coords.usrCoords[2]],e.board)},r=JXG.Math.Geometry.trueAngle(n,e.point1,e.point2).toFixed(4),i=JXG.Math.Geometry.trueAngle(n,e.point1,e.point3).toFixed(4);return this.drawWedge(e.visProp.fillcolor,e.visProp.fillopacity,e.point1.coords.usrCoords.slice(1),t,r,i)},addAngle:function(e){var t=e.radius,n={coords:new JXG.Coords(JXG.COORDS_BY_USER,[e.board.canvasWidth/e.board.unitY,e.point2.coords.usrCoords[2]],e.board)},r=JXG.Math.Geometry.trueAngle(n,e.point2,e.point1).toFixed(4),i=JXG.Math.Geometry.trueAngle(n,e.point2,e.point3).toFixed(4),s;return s=this.drawWedge(e.visProp.fillcolor,e.visProp.fillopacity,e.point2.coords.usrCoords.slice(1),t,r,i),s+="\\psarc[linecolor="+this.parseColor(e.visProp.strokecolor)+", linewidth="+e.visProp.strokewidth+"px]",s+="("+e.point2.coords.usrCoords.slice(1).join(",")+"){"+t+"}{"+r+"}{"+i+"}\n",s},parseColor:function(e){var t=JXG.rgbParser(e);return"{[rgb]{"+t[0]/255+","+t[1]/255+","+t[2]/255+"}}"}},JXG.Server=function(){},JXG.Server.modules=function(){},JXG.Server.runningCalls={},JXG.Server.handleError=function(e){alert("error occured, server says: "+e.message)},JXG.Server.callServer=function(e,t,n,r){var i,s,o,u,a,f,l;r=r||!1,u="";for(l in n)u+="&"+escape(l)+"="+escape(n[l]);f=JXG.toJSON(n);do a=e+Math.floor(Math.random()*4096);while(typeof this.runningCalls[a]!="undefined");this.runningCalls[a]={action:e},typeof n.module!="undefined"&&(this.runningCalls[a].module=n.module),i=JXG.serverBase+"JXGServer.py",s="action="+escape(e)+"&id="+a+"&dataJSON="+escape(JXG.Util.Base64.encode(f)),this.cbp=function(e){var n,r,i,s,o,u,a,f;n=(new JXG.Util.Unzip(JXG.Util.Base64.decodeAsArray(e))).unzip(),JXG.isArray(n)&&n.length>0&&(n=n[0][0]);if(typeof n!="string")return;r=window.JSON&&window.JSON.parse?window.JSON.parse(n):(new Function("return "+n))();if(r.type=="error")this.handleError(r);else if(r.type=="response"){u=r.id;for(a=0;a<r.fields.length;a++)i=r.fields[a],s=i.namespace+(typeof (new Function("return "+i.namespace))()=="object"?".":".prototype.")+i.name+" = "+i.value,(new Function(s))();for(a=0;a<r.handler.length;a++){i=r.handler[a],o=[];for(f=0;f<i.parameters.length;f++)o[f]='"'+i.parameters[f]+'": '+i.parameters[f];s="if(typeof JXG.Server.modules."+this.runningCalls[u].module+' == "undefined")'+"JXG.Server.modules."+this.runningCalls[u].module+" = {};",s+="JXG.Server.modules."+this.runningCalls[u].module+"."+i.name+"_cb = "+i.callback+";",s+="JXG.Server.modules."+this.runningCalls[u].module+"."+i.name+" = function ("+i.parameters.join(",")+", __JXGSERVER_CB__, __JXGSERVER_SYNC) {"+'if(typeof __JXGSERVER_CB__ == "undefined") __JXGSERVER_CB__ = JXG.Server.modules.'+this.runningCalls[u].module+"."+i.name+"_cb;"+"var __JXGSERVER_PAR__ = {"+o.join(",")+', "module": "'+this.runningCalls[u].module+'", "handler": "'+i.name+'" };'+'JXG.Server.callServer("exec", __JXGSERVER_CB__, __JXGSERVER_PAR__, __JXGSERVER_SYNC);'+"};",(new Function(s))()}delete this.runningCalls[u],t(r.data)}},this.cb=JXG.bind(this.cbp,this),window.XMLHttpRequest?(o=new XMLHttpRequest,o.overrideMimeType("text/plain; charset=iso-8859-1")):o=new ActiveXObject("Microsoft.XMLHTTP");if(!o)return!1;o.open("POST",i,!r),o.setRequestHeader("Content-type","application/x-www-form-urlencoded"),r||(o.onreadystatechange=function(e){return function(){switch(o.readyState){case 4:o.status==200&&e(o.responseText);break;default:return!1}}}(this.cb)),o.send(s),r&&this.cb(o.responseText)},JXG.Server.loadModule_cb=function(e){var t;for(t=0;t<e.length;t++)alert(e[t].name+": "+e[t].value)},JXG.Server.loadModule=function(e){return JXG.Server.callServer("load",JXG.Server.loadModule_cb,{module:e},!0)},JXG.Server.load=JXG.Server.loadModule,JXG.DataSource=function(){return this.data=[],this.columnHeaders=[],this.rowHeaders=[],this},JXG.extend(JXG.DataSource.prototype,{loadFromArray:function(e,t,n){var r,i,s;typeof t=="undefined"&&(t=!1),typeof n=="undefined"&&(n=!1),JXG.isArray(t)&&(this.columnHeaders=t,t=!1),JXG.isArray(n)&&(this.rowHeaders=n,n=!1),this.data=[],t&&(this.columnHeaders=[]),n&&(this.rowHeaders=[]);if(typeof e!="undefined"){this.data=new Array(e.length);for(r=0;r<e.length;r++){this.data[r]=new Array(e[r].length);for(i=0;i<e[r].length;i++)s=e[r][i],""+parseFloat(s)==s?this.data[r][i]=parseFloat(s):s!="-"?this.data[r][i]=s:this.data[r][i]=NaN}t&&(this.columnHeaders=this.data[0].slice(1),this.data=this.data.slice(1));if(n){this.rowHeaders=new Array;for(r=0;r<this.data.length;r++)this.rowHeaders.push(this.data[r][0]),this.data[r]=this.data[r].slice(1)}}return this},loadFromTable:function(e,t,n){var r,i,s,o,u,a;typeof t=="undefined"&&(t=!1),typeof n=="undefined"&&(n=!1),JXG.isArray(t)&&(this.columnHeaders=t,t=!1),JXG.isArray(n)&&(this.rowHeaders=n,n=!1),this.data=[],t&&(this.columnHeaders=[]),n&&(this.rowHeaders=[]),e=document.getElementById(e);if(typeof e!="undefined"){r=e.getElementsByTagName("tr"),this.data=new Array(r.length);for(i=0;i<r.length;i++){o=r[i].getElementsByTagName("td"),this.data[i]=new Array(o.length);for(s=0;s<o.length;s++)u=o[s].innerHTML,""+parseFloat(u)==u?this.data[i][s]=parseFloat(u):u!="-"?this.data[i][s]=u:this.data[i][s]=NaN}t&&(this.columnHeaders=this.data[0].slice(1),this.data=this.data.slice(1));if(n){this.rowHeaders=new Array;for(i=0;i<this.data.length;i++)this.rowHeaders.push(this.data[i][0]),this.data[i]=this.data[i].slice(1)}}return this},addColumn:function(e,t,n){},addRow:function(e,t,n){},getColumn:function(e){var t=new Array(this.data.length),n;if(typeof e=="string")for(n=0;n<this.columnHeaders.length;n++)if(e==this.columnHeaders[n]){e=n;break}for(n=0;n<this.data.length;n++)this.data[n].length>e&&(t[n]=parseFloat(this.data[n][e]));return t},getRow:function(e){var t,n;if(typeof e=="string")for(n=0;n<this.rowHeaders.length;n++)if(e==this.rowHeaders[n]){e=n;break}t=new Array(this.data[e].length);for(n=0;n<this.data[e].length;n++)t[n]=this.data[e][n];return t}}),JXG.JessieCode=function(e,t){var n;this.sstack=[{}],this.scope=0,this.pstack=[[]],this.dpstack=[[]],this.pscope=0,this.propstack=[{}],this.propscope=0,this.propobj=0,this.lhs=[],this.isLHS=!1,this.warnLog="jcwarn",this.builtIn=this.defineBuiltIn(),this.board=null,this.lineToElement={},this.countLines=!0,this.parCurLine=1,this.parCurColumn=0,this.line=1,this.col=1,this.code="",typeof e=="string"&&this.parse(e)},JXG.extend(JXG.JessieCode.prototype,{node:function(e,t,n){return{type:e,value:t,children:n}},createNode:function(e,t,n){var r=this.node(e,t,[]),i;for(i=2;i<arguments.length;i++)r.children.push(arguments[i]);return r.line=this.parCurLine,r.col=this.parCurColumn,r},getElementById:function(e){return this.board.objects[e]},creator:function(){var e={},t;return t=function(t){var n;return typeof e[this.board.id+t]=="function"?e[this.board.id+t]:(n=function(e){return function(n,r){var i;return JXG.exists(r)?i=r:i={name:e.lhs[e.scope]!==0?e.lhs[e.scope]:""},e.board.create(t,n,i)}}(this),n.creator=!0,e[this.board.id+t]=n,n)},t.clearCache=function(){e={}},t}(),letvar:function(e,t){this.builtIn[e]&&this._warn('"'+e+'" is a predefined value.'),this.sstack[this.scope][e]=t},isLocalVariable:function(e){var t;for(t=this.scope;t>-1;t--)if(JXG.exists(this.sstack[t][e]))return t;return-1},isCreator:function(e){return!!JXG.JSXGraph.elements[e]},isMathMethod:function(e){return e!=="E"&&!!Math[e]},isBuiltIn:function(e){return!!this.builtIn[e]},getvar:function(e,t){var n,r;t=JXG.def(t,!1),n=this.isLocalVariable(e);if(n>-1)return this.sstack[n][e];if(this.isCreator(e))return this.creator(e);if(this.isMathMethod(e))return Math[e];if(this.isBuiltIn(e))return this.builtIn[e];if(!t){n=JXG.getRef(this.board,e);if(n!==e)return n}return r},getvarJS:function(e,t,n){var r;t=JXG.def(t,!1),n=JXG.def(n,!1);if(JXG.indexOf(this.pstack[this.pscope],e)>-1)return e;r=this.isLocalVariable(e);if(r>-1&&!n)return"$jc$.sstack["+r+"]['"+e+"']";if(this.isCreator(e))return"(function () { var a = Array.prototype.slice.call(arguments, 0), props = "+(n?"a.pop()":"{}")+"; return $jc$.board.create.apply($jc$.board, ['"+e+"'].concat([a, props])); })";n&&this._error("Syntax error (attribute values are allowed with element creators only)");if(this.isMathMethod(e))return"Math."+e;if(this.isBuiltIn(e))return this.builtIn[e].src||this.builtIn[e];if(!t){if(JXG.isId(this.board,e))return"$jc$.board.objects['"+e+"']";if(JXG.isName(this.board,e))return"$jc$.board.elementsByName['"+e+"']";if(JXG.isGroup(this.board,e))return"$jc$.board.groups['"+e+"']"}return""},mergeAttributes:function(){var e,t={};for(e=0;e<arguments.length;e++)t=JXG.deepCopy(t,arguments[e],!0);return t},setProp:function(e,t,n){var r={},i,s;e.elementClass!