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| Rev | Author | Line No. | Line |
|---|---|---|---|
| 2071 | zjchen | 1 | !goto $wims_read_parm |
| 2 | |||
| 3 | :def |
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| 4 | title=Triangle with given vertices |
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| 5 | synonyme=triangle with vertices |
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| 6 | input=data2d |
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| 7 | !exit |
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| 8 | |||
| 9 | :proc |
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| 10 | !if $cnt!=3 |
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| 11 | error=bad_formula |
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| 12 | !exit |
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| 13 | !endif |
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| 14 | !distribute lines $fml into A,B,C |
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| 15 | pari_header=M=[$fml2]; A=M[1,]; B=M[2,]; C=M[3,];\ |
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| 16 | t1=B-C; s1=sqrt(t1[1]^2+t1[2]^2);\ |
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| 17 | t2=A-C; s2=sqrt(t2[1]^2+t2[2]^2);\ |
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| 18 | t3=A-B; s3=sqrt(t3[1]^2+t3[2]^2); |
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| 19 | result=!exec pari print(s1);\ |
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| 20 | print(s2);\ |
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| 21 | print(s3);\ |
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| 22 | area=abs(t1[1]*t2[2]-t1[2]*t2[1])/2;print(area);\ |
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| 23 | r1=acos((t2[1]*t3[1]+t2[2]*t3[2])/(s2*s3));print(r1);\ |
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| 24 | r2=acos(-(t1[1]*t3[1]+t1[2]*t3[2])/(s1*s3));print(r2);\ |
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| 25 | r3=pi-r1-r2;print(r3);\ |
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| 26 | d1=r1*180/pi;print(d1);\ |
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| 27 | d2=r2*180/pi;print(d2);\ |
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| 28 | d3=r3*180/pi;print(d3);\ |
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| 29 | h1=area/s1*2;print(h1);\ |
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| 30 | h2=area/s2*2;print(h2);\ |
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| 31 | h3=area/s3*2;print(h3);\ |
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| 32 | ri=2*area/(s1+s2+s3);print(ri);\ |
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| 33 | rc=(s1*s2*s3)/(4*area);print(rc);\ |
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| 34 | bc=(A+B+C)/3; print(bc); |
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| 35 | !distribute lines $result into s1,s2,s3,area,r1,r2,r3,d1,d2,d3,h1,h2,h3,\ |
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| 36 | ri,rc,bc |
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| 37 | l=!nonempty lines $result |
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| 38 | c=!linecnt $l |
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| 39 | !if $c<16 |
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| 40 | result= |
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| 41 | !endif |
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| 42 | insdraw_size=200,200 |
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| 43 | !exit |
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| 44 | |||
| 45 | :output |
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| 46 | Plane triangle with 3 vertices |
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| 47 | !distribute items $fml3 into aa,bb,cc |
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| 48 | !htmlmath A = $aa, B = $bb, C = $cc |
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| 49 | :<p> |
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| 50 | Side AB = $[$s3]<br> |
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| 51 | Side BC = $[$s1]<br> |
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| 52 | Side AC = $[$s2]<br> |
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| 53 | Area = $[$area]<br> |
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| 54 | Angle A = $[$d1]° = $[$r1] radians<br> |
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| 55 | Angle B = $[$d3]° = $[$r3] radians<br> |
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| 56 | Angle C = $[$d2]° = $[$r2] radians<br> |
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| 57 | Altitude to side AB = $[$h2]<br> |
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| 58 | Altitude to side BC = $[$h1]<br> |
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| 59 | Altitude to side AC = $[$h3]<p> |
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| 60 | Incircle radius = $[$ri]<br> |
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| 61 | Circumcircle radius = $[$rc]<br> |
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| 62 | Barycenter = ($bc)<br> |
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| 63 | |||
| 64 | <center> |
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| 65 | !!insdraw xrange $X1,$X2\ |
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| 66 | yrange $Y1,$Y2\ |
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| 67 | linewidth 2\ |
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| 68 | polygon blue,0,0,$s3,0,$x,$y\ |
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| 69 | fcircle 0,0,6,red\ |
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| 70 | fcircle $s3,0,6,red\ |
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| 71 | fcircle $x,$y,6,red\ |
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| 72 | text black,$s3*0.4,-0.05*$s3,small,$s3\ |
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| 73 | text black,0.55*$x,0.5*$y,small,$s2\ |
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| 74 | text black,0.53*($s3+$x),0.6*$y,small,$s1\ |
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| 75 | text red,-0.08*$s3,0,small,A\ |
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| 76 | text red,1.05*$s3,0,small,C\ |
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| 77 | text red,$x+0.05*$s3,$y+0.08*$s3,small,B |
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| 78 | |||
| 79 | </center> <br> |
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| 80 | !exit |
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| 81 |