==JXG.OBJECT_CLASS_POINT||t!=="X"&&t!=="Y"?e.type!==JXG.OBJECT_TYPE_TEXT||t!=="X"&&t!=="Y"?e.type&&e.elementClass&&e.visProp?(r[t]=n,e.setProperty(r)):e[t]=n:(typeof n=="number"?e[t]=function(){return n}:typeof n=="function"?(e.isDraggable=!1,e[t]=n):typeof n=="string"&&(e.isDraggable=!1,e[t]=JXG.createFunction(n,this.board,null,!0),e[t+"jc"]=n),e[t].origin=n,this.board.update()):(t=t.toLowerCase(),e.isDraggable&&typeof n=="number"?(i=t==="x"?n:e.X(),s=t==="y"?n:e.Y(),e.setPosition(JXG.COORDS_BY_USER,[i,s])):!e.isDraggable||typeof n!="function"&&typeof n!="string"?e.isDraggable||(i=t==="x"?n:e.XEval.origin,s=t==="y"?n:e.YEval.origin,e.addConstraint([i,s])):(i=t==="x"?n:e.coords.usrCoords[1],s=t==="y"?n:e.coords.usrCoords[2],e.addConstraint([i,s])),this.board.update())},utf8_encode:function(e){var t=[],n,r;for(n=0;n<e.length;n++)r=e.charCodeAt(n),r<128?t.push(String.fromCharCode(r)):t.push("&#x"+r.toString(16)+";");return t.join("")},parse:function(e,t,n){var r=0,i=[],s=[],o=this,u,a=["Abs","ACos","ASin","ATan","Ceil","Cos","Exp","Factorial","Floor","Log","Max","Min","Random","Round","Sin","Sqrt","Tan","Trunc","If","Deg","Rad","Dist"],f,l=JXG.Text.prototype.setText,c=e.replace(/\r\n/g,"\n").split("\n"),h,p,d=[];n||(this.code+=e+"\n"),JXG.Text.prototype.setText=JXG.Text.prototype.setTextJessieCode;try{JXG.exists(t)||(t=!1);for(h=0;h<c.length;h++)if(JXG.trim(c[h])[0]!=="/"||JXG.trim(c[h])[1]!=="/"){if(t)for(p=0;p<a.length;p++)f=new RegExp(a[p]+"\\(","g"),c[h]=c[h].replace(f,a[p].toLowerCase()+"(");d.push(c[h])}else d.push("");e=d.join("\n"),e=this.utf8_encode(e);if((r=this._parse(e,i,s))>0)for(h=0;h<r;h++)this.line=i[h].line,this._error("Parse error in line "+i[h].line+" near >"+e.substr(i[h].offset,30)+'<, expecting "'+s[h].join()+'"')}catch(v){throw JXG.Text.prototype.setText=l,v}JXG.Text.prototype.setText=l},snippet:function(e,t,n,r){var i,s,o,u;return i="jxg__tmp__intern_"+JXG.Util.genUUID().replace(/\-/g,""),JXG.exists(t)||(t=!0),JXG.exists(n)||(n=""),JXG.exists(r)||(r=!1),o=this.sstack[0][i],this.countLines=!1,s=i+" = "+(t?" function ("+n+") { return ":"")+e+(t?"; }":"")+";",this.parse(s,r,!0),u=this.sstack[0][i],JXG.exists(o)?this.sstack[0][i]=o:delete this.sstack[0][i],this.countLines=!0,u},replaceIDs:function(e){var t,n;e.replaced&&(n=this.board.objects[e.children[1].children[0].value],JXG.exists(n)&&JXG.exists(n)&&n.name!==""&&(e.type="node_var",e.value=n.name,e.children.length=0,delete e.replaced));if(e.children)for(t=e.children.length;t>0;t--)JXG.exists(e.children[t-1])&&(e.children[t-1]=this.replaceIDs(e.children[t-1]));return e},replaceNames:function(e){var t,n;n=e.value,e.type=="node_op"&&n=="op_lhs"&&e.children.length===1?this.isLHS=!0:e.type=="node_var"&&(this.isLHS?this.letvar(n,!0):!JXG.exists(this.getvar(n,!0))&&JXG.exists(this.board.elementsByName[n])&&(e=this.createReplacementNode(e)));if(e.children)for(t=e.children.length;t>0;t--)JXG.exists(e.children[t-1])&&(e.children[t-1]=this.replaceNames(e.children[t-1]));return e.type=="node_op"&&e.value=="op_lhs"&&e.children.length===1&&(this.isLHS=!1),e},createReplacementNode:function(e){var t=e.value,n=this.board.elementsByName[t];return e=this.createNode("node_op","op_execfun",this.createNode("node_var","$"),this.createNode("node_op","op_param",this.createNode("node_str",n.id))),e.replaced=!0,e},collectDependencies:function(e,t){var n,r,i;r=e.value,e.type=="node_var"&&(i=this.getvar(r),i&&i.visProp&&i.type&&i.elementClass&&i.id&&(t[i.id]=i)),e.type=="node_op"&&e.value=="op_execfun"&&e.children.length>1&&e.children[0].value=="$"&&e.children[1].children.length>0&&(i=e.children[1].children[0].value,t[i]=this.board.objects[i]);if(e.children)for(n=e.children.length;n>0;n--)JXG.exists(e.children[n-1])&&this.collectDependencies(e.children[n-1],t)},resolveProperty:function(e,t,n){return n=JXG.def(n,!1),e&&e.methodMap&&(t==="label"?(e=e.label,t="content"):JXG.exists(e.subs)&&JXG.exists(e.subs[t])?e=e.subs:JXG.exists(e.methodMap[t])?t=e.methodMap[t]:(e=e.visProp,t=t.toLowerCase())),JXG.exists(e)||this._error(e+" is not an object"),JXG.exists(e[t])||this._error("unknown property "+t),n&&typeof e[t]=="function"?function(){return e[t].apply(e,arguments)}:e[t]},execute:function(node){var ret,v,i,e,parents=[];ret=0;if(!node)return ret;this.line=node.line,this.col=node.col;switch(node.type){case"node_op":switch(node.value){case"op_none":node.children[0]&&this.execute(node.children[0]),node.children[1]&&(ret=this.execute(node.children[1]));break;case"op_assign":v=this.execute(node.children[0]),this.lhs[this.scope]=v[1],v[0].type&&v[0].elementClass&&v[0].methodMap&&v[1]==="label"&&this._error("Left-hand side of assignment is read-only."),v[0]!==this.sstack[this.scope]||JXG.isArray(v[0])&&typeof v[1]=="number"?this.setProp(v[0],v[1],this.execute(node.children[1])):this.letvar(v[1],this.execute(node.children[1])),this.lhs[this.scope]=0;break;case"op_noassign":ret=this.execute(node.children[0]);break;case"op_if":this.execute(node.children[0])&&(ret=this.execute(node.children[1]));break;case"op_if_else":this.execute(node.children[0])?ret=this.execute(node.children[1]):ret=this.execute(node.children[2]);break;case"op_while":while(this.execute(node.children[0]))this.execute(node.children[1]);break;case"op_do":do this.execute(node.children[0]);while(this.execute(node.children[1]));break;case"op_for":for(this.execute(node.children[0]);this.execute(node.children[1]);this.execute(node.children[2]))this.execute(node.children[3]);break;case"op_param":node.children[1]&&this.execute(node.children[1]),ret=node.children[0],this.pstack[this.pscope].push(ret),this.dpstack[this.pscope]&&this.dpstack[this.pscope].push({line:node.children[0].line,col:node.children[0].col});break;case"op_paramdef":node.children[1]&&this.execute(node.children[1]),ret=node.children[0],this.pstack[this.pscope].push(ret);break;case"op_proplst":node.children[0]&&this.execute(node.children[0]),node.children[1]&&this.execute(node.children[1]);break;case"op_proplst_val":this.propstack.push({}),this.propscope++,this.execute(node.children[0]),ret=this.propstack[this.propscope],this.propstack.pop(),this.propscope--;break;case"op_prop":this.propstack[this.propscope][node.children[0]]=this.execute(node.children[1]);break;case"op_array":var l;this.pstack.push([]),this.pscope++,this.execute(node.children[0]),ret=[],l=this.pstack[this.pscope].length;for(i=0;i<l;i++)ret.push(this.execute(this.pstack[this.pscope][i]));this.pstack.pop(),this.pscope--;break;case"op_extvalue":var undef;ret=this.execute(node.children[0]),i=this.execute(node.children[1]),typeof i=="number"&&Math.abs(Math.round(i)-i)<JXG.Math.eps?ret=ret[i]:ret=undef;break;case"op_return":if(this.scope!==0)return this.execute(node.children[0]);this._error("Unexpected return.");break;case"op_function":this.pstack.push([]),this.pscope++,this.execute(node.children[0]);if(this.board.options.jc.compile){this.sstack.push({}),this.scope++,this.isLHS=!1;for(i=0;i<this.pstack[this.pscope].length;i++)this.sstack[this.scope][this.pstack[this.pscope][i]]=this.pstack[this.pscope][i];this.replaceNames(node.children[1]),ret=function($jc$){var p=$jc$.pstack[$jc$.pscope].join(", "),str="var f = function ("+p+") {\n$jc$.sstack.push([]);\n$jc$.scope++;\nvar r = (function () {\n"+$jc$.compile(node.children[1],!0)+"})();\n$jc$.sstack.pop();\n$jc$.scope--;\nreturn r;\n}; f;";try{return eval(str)}catch(e){throw e}}(this),this.sstack.pop(),this.scope--}else ret=function(e,t){return function(){var n;t.sstack.push({}),t.scope++;for(n=0;n<e.length;n++)t.sstack[t.scope][e[n]]=arguments[n];return n=t.execute(node.children[1]),t.sstack.pop(),t.scope--,n}}(this.pstack[this.pscope],this);ret.node=node,ret.toJS=ret.toString,ret.toString=function(e){return function(){return e.compile(e.replaceIDs(JXG.deepCopy(node)))}}(this),ret.deps={},this.collectDependencies(node.children[1],ret.deps),this.pstack.pop(),this.pscope--;break;case"op_execfun":var fun,attr,sc;this.pstack.push([]),this.dpstack.push([]),this.pscope++,this.execute(node.children[1]);if(typeof node.children[2]!="undefined")if(node.children[3]){this.pstack.push([]),this.dpstack.push([]),this.pscope++,this.execute(node.children[2]),attr={};for(i=0;i<this.pstack[this.pscope].length;i++)attr=JXG.deepCopy(attr,this.execute(this.pstack[this.pscope][i]),!0);this.pscope--,this.pstack.pop(),this.dpstack.pop()}else attr=this.execute(node.children[2]);fun=this.execute(node.children[0]),fun&&fun.sc?sc=fun.sc:sc=this,!fun.creator&&typeof node.children[2]!="undefined"&&this._error("Unexpected value. Only element creators are allowed to have a value after the function call.");for(i=0;i<this.pstack[this.pscope].length;i++)parents[i]=this.execute(this.pstack[this.pscope][i]);if(typeof fun=="function"&&!fun.creator)ret=fun.apply(sc,parents);else if(typeof fun!="function"||!fun.creator)this._error("Function '"+fun+"' is undefined.");else{e=this.line;try{ret=fun(parents,attr),ret.jcLineStart=e,ret.jcLineEnd=node.line;for(i=e;i<=node.line;i++)this.lineToElement[i]=ret;ret.debugParents=this.dpstack[this.pscope]}catch(ex){this._error(ex.toString(),e)}}this.pstack.pop(),this.dpstack.pop(),this.pscope--;break;case"op_property":e=this.execute(node.children[0]),v=node.children[1],ret=this.resolveProperty(e,v,!1),JXG.exists(ret)&&(ret.sc=e);break;case"op_lhs":v=node.children[0],v.children&&v.type&&v.value&&(v=this.execute(v)),node.children.length===1?e=this.sstack[this.scope]:(e=this.execute(node.children[1]),e.type&&e.elementClass&&v.toLowerCase&&v.toLowerCase()!=="x"&&v.toLowerCase()!=="y"&&(v=v.toLowerCase())),ret=[e,v];break;case"op_use":var found=!1;for(var b in JXG.JSXGraph.boards)JXG.JSXGraph.boards[b].container===node.children[0].toString()&&(this.use(JXG.JSXGraph.boards[b]),found=!0);found||this._error("Board '"+node.children[0].toString()+"' not found!");break;case"op_delete":v=this.getvar(node.children[0]),typeof v=="object"&&JXG.exists(v.type)&&JXG.exists(v.elementClass)&&this.board.removeObject(v);break;case"op_equ":ret=this.execute(node.children[0])==this.execute(node.children[1]);break;case"op_neq":ret=this.execute(node.children[0])!=this.execute(node.children[1]);break;case"op_approx":ret=Math.abs(this.execute(node.children[0])-this.execute(node.children[1]))<JXG.Math.eps;break;case"op_grt":ret=this.execute(node.children[0])>this.execute(node.children[1]);break;case"op_lot":ret=this.execute(node.children[0])<this.execute(node.children[1]);break;case"op_gre":ret=this.execute(node.children[0])>=this.execute(node.children[1]);break;case"op_loe":ret=this.execute(node.children[0])<=this.execute(node.children[1]);break;case"op_or":ret=this.execute(node.children[0])||this.execute(node.children[1]);break;case"op_and":ret=this.execute(node.children[0])&&this.execute(node.children[1]);break;case"op_not":ret=!this.execute(node.children[0]);break;case"op_add":ret=JXG.Math.Statistics.add(this.execute(node.children[0]),this.execute(node.children[1]));break;case"op_sub":ret=JXG.Math.Statistics.subtract(this.execute(node.children[0]),this.execute(node.children[1]));break;case"op_div":ret=JXG.Math.Statistics.div(this.execute(node.children[0]),this.execute(node.children[1]));break;case"op_mod":ret=JXG.Math.Statistics.mod(this.execute(node.children[0]),this.execute(node.children[1]),!0);break;case"op_mul":ret=this.mul(this.execute(node.children[0]),this.execute(node.children[1]));break;case"op_exp":ret=Math.pow(this.execute(node.children[0]),this.execute(node.children[1]));break;case"op_neg":ret=this.execute(node.children[0])*-1}break;case"node_var":ret=this.getvar(node.value);break;case"node_const":ret=Number(node.value);break;case"node_const_bool":ret=node.value.toLowerCase()!=="false";break;case"node_str":ret=node.value}return ret},compile:function(e,t){var n,r,i,s;n="",JXG.exists(t)||(t=!1);if(!e)return n;switch(e.type){case"node_op":switch(e.value){case"op_none":e.children[0]&&(n=this.compile(e.children[0],t)),e.children[1]&&(n+=this.compile(e.children[1],t));break;case"op_assign":i=this.compile(e.children[0],t),t?JXG.isArray(i)?n="$jc$.setProp("+i[0]+", '"+i[1]+"', "+this.compile(e.children[1],t)+");\n":(this.isLocalVariable(i)!==this.scope&&(this.sstack[this.scope][i]=!0),n="$jc$.sstack["+this.scope+"]['"+i+"'] = "+this.compile(e.children[1],t)+";\n"):n=i+" = "+this.compile(e.children[1],t)+";\n";break;case"op_noassign":n=this.compile(e.children[0],t)+";\n";break;case"op_if":n=" if ("+this.compile(e.children[0],t)+") "+this.compile(e.children[1],t);break;case"op_if_else":n=" if ("+this.compile(e.children[0],t)+")"+this.compile(e.children[1],t),n+=" else "+this.compile(e.children[2],t);break;case"op_while":n=" while ("+this.compile(e.children[0],t)+") {\n"+this.compile(e.children[1],t)+"}\n";break;case"op_do":n=" do {\n"+this.compile(e.children[0],t)+"} while ("+this.compile(e.children[1],t)+");\n";break;case"op_for":n=" for ("+this.compile(e.children[0],t)+"; "+this.compile(e.children[1],t)+"; "+this.compile(e.children[2],t)+") {\n"+this.compile(e.children[3],t)+"\n}\n";break;case"op_param":e.children[1]&&(n=this.compile(e.children[1],t)+", "),n+=this.compile(e.children[0],t);break;case"op_paramdef":e.children[1]&&(n=this.compile(e.children[1],t)+", "),n+=e.children[0];break;case"op_proplst":e.children[0]&&(n=this.compile(e.children[0],t)+", "),n+=this.compile(e.children[1],t);break;case"op_prop":n=e.children[0]+": "+this.compile(e.children[1],t);break;case"op_proplst_val":n=this.compile(e.children[0],t);break;case"op_array":n="["+this.compile(e.children[0],t)+"]";break;case"op_extvalue":n=this.compile(e.children[0],t)+"["+this.compile(e.children[1],t)+"]";break;case"op_return":n=" return "+this.compile(e.children[0],t)+";\n";break;case"op_function":n=" function ("+this.compile(e.children[0],t)+") {\n"+this.compile(e.children[1],t)+"}";break;case"op_execfun":e.children[2]&&(i=this.compile(e.children[2],t),t&&(i="$jc$.mergeAttributes("+i+")")),e.children[0].withProps=!!e.children[2],n=this.compile(e.children[0],t)+"("+this.compile(e.children[1],t)+(e.children[2]&&t?", "+i:"")+")"+(e.children[2]&&!t?i:""),t&&e.children[0].value==="$"&&(n="$jc$.board.objects["+this.compile(e.children[1],t)+"]");break;case"op_property":t&&e.children[1]!=="X"&&e.children[1]!=="Y"?n="$jc$.resolveProperty("+this.compile(e.children[0],t)+", '"+e.children[1]+"', true)":n=this.compile(e.children[0],t)+"."+e.children[1];break;case"op_lhs":e.children.length===1?n=e.children[0]:e.children[2]==="dot"?t?n=[this.compile(e.children[1],t),e.children[0]]:n=this.compile(e.children[1],t)+"."+e.children[0]:e.children[2]==="bracket"&&(t?n=[this.compile(e.children[1],t),this.compile(e.children[0],t)]:n=this.compile(e.children[1],t)+"["+this.compile(e.children[0],t)+"]");break;case"op_use":t?n="$jc$.use(JXG.JSXGraph.boards['"+e.children[0]+"'])":n="use "+e.children[0]+";";break;case"op_delete":n="delete "+e.children[0];break;case"op_equ":n="("+this.compile(e.children[0],t)+" == "+this.compile(e.children[1],t)+")";break;case"op_neq":n="("+this.compile(e.children[0],t)+" != "+this.compile(e.children[1],t)+")";break;case"op_approx":n="("+this.compile(e.children[0],t)+" ~= "+this.compile(e.children[1],t)+")";break;case"op_grt":n="("+this.compile(e.children[0],t)+" > "+this.compile(e.children[1],t)+")";break;case"op_lot":n="("+this.compile(e.children[0],t)+" < "+this.compile(e.children[1],t)+")";break;case"op_gre":n="("+this.compile(e.children[0],t)+" >= "+this.compile(e.children[1],t)+")";break;case"op_loe":n="("+this.compile(e.children[0],t)+" <= "+this.compile(e.children[1],t)+")";break;case"op_or":n="("+this.compile(e.children[0],t)+" || "+this.compile(e.children[1],t)+")";break;case"op_and":n="("+this.compile(e.children[0],t)+" && "+this.compile(e.children[1],t)+")";break;case"op_not":n="!("+this.compile(e.children[0],t)+")";break;case"op_add":t?n="JXG.Math.Statistics.add("+this.compile(e.children[0],t)+", "+this.compile(e.children[1],t)+")":n="("+this.compile(e.children[0],t)+" + "+this.compile(e.children[1],t)+")";break;case"op_sub":t?n="JXG.Math.Statistics.subtract("+this.compile(e.children[0],t)+", "+this.compile(e.children[1],t)+")":n="("+this.compile(e.children[0],t)+" - "+this.compile(e.children[1],t)+")";break;case"op_div":t?n="JXG.Math.Statistics.div("+this.compile(e.children[0],t)+", "+this.compile(e.children[1],t)+")":n="("+this.compile(e.children[0],t)+" / "+this.compile(e.children[1],t)+")";break;case"op_mod":t?n="JXG.Math.mod("+this.compile(e.children[0],t)+", "+this.compile(e.children[1],t)+", true)":n="("+this.compile(e.children[0],t)+" % "+this.compile(e.children[1],t)+")";break;case"op_mul":t?n="$jc$.mul("+this.compile(e.children[0],t)+", "+this.compile(e.children[1],t)+")":n="("+this.compile(e.children[0],t)+" * "+this.compile(e.children[1],t)+")";break;case"op_exp":t?n="Math.pow("+this.compile(e.children[0],t)+", "+this.compile(e.children[1],t)+")":n="("+this.compile(e.children[0],t)+"^"+this.compile(e.children[1],t)+")";break;case"op_neg":n="(-"+this.compile(e.children[0],t)+")"}break;case"node_var":t?n=this.getvarJS(e.value,!1,e.withProps):n=e.value;break;case"node_const":n=e.value;break;case"node_const_bool":n=e.value;break;case"node_str":n="'"+e.value.replace(/'/g,"\\'")+"'"}return e.needsBrackets&&(n="{\n"+n+"}\n"),n},X:function(e){return e.X()},Y:function(e){return e.Y()},V:function(e){return e.Value()},L:function(e){return e.L()},dist:function(e,t){return(!JXG.exists(e)||!JXG.exists(e.Dist))&&this._error("Error: Can't calculate distance."),e.Dist(t)},mul:function(e,t){return JXG.isArray(e)*JXG.isArray(t)?JXG.Math.innerProduct(e,t,Math.min(e.length,t.length)):JXG.Math.Statistics.multiply(e,t)},use:function(e){this.board=e,this.builtIn.$board=e,this.builtIn.$board.src="$jc$.board"},findSymbol:function(e,t){var n,r;t=JXG.def(t,-1),t===-1&&(t=this.scope);for(n=t;n>=0;n--)for(r in this.sstack[n])if(this.sstack[n][r]===e)return[r,n];return[]},defineBuiltIn:function(){var e=this,t={PI:Math.PI,EULER:Math.E,X:e.X,Y:e.Y,V:e.V,L:e.L,dist:e.dist,rad:JXG.Math.Geometry.rad,deg:JXG.Math.Geometry.trueAngle,factorial:JXG.Math.factorial,trunc:JXG.trunc,$:e.getElementById,$board:e.board};return t.rad.sc=JXG.Math.Geometry,t.deg.sc=JXG.Math.Geometry,t.factorial.sc=JXG.Math,t.PI.src="Math.PI",t.EULER.src="Math.E",t.X.src="$jc$.X",t.Y.src="$jc$.Y",t.V.src="$jc$.V",t.L.src="$jc$.L",t.dist.src="$jc$.dist",t.rad.src="JXG.Math.Geometry.rad",t.deg.src="JXG.Math.Geometry.trueAngle",t.factorial.src="JXG.Math.factorial",t.trunc.src="JXG.trunc",t.$.src="(function (n) { return JXG.getRef($jc$.board, n); })",t.$board&&(t.$board.src="$jc$.board"),t},_debug:function(e){typeof console!="undefined"?console.log(e):document&&document.getElementById("debug")!==null&&(document.getElementById("debug").innerHTML+=e+" ")},_error:function(e){var t=new Error("Error("+this.line+"): "+e);throw t.line=this.line,t},_warn:function(e){typeof console!="undefined"?console.log("Warning("+this.line+"): "+e):document&&document.getElementById(this.warnLog)!==null&&(document.getElementById(this.warnLog).innerHTML+="Warning("+this.line+"): "+e+" ")},_log:function(e){typeof window=="undefined"&&typeof self!="undefined"&&self.postMessage?self.postMessage({type:"log",msg:"Log: "+e.toString()}):console.log("Log: ",arguments)}}),JXG.extend(JXG.JessieCode.prototype,{_lex:function(e){var t,n=-1,r=0,i=0,s,o;for(;;){t=0,n=-1,r=0,i=0,s=e.offset+1+(r-i);do{s--,t=0,n=-2,i=s;if(e.src.length<=i)return 68;do{o=e.src.charCodeAt(s);switch(t){case 0:o>=9&&o<=10||o==13||o==32?t=1:o==33?t=2:o==35?t=3:o==36||o>=65&&o<=67||o>=71&&o<=72||o>=74&&o<=77||o>=79&&o<=81||o==83||o==86||o>=88&&o<=90||o==95||o>=97&&o<=99||o>=103&&o<=104||o>=106&&o<=113||o==115||o==118||o>=120&&o<=122?t=4:o==37?t=5:o==40?t=6:o==41?t=7:o==42?t=8:o==43?t=9:o==44?t=10:o==45?t=11:o==46?t=12:o==47?t=13:o>=48&&o<=57?t=14:o==58?t=15:o==59?t=16:o==60?t=17:o==61?t=18:o==62?t=19:o==91?t=20:o==93?t=21:o==94?t=22:o==123?t=23:o==124?t=24:o==125?t=25:o==38?t=49:o==68||o==100?t=50:o==39?t=52:o==73||o==105?t=53:o==126?t=54:o==70||o==102?t=66:o==78?t=67:o==85||o==117?t=68:o==69||o==101?t=76:o==84||o==116?t=77:o==87||o==119?t=83:o==82||o==114?t=87:t=-1;break;case 1:t=-1,n=2,r=s;break;case 2:o==61?t=26:t=-1,n=31,r=s;break;case 3:t=-1,n=41,r=s;break;case 4:o>=48&&o<=57||o>=65&&o<=90||o==95||o>=97&&o<=122?t=4:t=-1,n=46,r=s;break;case 5:t=-1,n=35,r=s;break;case 6:t=-1,n=38,r=s;break;case 7:t=-1,n=39,r=s;break;case 8:t=-1,n=36,r=s;break;case 9:t=-1,n=32,r=s;break;case 10:t=-1,n=40,r=s;break;case 11:t=-1,n=33,r=s;break;case 12:o>=48&&o<=57?t=29:t=-1,n=44,r=s;break;case 13:t=-1,n=34,r=s;break;case 14:o>=48&&o<=57?t=14:o==46?t=29:t=-1,n=48,r=s;break;case 15:t=-1,n=42,r=s;break;case 16:t=-1,n=20,r=s;break;case 17:o==60?t=30:o==61?t=31:t=-1,n=28,r=s;break;case 18:o==61?t=32:t=-1,n=21,r=s;break;case 19:o==61?t=33:o==62?t=34:t=-1,n=27,r=s;break;case 20:t=-1,n=16,r=s;break;case 21:t=-1,n=17,r=s;break;case 22:t=-1,n=37,r=s;break;case 23:t=-1,n=18,r=s;break;case 24:o==124?t=37:t=-1,n=43,r=s;break;case 25:t=-1,n=19,r=s;break;case 26:t=-1,n=23,r=s;break;case 27:t=-1,n=30,r=s;break;case 28:t=-1,n=47,r=s;break;case 29:o>=48&&o<=57?t=29:t=-1,n=49,r=s;break;case 30:t=-1,n=14,r=s;break;case 31:t=-1,n=25,r=s;break;case 32:t=-1,n=22,r=s;break;case 33:t=-1,n=26,r=s;break;case 34:t=-1,n=15,r=s;break;case 35:o>=48&&o<=57||o>=65&&o<=90||o==95||o>=97&&o<=122?t=4:t=-1,n=6,r=s;break;case 36:o>=48&&o<=57||o>=65&&o<=90||o==95||o>=97&&o<=122?t=4:t=-1,n=3,r=s;break;case 37:t=-1,n=29,r=s;break;case 38:t=-1,n=24,r=s;break;case 39:o>=48&&o<=57||o>=65&&o<=90||o==95||o>=97&&o<=122?t=4:t=-1,n=7,r=s;break;case 40:o>=48&&o<=57||o>=65&&o<=90||o==95||o>=97&&o<=122?t=4:t=-1,n=45,r=s;break;case 41:o>=48&&o<=57||o>=65&&o<=90||o==95||o>=97&&o<=122?t=4:t=-1,n=9,r=s;break;case 42:o>=48&&o<=57||o>=65&&o<=90||o==95||o>=97&&o<=122?t=4:t=-1,n=4,r=s;break;case 43:o>=48&&o<=57||o>=65&&o<=90||o==95||o>=97&&o<=122?t=4:t=-1,n=12,r=s;break;case 44:o>=48&&o<=57||o>=65&&o<=90||o==95||o>=97&&o<=122?t=4:t=-1,n=13,r=s;break;case 45:o>=48&&o<=57||o>=65&&o<=90||o==95||o>=97&&o<=122?t=4:t=-1,n=5,r=s;break;case 46:o>=48&&o<=57||o>=65&&o<=90||o==95||o>=97&&o<=122?t=4:t=-1,n=11,r=s;break;case 47:o>=48&&o<=57||o>=65&&o<=90||o==95||o>=97&&o<=122?t=4:t=-1,n=10,r=s;break;case 48:o>=48&&o<=57||o>=65&&o<=90||o==95||o>=97&&o<=122?t=4:t=-1,n=8,r=s;break;case 49:o==38?t=27:t=-1;break;case 50:o>=48&&o<=57||o>=65&&o<=68||o>=70&&o<=78||o>=80&&o<=90||o==95||o>=97&&o<=100||o>=102&&o<=110||o>=112&&o<=122?t=4:o==79||o==111?t=35:o==69||o==101?t=84:t=-1,n=46,r=s;break;case 51:o==39?t=28:o>=0&&o<=38||o>=40&&o<=91||o>=93&&o<=254?t=52:o==92?t=56:t=-1,n=47,r=s;break;case 52:o==39?t=28:o>=0&&o<=38||o>=40&&o<=91||o>=93&&o<=254?t=52:o==92?t=56:t=-1;break;case 53:o>=48&&o<=57||o>=65&&o<=69||o>=71&&o<=90||o==95||o>=97&&o<=101||o>=103&&o<=122?t=4:o==70||o==102?t=36:t=-1,n=46,r=s;break;case 54:o==61?t=38:t=-1;break;case 55:o>=48&&o<=57||o>=65&&o<=81||o>=83&&o<=90||o==95||o>=97&&o<=113||o>=115&&o<=122?t=4:o==82||o==114?t=39:t=-1,n=46,r=s;break;case 56:o==39?t=51:o>=0&&o<=38||o>=40&&o<=91||o>=93&&o<=254?t=52:o==92?t=56:t=-1;break;case 57:o>=48&&o<=57||o>=65&&o<=77||o>=79&&o<=90||o==95||o>=97&&o<=122?t=4:o==78?t=40:t=-1,n=46,r=s;break;case 58:o>=48&&o<=57||o>=65&&o<=68||o>=70&&o<=90||o==95||o>=97&&o<=100||o>=102&&o<=122?t=4:o==69||o==101?t=41:t=-1,n=46,r=s;break;case 59:o>=48&&o<=57||o>=65&&o<=68||o>=70&&o<=90||o==95||o>=97&&o<=100||o>=102&&o<=122?t=4:o==69||o==101?t=42:t=-1,n=46,r=s;break;case 60:o>=48&&o<=57||o>=65&&o<=68||o>=70&&o<=90||o==95||o>=97&&o<=100||o>=102&&o<=122?t=4:o==69||o==101?t=43:t=-1,n=46,r=s;break;case 61:o>=48&&o<=57||o>=65&&o<=68||o>=70&&o<=90||o==95||o>=97&&o<=100||o>=102&&o<=122?t=4:o==69||o==101?t=44:t=-1,n=46,r=s;break;case 62:o>=48&&o<=57||o>=65&&o<=68||o>=70&&o<=90||o==95||o>=97&&o<=100||o>=102&&o<=122?t=4:o==69||o==101?t=45:t=-1,n=46,r=s;break;case 63:o>=48&&o<=57||o>=65&&o<=68||o>=70&&o<=90||o==95||o>=97&&o<=100||o>=102&&o<=122?t=4:o==69||o==101?t=46:t=-1,n=46,r=s;break;case 64:o>=48&&o<=57||o>=65&&o<=77||o>=79&&o<=90||o==95||o>=97&&o<=109||o>=111&&o<=122?t=4:o==78||o==110?t=47:t=-1,n=46,r=s;break;case 65:o>=48&&o<=57||o>=65&&o<=77||o>=79&&o<=90||o==95||o>=97&&o<=109||o>=111&&o<=122?t=4:o==78||o==110?t=48:t=-1,n=46,r=s;break;case 66:o>=48&&o<=57||o>=66&&o<=78||o>=80&&o<=84||o>=86&&o<=90||o==95||o>=98&&o<=110||o>=112&&o<=116||o>=118&&o<=122?t=4:o==79||o==111?t=55:o==65||o==97?t=78:o==85||o==117?t=89:t=-1,n=46,r=s;break;case 67:o>=48&&o<=57||o>=65&&o<=90||o==95||o>=98&&o<=122?t=4:o==97?t=57:t=-1,n=46,r=s;break;case 68:o>=48&&o<=57||o>=65&&o<=82||o>=84&&o<=90||o==95||o>=97&&o<=114||o>=116&&o<=122?t=4:o==83||o==115?t=58:t=-1,n=46,r=s;break;case 69:o>=48&&o<=57||o>=65&&o<=82||o>=84&&o<=90||o==95||o>=97&&o<=114||o>=116&&o<=122?t=4:o==83||o==115?t=59:t=-1,n=46,r=s;break;case 70:o>=48&&o<=57||o>=65&&o<=84||o>=86&&o<=90||o==95||o>=97&&o<=116||o>=118&&o<=122?t=4:o==85||o==117?t=60:t=-1,n=46,r=s;break;case 71:o>=48&&o<=57||o>=65&&o<=82||o>=84&&o<=90||o==95||o>=97&&o<=114||o>=116&&o<=122?t=4:o==83||o==115?t=61:t=-1,n=46,r=s;break;case 72:o>=48&&o<=57||o>=65&&o<=75||o>=77&&o<=90||o==95||o>=97&&o<=107||o>=109&&o<=122?t=4:o==76||o==108?t=62:t=-1,n=46,r=s;break;case 73:o>=48&&o<=57||o>=65&&o<=83||o>=85&&o<=90||o==95||o>=97&&o<=115||o>=117&&o<=122?t=4:o==84||o==116?t=63:t=-1,n=46,r=s;break;case 74:o>=48&&o<=57||o>=65&&o<=81||o>=83&&o<=90||o==95||o>=97&&o<=113||o>=115&&o<=122?t=4:o==82||o==114?t=64:t=-1,n=46,r=s;break;case 75:o>=48&&o<=57||o>=65&&o<=78||o>=80&&o<=90||o==95||o>=97&&o<=110||o>=112&&o<=122?t=4:o==79||o==111?t=65:t=-1,n=46,r=s;break;case 76:o>=48&&o<=57||o>=65&&o<=75||o>=77&&o<=90||o==95||o>=97&&o<=107||o>=109&&o<=122?t=4:o==76||o==108?t=69:t=-1,n=46,r=s;break;case 77:o>=48&&o<=57||o>=65&&o<=81||o>=83&&o<=90||o==95||o>=97&&o<=113||o>=115&&o<=122?t=4:o==82||o==114?t=70:t=-1,n=46,r=s;break;case 78:o>=48&&o<=57||o>=65&&o<=75||o>=77&&o<=90||o==95||o>=97&&o<=107||o>=109&&o<=122?t=4:o==76||o==108?t=71:t=-1,n=46,r=s;break;case 79:o>=48&&o<=57||o>=65&&o<=72||o>=74&&o<=90||o==95||o>=97&&o<=104||o>=106&&o<=122?t=4:o==73||o==105?t=72:t=-1,n=46,r=s;break;case 80:o>=48&&o<=57||o>=65&&o<=68||o>=70&&o<=90||o==95||o>=97&&o<=100||o>=102&&o<=122?t=4:o==69||o==101?t=73:t=-1,n=46,r=s;break;case 81:o>=48&&o<=57||o>=65&&o<=84||o>=86&&o<=90||o==95||o>=97&&o<=116||o>=118&&o<=122?t=4:o==85||o==117?t=74:t=-1,n=46,r=s;break;case 82:o>=48&&o<=57||o>=65&&o<=72||o>=74&&o<=90||o==95||o>=97&&o<=104||o>=106&&o<=122?t=4:o==73||o==105?t=75:t=-1,n=46,r=s;break;case 83:o>=48&&o<=57||o>=65&&o<=71||o>=73&&o<=90||o==95||o>=97&&o<=103||o>=105&&o<=122?t=4:o==72||o==104?t=79:t=-1,n=46,r=s;break;case 84:o>=48&&o<=57||o>=65&&o<=75||o>=77&&o<=90||o==95||o>=97&&o<=107||o>=109&&o<=122?t=4:o==76||o==108?t=80:t=-1,n=46,r=s;break;case 85:o>=48&&o<=57||o>=65&&o<=83||o>=85&&o<=90||o==95||o>=97&&o<=115||o>=117&&o<=122?t=4:o==84||o==116?t=81:t=-1,n=46,r=s;break;case 86:o>=48&&o<=57||o>=65&&o<=83||o>=85&&o<=90||o==95||o>=97&&o<=115||o>=117&&o<=122?t=4:o==84||o==116?t=82:t=-1,n=46,r=s;break;case 87:o>=48&&o<=57||o>=65&&o<=68||o>=70&&o<=90||o==95||o>=97&&o<=100||o>=102&&o<=122?t=4:o==69||o==101?t=85:t=-1,n=46,r=s;break;case 88:o>=48&&o<=57||o>=65&&o<=66||o>=68&&o<=90||o==95||o>=97&&o<=98||o>=100&&o<=122?t=4:o==67||o==99?t=86:t=-1,n=46,r=s;break;case 89:o>=48&&o<=57||o>=65&&o<=77||o>=79&&o<=90||o==95||o>=97&&o<=109||o>=111&&o<=122?t=4:o==78||o==110?t=88:t=-1,n=46,r=s}t>-1&&(o==10&&(e.line++,e.column=0,this.countLines&&(this.parCurLine=e.line)),e.column++,this.countLines&&(this.parCurColumn=e.column)),s++}while(t>-1)}while(n==2);n>-1?(e.att=e.src.substr(i,r-i),e.offset=r,n==47&&(e.att=e.att.substr(1,e.att.length-2),e.att=e.att.replace(/\\\'/g,"'"))):(e.att=new String,n=-1);break}return n},_parse:function(e,t,n){var r=[],i=[],s=0,o,u,a,f={la:0,act:0,offset:0,src:e,att:"",line:1,column:1,error_step:0},l=new Array(new Array(0,1),new Array(50,2),new Array(50,0),new Array(52,2),new Array(52,0),new Array(53,3),new Array(53,1),new Array(53,0),new Array(55,3),new Array(55,1),new 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");for(a=0;a<p;a++)f=e.ticks[a].scrCoords,e.ticks[a].major&&(e.board.needsFullUpdate||e.needsRegularUpdate)&&e.labels[a]&&e.labels[a].visProp.visible&&this.updateText(e.labels[a]);l=this.getElementById(e.id),JXG.exists(l)||(l=this.createPrim("path",e.id),this.appendChildPrim(l,e.visProp.layer),this.appendNodesToElement(e,"path")),l.setAttributeNS(null,"stroke",e.visProp.strokecolor),l.setAttributeNS(null,"stroke-opacity",e.visProp.strokeopacity),l.setAttributeNS(null,"stroke-width",e.visProp.strokewidth),this.updatePathPrim(l,u,e.board)},displayCopyright:function(e,t){var n=this.createPrim("text","licenseText"),r;n.setAttributeNS(null,"x","20px"),n.setAttributeNS(null,"y",2+t+"px"),n.setAttributeNS(null,"style","font-family:Arial,Helvetica,sans-serif; font-size:"+t+"px; fill:#356AA0; opacity:0.3;"),r=document.createTextNode(e),n.appendChild(r),this.appendChildPrim(n,0)},drawInternalText:function(e){var t=this.createPrim("text",e.id);return t.setAttributeNS(null,"class",e.visProp.cssclass),e.rendNodeText=document.createTextNode(""),t.appendChild(e.rendNodeText),this.appendChildPrim(t,e.visProp.layer),t},updateInternalText:function(e){var t=e.plaintext;isNaN(e.coords.scrCoords[1]+e.coords.scrCoords[2])||(e.rendNode.setAttributeNS(null,"x",e.coords.scrCoords[1]+"px"),e.rendNode.setAttributeNS(null,"y",e.coords.scrCoords[2]+this.vOffsetText*.5+"px"),e.visProp.anchorx==="right"?e.rendNode.setAttributeNS(null,"text-anchor","end"):e.visProp.anchorx==="middle"&&e.rendNode.setAttributeNS(null,"text-anchor","middle"),e.visProp.anchory==="top"?e.rendNode.setAttributeNS(null,"dominant-baseline","text-before-edge"):e.visProp.anchory==="middle"&&e.rendNode.setAttributeNS(null,"dominant-baseline","middle")),e.htmlStr!==t&&(e.rendNodeText.data=t,e.htmlStr=t),this.transformImage(e,e.transformations)},updateInternalTextStyle:function(e,t,n){this.setObjectFillColor(e,t,n)},drawImage:function(e){var t=this.createPrim("image",e.id);t.setAttributeNS(null,"preserveAspectRatio","none"),this.appendChildPrim(t,e.visProp.layer),e.rendNode=t,this.updateImage(e)},transformImage:function(e,t){var n=e.rendNode,r,i="",s,o=t.length;o>0&&(r=this.joinTransforms(e,t),s=[r[1][1],r[2][1],r[1][2],r[2][2],r[1][0],r[2][0]].join(","),i+=" matrix("+s+") ",n.setAttributeNS(null,"transform",i))},updateImageURL:function(e){var t=JXG.evaluate(e.url);e.rendNode.setAttributeNS(this.xlinkNamespace,"xlink:href",t)},updateImageStyle:function(e,t){var n=t?e.visProp.highlightcssclass:e.visProp.cssclass;e.rendNode.setAttributeNS(null,"class",n)},appendChildPrim:function(e,t){JXG.exists(t)?t>=JXG.Options.layer.numlayers&&(t=JXG.Options.layer.numlayers-1):t=0,this.layer[t].appendChild(e)},appendNodesToElement:function(e){e.rendNode=this.getElementById(e.id)},createPrim:function(e,t){var n=this.container.ownerDocument.createElementNS(this.svgNamespace,e);return n.setAttributeNS(null,"id",this.container.id+"_"+t),n.style.position="absolute",e==="path"&&(n.setAttributeNS(null,"stroke-linecap","butt"),n.setAttributeNS(null,"stroke-linejoin","round")),n},remove:function(e){JXG.exists(e)&&JXG.exists(e.parentNode)&&e.parentNode.removeChild(e)},makeArrows:function(e){var t;if(e.visPropOld.firstarrow===e.visProp.firstarrow&&e.visPropOld.lastarrow===e.visProp.lastarrow)return;e.visProp.firstarrow?(t=e.rendNodeTriangleStart,JXG.exists(t)?this.defs.appendChild(t):(t=this._createArrowHead(e,"End"),this.defs.appendChild(t),e.rendNodeTriangleStart=t,e.rendNode.setAttributeNS(null,"marker-start","url(#"+this.container.id+"_"+e.id+"TriangleEnd)"))):(t=e.rendNodeTriangleStart,JXG.exists(t)&&this.remove(t)),e.visProp.lastarrow?(t=e.rendNodeTriangleEnd,JXG.exists(t)?this.defs.appendChild(t):(t=this._createArrowHead(e,"Start"),this.defs.appendChild(t),e.rendNodeTriangleEnd=t,e.rendNode.setAttributeNS(null,"marker-end","url(#"+this.container.id+"_"+e.id+"TriangleStart)"))):(t=e.rendNodeTriangleEnd,JXG.exists(t)&&this.remove(t)),e.visPropOld.firstarrow=e.visProp.firstarrow,e.visPropOld.lastarrow=e.visProp.lastarrow},updateEllipsePrim:function(e,t,n,r,i){e.setAttributeNS(null,"cx",t),e.setAttributeNS(null,"cy",n),e.setAttributeNS(null,"rx",Math.abs(r)),e.setAttributeNS(null,"ry",Math.abs(i))},updateLinePrim:function(e,t,n,r,i){isNaN(t+n+r+i)||(e.setAttributeNS(null,"x1",t),e.setAttributeNS(null,"y1",n),e.setAttributeNS(null,"x2",r),e.setAttributeNS(null,"y2",i))},updatePathPrim:function(e,t){t==""&&(t="M 0 0"),e.setAttributeNS(null,"d",t)},updatePathStringPoint:function(e,t,n){var r="",i=e.coords.scrCoords,s=t*Math.sqrt(3)*.5,o=t*.5;return n==="x"?r=" M "+(i[1]-t)+" "+(i[2]-t)+" L "+(i[1]+t)+" "+(i[2]+t)+" M "+(i[1]+t)+" "+(i[2]-t)+" L "+(i[1]-t)+" "+(i[2]+t):n==="+"?r=" M "+(i[1]-t)+" "+i[2]+" L "+(i[1]+t)+" "+i[2]+" M "+i[1]+" "+(i[2]-t)+" L "+i[1]+" "+(i[2]+t):n==="<>"?r=" M "+(i[1]-t)+" "+i[2]+" L "+i[1]+" "+(i[2]+t)+" L "+(i[1]+t)+" "+i[2]+" L "+i[1]+" "+(i[2]-t)+" Z ":n==="^"?r=" M "+i[1]+" "+(i[2]-t)+" L "+(i[1]-s)+" "+(i[2]+o)+" L "+(i[1]+s)+" "+(i[2]+o)+" Z ":n==="v"?r=" M "+i[1]+" "+(i[2]+t)+" L "+(i[1]-s)+" "+(i[2]-o)+" L "+(i[1]+s)+" "+(i[2]-o)+" Z ":n===">"?r=" M "+(i[1]+t)+" "+i[2]+" L "+(i[1]-o)+" "+(i[2]-s)+" L "+(i[1]-o)+" "+(i[2]+s)+" Z ":n==="<"&&(r=" M "+(i[1]-t)+" "+i[2]+" L "+(i[1]+o)+" "+(i[2]-s)+" L "+(i[1]+o)+" "+(i[2]+s)+" Z "),r},updatePathStringPrim:function(e){var t=" M ",n=" L ",r=" C ",i=t,s=5e3,o="",u,a,f=e.visProp.curvetype!=="plot",l;if(e.numberPoints<=0)return"";l=Math.min(e.points.length,e.numberPoints);if(e.bezierDegree==1){f&&e.board.options.curve.RDPsmoothing&&(e.points=JXG.Math.Numerics.RamerDouglasPeuker(e.points,.5));for(u=0;u<l;u++)a=e.points[u].scrCoords,isNaN(a[1])||isNaN(a[2])?i=t:(a[1]>s?a[1]=s:a[1]<-s&&(a[1]=-s),a[2]>s?a[2]=s:a[2]<-s&&(a[2]=-s),o+=i+a[1]+" "+a[2],i=n)}else if(e.bezierDegree==3){u=0;while(u<l)a=e.points[u].scrCoords,isNaN(a[1])||isNaN(a[2])?i=t:(o+=i+a[1]+" "+a[2],i==r&&(u++,a=e.points[u].scrCoords,o+=" "+a[1]+" "+a[2],u++,a=e.points[u].scrCoords,o+=" "+a[1]+" "+a[2]),i=r),u++}return o},updatePathStringBezierPrim:function(e){var t=" M ",n=" C ",r=t,i=5e3,s="",o,u,a,f,l,c=e.visProp.strokewidth,h=e.visProp.curvetype!=="plot",p;if(e.numberPoints<=0)return"";h&&e.board.options.curve.RDPsmoothing&&(e.points=JXG.Math.Numerics.RamerDouglasPeuker(e.points,.5)),p=Math.min(e.points.length,e.numberPoints);for(u=1;u<3;u++){r=t;for(o=0;o<p;o++)a=e.points[o].scrCoords,isNaN(a[1])||isNaN(a[2])?r=t:(a[1]>i?a[1]=i:a[1]<-i&&(a[1]=-i),a[2]>i?a[2]=i:a[2]<-i&&(a[2]=-i),r==t?s+=[r,a[1]+0*c*(2*u*Math.random()-u)," ",a[2]+0*c*(2*u*Math.random()-u)].join(""):s+=[r,f+(a[1]-f)*.333+c*(2*u*Math.random()-u)," ",l+(a[2]-l)*.333+c*(2*u*Math.random()-u)," ",f+2*(a[1]-f)*.333+c*(2*u*Math.random()-u)," ",l+2*(a[2]-l)*.333+c*(2*u*Math.random()-u)," ",a[1]," ",a[2]].join(""),r=n,f=a[1],l=a[2])}return s},updatePolygonPrim:function(e,t){var n="",r,i,s=t.vertices.length;e.setAttributeNS(null,"stroke","none");for(i=0;i<s-1;i++){if(!t.vertices[i].isReal){e.setAttributeNS(null,"points","");return}r=t.vertices[i].coords.scrCoords,n=n+r[1]+","+r[2],i<s-2&&(n+=" ")}n.indexOf("NaN")==-1&&e.setAttributeNS(null,"points",n)},updateRectPrim:function(e,t,n,r,i){e.setAttributeNS(null,"x",t),e.setAttributeNS(null,"y",n),e.setAttributeNS(null,"width",r),e.setAttributeNS(null,"height",i)},setPropertyPrim:function(e,t,n){if(t==="stroked")return;e.setAttributeNS(null,t,n)},show:function(e){var t;e&&e.rendNode&&(t=e.rendNode,t.setAttributeNS(null,"display","inline"),t.style.visibility="inherit")},hide:function(e){var t;e&&e.rendNode&&(t=e.rendNode,t.setAttributeNS(null,"display","none"),t.style.visibility="hidden")},setBuffering:function(e,t){e.rendNode.setAttribute("buffered-rendering",t)},setDashStyle:function(e){var t=e.visProp.dash,n=e.rendNode;e.visProp.dash>0?n.setAttributeNS(null,"stroke-dasharray",this.dashArray[t-1]):n.hasAttributeNS(null,"stroke-dasharray")&&n.removeAttributeNS(null,"stroke-dasharray")},setGradient:function(e){var t=e.rendNode,n,r,i,s,o,u,a,f,l;r=JXG.evaluate(e.visProp.fillopacity),r=r>0?r:0,n=JXG.evaluate(e.visProp.fillcolor),e.visProp.gradient==="linear"?(i=this.createPrim("linearGradient",e.id+"_gradient"),u="0%",a="100%",f="0%",l="0%",i.setAttributeNS(null,"x1",u),i.setAttributeNS(null,"x2",a),i.setAttributeNS(null,"y1",f),i.setAttributeNS(null,"y2",l),s=this.createPrim("stop",e.id+"_gradient1"),s.setAttributeNS(null,"offset","0%"),s.setAttributeNS(null,"style","stop-color:"+n+";stop-opacity:"+r),o=this.createPrim("stop",e.id+"_gradient2"),o.setAttributeNS(null,"offset","100%"),o.setAttributeNS(null,"style","stop-color:"+e.visProp.gradientsecondcolor+";stop-opacity:"+e.visProp.gradientsecondopacity),i.appendChild(s),i.appendChild(o),this.defs.appendChild(i),t.setAttributeNS(null,"style","fill:url(#"+this.container.id+"_"+e.id+"_gradient)"),e.gradNode1=s,e.gradNode2=o):e.visProp.gradient==="radial"?(i=this.createPrim("radialGradient",e.id+"_gradient"),i.setAttributeNS(null,"cx","50%"),i.setAttributeNS(null,"cy","50%"),i.setAttributeNS(null,"r","50%"),i.setAttributeNS(null,"fx",e.visProp.gradientpositionx*100+"%"),i.setAttributeNS(null,"fy",e.visProp.gradientpositiony*100+"%"),s=this.createPrim("stop",e.id+"_gradient1"),s.setAttributeNS(null,"offset","0%"),s.setAttributeNS(null,"style","stop-color:"+e.visProp.gradientsecondcolor+";stop-opacity:"+e.visProp.gradientsecondopacity),o=this.createPrim("stop",e.id+"_gradient2"),o.setAttributeNS(null,"offset","100%"),o.setAttributeNS(null,"style","stop-color:"+n+";stop-opacity:"+r),i.appendChild(s),i.appendChild(o),this.defs.appendChild(i),t.setAttributeNS(null,"style","fill:url(#"+this.container.id+"_"+e.id+"_gradient)"),e.gradNode1=s,e.gradNode2=o):t.removeAttributeNS(null,"style")},updateGradient:function(e){var t=e.gradNode1,n=e.gradNode2,r,i;if(!JXG.exists(t)||!JXG.exists(n))return;i=JXG.evaluate(e.visProp.fillopacity),i=i>0?i:0,r=JXG.evaluate(e.visProp.fillcolor),e.visProp.gradient==="linear"?(t.setAttributeNS(null,"style","stop-color:"+r+";stop-opacity:"+i),n.setAttributeNS(null,"style","stop-color:"+e.visProp.gradientsecondcolor+";stop-opacity:"+e.visProp.gradientsecondopacity)):e.visProp.gradient==="radial"&&(t.setAttributeNS(null,"style","stop-color:"+e.visProp.gradientsecondcolor+";stop-opacity:"+e.visProp.gradientsecondopacity),n.setAttributeNS(null,"style","stop-color:"+r+";stop-opacity:"+i))},setObjectFillColor:function(e,t,n){var r,i=JXG.evaluate(t),s,o,u=JXG.evaluate(n),a;u=u>0?u:0;if(e.visPropOld.fillcolor===i&&e.visPropOld.fillopacity===u)return;JXG.exists(i)&&i!==!1&&(i.length!=9?(s=i,a=u):(o=JXG.rgba2rgbo(i),s=o[0],a=u*o[1]),r=e.rendNode,s!="none"?r.setAttributeNS(null,"fill",s):a=0,e.type===JXG.OBJECT_TYPE_IMAGE?r.setAttributeNS(null,"opacity",a):r.setAttributeNS(null,"fill-opacity",a),JXG.exists(e.visProp.gradient)&&this.updateGradient(e)),e.visPropOld.fillcolor=i,e.visPropOld.fillopacity=u},setObjectStrokeColor:function(e,t,n){var r=JXG.evaluate(t),i,s,o=JXG.evaluate(n),u,a;o=o>0?o:0;if(e.visPropOld.strokecolor===r&&e.visPropOld.strokeopacity===o)return;if(JXG.exists(r)&&r!==!1){r.length!=9?(i=r,u=o):(s=JXG.rgba2rgbo(r),i=s[0],u=o*s[1]),a=e.rendNode,e.type===JXG.OBJECT_TYPE_TEXT?e.visProp.display==="html"?(a.style.color=i,a.style.opacity=u):(a.setAttributeNS(null,"style","fill:"+i),a.setAttributeNS(null,"style","fill-opacity:"+u)):(a.setAttributeNS(null,"stroke",i),a.setAttributeNS(null,"stroke-opacity",u));if(e.type===JXG.OBJECT_TYPE_ARROW)this._setArrowAtts(e.rendNodeTriangle,i,u,e.visProp.strokewidth);else if(e.elementClass===JXG.OBJECT_CLASS_CURVE||e.elementClass===JXG.OBJECT_CLASS_LINE)e.visProp.firstarrow&&this._setArrowAtts(e.rendNodeTriangleStart,i,u,e.visProp.strokewidth),e.visProp.lastarrow&&this._setArrowAtts(e.rendNodeTriangleEnd,i,u,e.visProp.strokewidth)}e.visPropOld.strokecolor=r,e.visPropOld.strokeopacity=o},setObjectStrokeWidth:function(e,t){var n=JXG.evaluate(t),r;if(e.visPropOld.strokewidth===n)return;r=e.rendNode,this.setPropertyPrim(r,"stroked","true");if(JXG.exists(n)){this.setPropertyPrim(r,"stroke-width",n+"px");if(e.type===JXG.OBJECT_TYPE_ARROW)this._setArrowAtts(e.rendNodeTriangle,e.visProp.strokecolor,e.visProp.strokeopacity,n);else if(e.elementClass===JXG.OBJECT_CLASS_CURVE||e.elementClass===JXG.OBJECT_CLASS_LINE)e.visProp.firstarrow&&this._setArrowAtts(e.rendNodeTriangleStart,e.visProp.strokecolor,e.visProp.strokeopacity,n),e.visProp.lastarrow&&this._setArrowAtts(e.rendNodeTriangleEnd,e.visProp.strokecolor,e.visProp.strokeopacity,n)}e.visPropOld.strokewidth=n},setShadow:function(e){if(e.visPropOld.shadow===e.visProp.shadow)return;JXG.exists(e.rendNode)&&(e.visProp.shadow?e.rendNode.setAttributeNS(null,"filter","url(#"+this.container.id+"_"+"f1)"):e.rendNode.removeAttributeNS(null,"filter")),e.visPropOld.shadow=e.visProp.shadow},suspendRedraw:function(){},unsuspendRedraw:function(){},resize:function(e,t){this.svgRoot.style.width=parseFloat(e)+"px",this.svgRoot.style.height=parseFloat(t)+"px"}}),JXG.VMLRenderer=function(e){this.type="vml",this.container=e,this.container.style.overflow="hidden",this.container.onselectstart=function(){return!1},this.resolution=10,JXG.exists(JXG.vmlStylesheet)||(e.ownerDocument.namespaces.add("jxgvml","urn:schemas-microsoft-com:vml"),JXG.vmlStylesheet=this.container.ownerDocument.createStyleSheet(),JXG.vmlStylesheet.addRule(".jxgvml","behavior:url(#default#VML)"));try{!e.ownerDocument.namespaces.jxgvml&&e.ownerDocument.namespaces.add("jxgvml","urn:schemas-microsoft-com:vml"),this.createNode=function(t){return e.ownerDocument.createElement("<jxgvml:"+t+' class="jxgvml">')}}catch(t){this.createNode=function(t){return e.ownerDocument.createElement("<"+t+' xmlns="urn:schemas-microsoft.com:vml" class="jxgvml">')}}this.dashArray=["Solid","1 1","ShortDash","Dash","LongDash","ShortDashDot","LongDashDot"]},JXG.VMLRenderer.prototype=new JXG.AbstractRenderer,JXG.extend(JXG.VMLRenderer.prototype,{_setAttr:function(e,t,n,r){try{document.documentMode===8?e[t]=n:e.setAttribute(t,n,r)}catch(i){JXG.debug("_setAttr: "+t+" "+n+" \n")}},updateTicks:function(e,t,n,r,i){var s=[],o,u,a,f,l=this.resolution;u=e.ticks.length;for(o=0;o<u;o++)a=e.ticks[o],x=a[0],y=a[1],typeof x[0]!="undefined"&&typeof x[1]!="undefined"&&s.push(" m "+Math.round(l*x[0])+", "+Math.round(l*y[0])+" l "+Math.round(l*x[1])+", "+Math.round(l*y[1])+" ");for(o=0;o<u;o++)a=e.ticks[o].scrCoords,e.ticks[o].major&&(e.board.needsFullUpdate||e.needsRegularUpdate)&&e.labels[o]&&e.labels[o].visProp.visible&&this.updateText(e.labels[o]);JXG.exists(e)||(f=this.createPrim("path",e.id),this.appendChildPrim(f,e.visProp.layer),this.appendNodesToElement(e,"path")),this._setAttr(e.rendNode,"stroked","true"),this._setAttr(e.rendNode,"strokecolor",e.visProp.strokecolor,1),this._setAttr(e.rendNode,"strokeweight",e.visProp.strokewidth),this._setAttr(e.rendNodeStroke,"opacity",e.visProp.strokeopacity*100+"%"),this.updatePathPrim(e.rendNode,s,e.board)},displayCopyright:function(e,t){var n,r;n=this.createNode("textbox"),n.style.position="absolute",this._setAttr(n,"id",this.container.id+"_"+"licenseText"),n.style.left=20,n.style.top=2,n.style.fontSize=t,n.style.color="#356AA0",n.style.fontFamily="Arial,Helvetica,sans-serif",this._setAttr(n,"opacity","30%"),n.style.filter="alpha(opacity = 30)",r=document.createTextNode(e),n.appendChild(r),this.appendChildPrim(n,0)},drawInternalText:function(e){var t;return t=this.createNode("textbox"),t.style.position="absolute",e.rendNodeText=document.createTextNode(""),t.appendChild(e.rendNodeText),this.appendChildPrim(t,9),t},updateInternalText:function(e){var t=e.plaintext;isNaN(e.coords.scrCoords[1]+e.coords.scrCoords[2])||(e.visProp.anchorx==="right"?e.rendNode.style.right=parseInt(e.board.canvasWidth-e.coords.scrCoords[1])+"px":e.visProp.anchorx==="middle"?e.rendNode.style.left=parseInt(e.coords.scrCoords[1]-.5*e.size[0])+"px":e.rendNode.style.left=parseInt(e.coords.scrCoords[1])+"px",e.rendNode.style.top=parseInt(e.coords.scrCoords[2]-e.visProp.fontsize+this.vOffsetText)+"px",e.visProp.anchory==="top"?e.rendNode.style.top=parseInt(e.coords.scrCoords[2]+this.vOffsetText)+"px":e.visProp.anchory==="middle"?e.rendNode.style.top=parseInt(e.coords.scrCoords[2]-.5*e.size[1]+this.vOffsetText)+"px":e.rendNode.style.top=parseInt(e.coords.scrCoords[2]-e.size[1]+this.vOffsetText)+"px"),e.htmlStr!==t&&(e.rendNodeText.data=t,e.htmlStr=t),this.transformImage(e,e.transformations)},drawImage:function(e){var t;t=this.container.ownerDocument.createElement("img"),t.style.position="absolute",this._setAttr(t,"id",this.container.id+"_"+e.id),this.container.appendChild(t),this.appendChildPrim(t,e.visProp.layer),t.style.filter="progid:DXImageTransform.Microsoft.Matrix(M11='1.0', sizingMethod='auto expand')",e.rendNode=t,this.updateImage(e)},transformImage:function(e,t){var n=e.rendNode,r,i=[],s,o=t.length,u,a,f,l,c,h;e.type===JXG.OBJECT_TYPE_TEXT&&e.updateSize();if(o>0){h=e.rendNode.style.filter.toString(),h.match(/DXImageTransform/)||(n.style.filter="progid:DXImageTransform.Microsoft.Matrix(M11='1.0', sizingMethod='auto expand') 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t=JXG.evaluate(e.url);this._setAttr(e.rendNode,"src",t)},appendChildPrim:function(e,t){JXG.exists(t)||(t=0),e.style.zIndex=t,this.container.appendChild(e)},appendNodesToElement:function(e,t){if(t==="shape"||t==="path"||t==="polygon")e.rendNodePath=this.getElementById(e.id+"_path");e.rendNodeFill=this.getElementById(e.id+"_fill"),e.rendNodeStroke=this.getElementById(e.id+"_stroke"),e.rendNodeShadow=this.getElementById(e.id+"_shadow"),e.rendNode=this.getElementById(e.id)},createPrim:function(e,t){var n,r=this.createNode("fill"),i=this.createNode("stroke"),s=this.createNode("shadow"),o;return 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t=e.rendNodeFill;e.visProp.gradient==="linear"?(this._setAttr(t,"type","gradient"),this._setAttr(t,"color2",e.visProp.gradientsecondcolor),this._setAttr(t,"opacity2",e.visProp.gradientsecondopacity),this._setAttr(t,"angle",e.visProp.gradientangle)):e.visProp.gradient==="radial"?(this._setAttr(t,"type","gradientradial"),this._setAttr(t,"color2",e.visProp.gradientsecondcolor),this._setAttr(t,"opacity2",e.visProp.gradientsecondopacity),this._setAttr(t,"focusposition",e.visProp.gradientpositionx*100+"%,"+e.visProp.gradientpositiony*100+"%"),this._setAttr(t,"focussize","0,0")):this._setAttr(t,"type","solid")},setObjectFillColor:function(e,t,n){var r=JXG.evaluate(t),i,s,o=JXG.evaluate(n),u,a=e.rendNode,f;o=o>0?o:0;if(e.visPropOld.fillcolor===r&&e.visPropOld.fillopacity===o)return;JXG.exists(r)&&r!==!1&&(r.length!=9?(i=r,u=o):(s=JXG.rgba2rgbo(r),i=s[0],u=o*s[1]),i==="none"||i===!1?this._setAttr(e.rendNode,"filled","false"):(this._setAttr(e.rendNode,"filled","true"),this._setAttr(e.rendNode,"fillcolor",i),JXG.exists(u)&&e.rendNodeFill&&this._setAttr(e.rendNodeFill,"opacity",u*100+"%")),e.type===JXG.OBJECT_TYPE_IMAGE&&(f=e.rendNode.style.filter.toString(),f.match(/alpha/)?e.rendNode.style.filter=f.replace(/alpha$opacity *= *[0-9\.]+$/,"alpha(opacity = "+u*100+")"):e.rendNode.style.filter+=" alpha(opacity = "+u*100+")")),e.visPropOld.fillcolor=r,e.visPropOld.fillopacity=o},setObjectStrokeColor:function(e,t,n){var r=JXG.evaluate(t),i,s,o=JXG.evaluate(n),u,a=e.rendNode,f;o=o>0?o:0;if(e.visPropOld.strokecolor===r&&e.visPropOld.strokeopacity===o)return;JXG.exists(r)&&r!==!1&&(r.length!=9?(i=r,u=o):(s=JXG.rgba2rgbo(r),i=s[0],u=o*s[1]),e.type===JXG.OBJECT_TYPE_TEXT?(u=Math.round(u*100),a.style.filter=" alpha(opacity = "+u+")",a.style.color=i):(i!==!1&&(this._setAttr(a,"stroked","true"),this._setAttr(a,"strokecolor",i)),f=e.rendNodeStroke,JXG.exists(u)&&e.type!==JXG.OBJECT_TYPE_IMAGE&&this._setAttr(f,"opacity",u*100+"%"))),e.visPropOld.strokecolor=r,e.visPropOld.strokeopacity=o},setObjectStrokeWidth:function(e,t){var n=JXG.evaluate(t),r;if(e.visPropOld.strokewidth===n)return;r=e.rendNode,this.setPropertyPrim(r,"stroked","true"),JXG.exists(n)&&this.setPropertyPrim(r,"stroke-width",n),e.visPropOld.strokewidth=n},setShadow:function(e){var t=e.rendNodeShadow;if(!t||e.visPropOld.shadow===e.visProp.shadow)return;e.visProp.shadow?(this._setAttr(t,"On","True"),this._setAttr(t,"Offset","3pt,3pt"),this._setAttr(t,"Opacity","60%"),this._setAttr(t,"Color","#aaaaaa")):this._setAttr(t,"On","False"),e.visPropOld.shadow=e.visProp.shadow},suspendRedraw:function(){this.container.style.display="none"},unsuspendRedraw:function(){this.container.style.display=""}}),JXG.CanvasRenderer=function(e){var t;this.type="canvas",this.canvasRoot=null,this.suspendHandle=null,this.canvasId=JXG.Util.genUUID(),this.canvasNamespace=null,typeof document!="undefined"?(this.container=e,this.container.style.MozUserSelect="none",this.container.style.overflow="hidden",this.container.style.position===""&&(this.container.style.position="relative"),this.container.innerHTML=['<canvas id="',this.canvasId,'" width="',JXG.getStyle(this.container,"width"),'" 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r},_setColor:function(e,t,n){var r=!0,i=!1,s=e.visProp,o,u,a,f,l,c;t=t||"stroke",n=n||t;if(!JXG.exists(e.board)||!JXG.exists(e.board.highlightedObjects))i=!0;return!i&&JXG.exists(e.board.highlightedObjects[e.id])?o="highlight":o="",u=JXG.evaluate(s[o+t+"color"]),u!=="none"&&u!==!1?(l=JXG.evaluate(s[o+t+"opacity"]),l=l>0?l:0,u.length!=9?(f=u,c=l):(a=JXG.rgba2rgbo(u),f=a[0],c=l*a[1]),this.context.globalAlpha=c,this.context[n+"Style"]=f):r=!1,t==="stroke"&&(this.context.lineWidth=parseFloat(s.strokewidth)),r},_stroke:function(e){var t=this.context;t.save(),e.visProp.dash>0?t.setLineDash&&t.setLineDash(this.dashArray[e.visProp.dash]):this.context.lineDashArray=[],this._setColor(e,"stroke")&&t.stroke(),t.restore()},_translateShape:function(e,t,n){var r,i=[],s=e.length;if(s<=0)return e;for(r=0;r<s;r++)i.push([e[r][0]+t,e[r][1]+n]);return i},drawPoint:function(e){var t=e.visProp.face,n=e.visProp.size,r=e.coords.scrCoords,i=n*Math.sqrt(3)*.5,s=n*.5,o=parseFloat(e.visProp.strokewidth)/2,u=this.context;switch(t){case"cross":case"x":u.beginPath(),u.moveTo(r[1]-n,r[2]-n),u.lineTo(r[1]+n,r[2]+n),u.moveTo(r[1]+n,r[2]-n),u.lineTo(r[1]-n,r[2]+n),u.closePath(),this._stroke(e);break;case"circle":case"o":u.beginPath(),u.arc(r[1],r[2],n+1+o,0,2*Math.PI,!1),u.closePath(),this._fill(e),this._stroke(e);break;case"square":case"[]":if(n<=0)break;u.save(),this._setColor(e,"stroke","fill")&&u.fillRect(r[1]-n-o,r[2]-n-o,n*2+3*o,n*2+3*o),u.restore(),u.save(),this._setColor(e,"fill"),u.fillRect(r[1]-n+o,r[2]-n+o,n*2-o,n*2-o),u.restore();break;case"plus":case"+":u.beginPath(),u.moveTo(r[1]-n,r[2]),u.lineTo(r[1]+n,r[2]),u.moveTo(r[1],r[2]-n),u.lineTo(r[1],r[2]+n),u.closePath(),this._stroke(e);break;case"diamond":case"<>":u.beginPath(),u.moveTo(r[1]-n,r[2]),u.lineTo(r[1],r[2]+n),u.lineTo(r[1]+n,r[2]),u.lineTo(r[1],r[2]-n),u.closePath(),this._fill(e),this._stroke(e);break;case"triangleup":case"a":case"^":u.beginPath(),u.moveTo(r[1],r[2]-n),u.lineTo(r[1]-i,r[2]+s),u.lineTo(r[1]+i,r[2]+s),u.closePath(),this._fill(e),this._stroke(e);break;case"triangledown":case"v":u.beginPath(),u.moveTo(r[1],r[2]+n),u.lineTo(r[1]-i,r[2]-s),u.lineTo(r[1]+i,r[2]-s),u.closePath(),this._fill(e),this._stroke(e);break;case"triangleleft":case"<":u.beginPath(),u.moveTo(r[1]-n,r[2]),u.lineTo(r[1]+s,r[2]-i),u.lineTo(r[1]+s,r[2]+i),u.closePath(),this.fill(e),this._stroke(e);break;case"triangleright":case">":u.beginPath(),u.moveTo(r[1]+n,r[2]),u.lineTo(r[1]-s,r[2]-i),u.lineTo(r[1]-s,r[2]+i),u.closePath(),this._fill(e),this._stroke(e)}},updatePoint:function(e){this.drawPoint(e)},drawLine:function(e){var t=new JXG.Coords(JXG.COORDS_BY_USER,e.point1.coords.usrCoords,e.board),n=new JXG.Coords(JXG.COORDS_BY_USER,e.point2.coords.usrCoords,e.board);JXG.Math.Geometry.calcStraight(e,t,n),this.context.beginPath(),this.context.moveTo(t.scrCoords[1],t.scrCoords[2]),this.context.lineTo(n.scrCoords[1],n.scrCoords[2]),this._stroke(e),this.makeArrows(e,t,n)},updateLine:function(e){this.drawLine(e)},drawTicks:function(){},updateTicks:function(e,t,n,r,i){var s,o,u=e.ticks.length,a=this.context;a.beginPath();for(s=0;s<u;s++)o=e.ticks[s],x=o[0],y=o[1],a.moveTo(x[0],y[0]),a.lineTo(x[1],y[1]);for(s=0;s<u;s++)o=e.ticks[s].scrCoords,e.ticks[s].major&&(e.board.needsFullUpdate||e.needsRegularUpdate)&&e.labels[s]&&e.labels[s].visProp.visible&&this.updateText(e.labels[s]);this._stroke(e)},drawCurve:function(e){e.visProp.handdrawing?this.updatePathStringBezierPrim(e):this.updatePathStringPrim(e)},updateCurve:function(e){this.drawCurve(e)},drawEllipse:function(e){var t=e.center.coords.scrCoords[1],n=e.center.coords.scrCoords[2],r=e.board.unitX,i=e.board.unitY,s=2*e.Radius(),o=2*e.Radius(),u=s*r,a=o*i,f=t-u/2,l=n-a/2,c=u/2*.5522848,h=a/2*.5522848,p=f+u,d=l+a,v=f+u/2,m=l+a/2,g=this.context;s>0&&o>0&&!isNaN(t+n)&&(g.beginPath(),g.moveTo(f,m),g.bezierCurveTo(f,m-h,v-c,l,v,l),g.bezierCurveTo(v+c,l,p,m-h,p,m),g.bezierCurveTo(p,m+h,v+c,d,v,d),g.bezierCurveTo(v-c,d,f,m+h,f,m),g.closePath(),this._fill(e),this._stroke(e))},updateEllipse:function(e){return this.drawEllipse(e)},displayCopyright:function(e,t){var n=this.context;n.save(),n.font=t+"px Arial",n.fillStyle="#aaa",n.lineWidth=.5,n.fillText(e,10,2+t),n.restore()},drawInternalText:function(e){var t,n=this.context;return n.save(),this._setColor(e,"stroke","fill")&&!isNaN(e.coords.scrCoords[1]+e.coords.scrCoords[2])&&(e.visProp.fontsize&&(typeof e.visProp.fontsize=="function"?(t=e.visProp.fontsize(),n.font=(t>0?t:0)+"px Arial"):n.font=e.visProp.fontsize+"px Arial"),this.transformImage(e,e.transformations),e.visProp.anchorx==="right"?n.textAlign="right":e.visProp.anchorx==="middle"&&(n.textAlign="center"),e.visProp.anchory==="top"?n.textBaseline="top":e.visProp.anchory==="middle"&&(n.textBaseline="middle"),n.fillText(e.plaintext,e.coords.scrCoords[1],e.coords.scrCoords[2])),n.restore(),null},updateInternalText:function(e){this.drawInternalText(e)},setObjectStrokeColor:function(e,t,n){var r=JXG.evaluate(t),i,s,o=JXG.evaluate(n),u,a;o=o>0?o:0;if(e.visPropOld.strokecolor===r&&e.visPropOld.strokeopacity===o)return;JXG.exists(r)&&r!==!1&&(r.length!=9?(i=r,u=o):(s=JXG.rgba2rgbo(r),i=s[0],u=o*s[1]),a=e.rendNode,e.type===JXG.OBJECT_TYPE_TEXT&&e.visProp.display==="html"&&(a.style.color=i,a.style.opacity=u)),e.visPropOld.strokecolor=r,e.visPropOld.strokeopacity=o},drawImage:function(e){e.rendNode=new Image,e._src="",this.updateImage(e)},updateImage:function(e){var t=this.context,n=JXG.evaluate(e.visProp.fillopacity),r=JXG.bind(function(){e.imgIsLoaded=!0;if(e.size[0]<=0||e.size[1]<=0)return;t.save(),t.globalAlpha=n,this.transformImage(e,e.transformations),t.drawImage(e.rendNode,e.coords.scrCoords[1],e.coords.scrCoords[2]-e.size[1],e.size[0],e.size[1]),t.restore()},this);this.updateImageURL(e)?e.rendNode.onload=r:e.imgIsLoaded&&r()},transformImage:function(e,t){var n,r=t.length,i=this.context;r>0&&(n=this.joinTransforms(e,t),Math.abs(JXG.Math.Numerics.det(n))>=JXG.Math.eps&&i.transform(n[1][1],n[2][1],n[1][2],n[2][2],n[1][0],n[2][0]))},updateImageURL:function(e){var t;return t=JXG.evaluate(e.url),e._src!==t?(e.imgIsLoaded=!1,e.rendNode.src=t,e._src=t,!0):!1},remove:function(e){JXG.exists(e)&&JXG.exists(e.parentNode)&&e.parentNode.removeChild(e)},makeArrows:function(e,t,n){var r=Math.min(e.visProp.strokewidth/2,3),i=[[2,0],[-10,-4*r],[-10,4*r],[2,0]],s=[[-2,0],[10,-4*r],[10,4*r]],o,u,a,f,l,c=this.context;if(e.visProp.strokecolor!=="none"&&(e.visProp.lastarrow||e.visProp.firstarrow)){if(e.elementClass!==JXG.OBJECT_CLASS_LINE)return;o=t.scrCoords[1],u=t.scrCoords[2],a=n.scrCoords[1],f=n.scrCoords[2],c.save(),this._setColor(e,"stroke","fill")&&(l=Math.atan2(f-u,a-o),e.visProp.lastarrow&&this._drawFilledPolygon(this._translateShape(this._rotateShape(i,l),a,f)),e.visProp.firstarrow&&this._drawFilledPolygon(this._translateShape(this._rotateShape(s,l),o,u))),c.restore()}},updatePathStringPrim:function(e){var t="M",n="L",r="C",i=t,s=5e3,o,u,a,f,l=e.visProp.curvetype!=="plot",c,h=this.context;if(e.numberPoints<=0)return;c=Math.min(e.points.length,e.numberPoints),h.beginPath();if(e.bezierDegree==1){l&&e.board.options.curve.RDPsmoothing&&(e.points=JXG.Math.Numerics.RamerDouglasPeuker(e.points,.5));for(o=0;o<c;o++)u=e.points[o].scrCoords,isNaN(u[1])||isNaN(u[2])?i=t:(u[1]>s?u[1]=s:u[1]<-s&&(u[1]=-s),u[2]>s?u[2]=s:u[2]<-s&&(u[2]=-s),i===t?h.moveTo(u[1],u[2]):h.lineTo(u[1],u[2]),i=n)}else if(e.bezierDegree==3){o=0;while(o<c)u=e.points[o].scrCoords,isNaN(u[1])||isNaN(u[2])?i=t:(i===t?h.moveTo(u[1],u[2]):(o++,a=e.points[o].scrCoords,o++,f=e.points[o].scrCoords,h.bezierCurveTo(u[1],u[2],a[1],a[2],f[1],f[2])),i=r),o++}this._fill(e),this._stroke(e)},updatePathStringBezierPrim:function(e){var t="M",n="C",r=t,i=5e3,s,o,u,a,f,l=e.visProp.strokewidth,c=e.visProp.curvetype!=="plot",h,p=this.context;if(e.numberPoints<=0)return;c&&e.board.options.curve.RDPsmoothing&&(e.points=JXG.Math.Numerics.RamerDouglasPeuker(e.points,.5)),h=Math.min(e.points.length,e.numberPoints),p.beginPath();for(o=1;o<3;o++){r=t;for(s=0;s<h;s++)u=e.points[s].scrCoords,isNaN(u[1])||isNaN(u[2])?r=t:(u[1]>i?u[1]=i:u[1]<-i&&(u[1]=-i),u[2]>i?u[2]=i:u[2]<-i&&(u[2]=-i),r==t?p.moveTo(u[1]+0*l*(2*o*Math.random()-o),u[2]+0*l*(2*o*Math.random()-o)):p.bezierCurveTo(a+(u[1]-a)*.333+l*(2*o*Math.random()-o),f+(u[2]-f)*.333+l*(2*o*Math.random()-o),a+2*(u[1]-a)*.333+l*(2*o*Math.random()-o),f+2*(u[2]-f)*.333+l*(2*o*Math.random()-o),u[1],u[2]),r=n,a=u[1],f=u[2])}this._fill(e),this._stroke(e)},updatePolygonPrim:function(e,t){var n,r,i=t.vertices.length,s=this.context,o=!0;if(i<=0)return;s.beginPath(),r=0;while(!t.vertices[r].isReal&&r<i-1)r++,o=!1;n=t.vertices[r].coords.scrCoords,s.moveTo(n[1],n[2]);for(r=r;r<i-1;r++)t.vertices[r].isReal||(o=!1),n=t.vertices[r].coords.scrCoords,s.lineTo(n[1],n[2]);s.closePath(),o&&this._fill(t)},show:function(e){JXG.exists(e.rendNode)&&(e.rendNode.style.visibility="inherit")},hide:function(e){JXG.exists(e.rendNode)&&(e.rendNode.style.visibility="hidden")},setGradient:function(e){var t,n;n=JXG.evaluate(e.visProp.fillopacity),n=n>0?n:0,t=JXG.evaluate(e.visProp.fillcolor)},setShadow:function(e){if(e.visPropOld.shadow===e.visProp.shadow)return;e.visPropOld.shadow=e.visProp.shadow},highlight:function(e){return e.type===JXG.OBJECT_TYPE_TEXT&&e.visProp.display==="html"?this.updateTextStyle(e,!0):(e.board.prepareUpdate(),e.board.renderer.suspendRedraw(e.board),e.board.updateRenderer(),e.board.renderer.unsuspendRedraw()),this},noHighlight:function(e){return e.type===JXG.OBJECT_TYPE_TEXT&&e.visProp.display==="html"?this.updateTextStyle(e,!1):(e.board.prepareUpdate(),e.board.renderer.suspendRedraw(e.board),e.board.updateRenderer(),e.board.renderer.unsuspendRedraw()),this},suspendRedraw:function(e){this.context.save(),this.context.clearRect(0,0,this.canvasRoot.width,this.canvasRoot.height),e&&e.showCopyright&&this.displayCopyright(JXG.JSXGraph.licenseText,12)},unsuspendRedraw:function(){this.context.restore()},resize:function(e,t){this.container?(this.canvasRoot.style.width=parseFloat(e)+"px",this.canvasRoot.style.height=parseFloat(t)+"px",this.canvasRoot.setAttribute("width",parseFloat(e)+"px"),this.canvasRoot.setAttribute("height",parseFloat(t)+"px")):(this.canvasRoot.width=parseFloat(e),this.canvasRoot.height=parseFloat(t))}});

Subversion Repositories wimsdev

(root)/trunk/wims/public_html/scripts/js/jsxgraph/jsxgraphcore.js – Rev 6939