Subversion Repositories wimsdev

\\ Les variables commentées sont mis par defaut dans wims

\\color=red
\\LIM = 15; 
\\NTEST  =  50;
\\MINDIV  =  2; \\
\\MAXCOUNT  =  50; \\ ??
\\XDIV  =  25; \\ on découpe le carré en petits carrés
\\YDIV  =  25;
\\ zoom =  4.0; 
\\XMIN  =  (-zoom);
\\YMIN  =  (-zoom);
\\XMAX  =  (zoom);
\\YMAX  =  (zoom);
\\dx(x,y) = funct[1]; 
\\dy(x,y) = funct[2];
ARROW_LEN  =  5; \\ taille de la flèche
ARROW_WIDTH = 8;
XSTEP  =  1.0*(XMAX-XMIN)/XDIV;
YSTEP  =  1.0*((YMAX-YMIN)/YDIV);
XDEN  =  (1.0/XSTEP);
YDEN  =  (1.0/YSTEP);
RAND_MAX  =  2^31;
MIN_STEP  =  2; /* minimum steps to draw arrows */
width = 200; /*en fait le résultat n'en dépend. Définit plutot la precision
en pixels*/
height = 200; \\à mettre à l'extérieur ?

pr  =  matrix(XDIV,YDIV); /* footprint */
xr  =  matrix(XDIV,YDIV);
nr  =  matrix(XDIV,YDIV); /* used by get_point() */

gxden = 1.*width/(XMAX - XMIN);
gxden1  =  gxden^(-1); 
gyden = 1.*height/(YMAX - YMIN);
gyden1  =  gyden^(-1); 

img  =  [];
ARROW = matrix(7,1);
transx( x)  =  round((x - XMIN)*XDEN);
transy( y)  =  round((y - YMIN)*YDEN);

/* returns 0 for success,  - 1 for out - of - bound or already - gone - to (x,y) 
et met 1 dans la matrice pr */

footprint( px, py)  = 
{
  if (px >= 1 && px <=  XDIV && py >= 1 && py<= YDIV && !pr[px,py], 
    pr[px,py]  =  1; 0, - 1
  );
}

/* returns 0 for success, -1 for fail */
get_point()  = 
{
  local(div, i, j,
  mdiv, mi = 0, mj = 0,found);   
  mdiv = 0;
  div = 1;
  xr  =   pr; 
  while (1,
      if (div > XDIV, break); 
      found = 0;
      for (i = 1, XDIV-div+1,
       for (j = 1,YDIV-div+1,
        if (xr[i,j] == 0,
         found = 1; mdiv = div;
         mi = i; mj = j; break;
        )
       )
      );
      if (!found, break);
       xr  =  matrix(XDIV-div,YDIV-div,i,j,
       if( (xr[i,j]+xr[i,j+1]+xr[i+1,j]+xr[i+1,j+1]), 1, 0)
        );
      div ++;
    );
  if (mdiv >=  MINDIV, 
      x0  =  XMIN + (mi + (mdiv - 1)*0.5)*XSTEP;
      y0  =  YMIN + (mj + (mdiv - 1)*0.5)*YSTEP;
      return(0)
     ,
      return(-1)
  );
}

draw_init()  =  pr  =   matrix(XDIV,YDIV);   
 
frand( mmin,  mmax) = mmin + (mmax - mmin)*random(RAND_MAX)/RAND_MAX*1.;


get_dt()  = 
{
  local(dt,
   x1, y1, xp, yp, i);
  
  dt = 1.0;
\\ initialiser au hasard le random ??

  for (i = 1, NTEST,
      x1 = frand(XMIN, XMAX);
      y1 = frand(YMIN, YMAX);
\\    xp = abs(subst(subst( dx, x,x1), y,y1));
\\    yp = abs(subst(subst( dy, x,x1), y,y1));
      xp = abs(dx(x1,y1));
      yp = abs(dy(x1,y1));
      if (xp*dt > XSTEP, dt = XSTEP/xp);
      if (yp*dt > YSTEP, dt = YSTEP/yp);
    );
  dt*0.5; /* for precision */
}

do_loop( x0,  y0,  dt)  = 
{
  local(i, count = 0, steps = 0,
   px, py, x1,y1, lx, ly,
   xa  = vector(5), ya  = vector(5),img1);
   x1  =  x0; y1  =  y0;
   img1 = [round((x1 - XMIN)*gxden)*gxden1 + XMIN, round((y1 - YMIN)*gyden)*gyden1 + YMIN]; 
   while (1,
      steps ++;
      px = transx(x1); py = transy(y1);
      if (footprint(px, py)<0 && steps > 1, break);
      lx = x1; ly = y1;
      count = 0;
      while (count < MAXCOUNT,
        count ++;
        xa[1] = x1; ya[1] = y1;
        for (i = 2, 5,
        xa[i] = xa[1] + dx(xa[i-1],ya[i-1])*dt;
        ya[i] = ya[1] + dy(xa[i-1],ya[i-1])*dt
         ); 
        x1 = (xa[2]+2.0*xa[3]+xa[4]-xa[5])*(1/3.0);
        y1 = (ya[2]+2.0*ya[3]+ya[4]-ya[5])*(1/3.0);
        if (transx(x1) !=  px, break);
        if (transy(y1) !=  py, break);
      );
      if (dt>0 && steps == 1,
        dir_angle =  if( x1 !=  x0, atan((y1-y0)/(x1-x0))+if(x1-x0 <0,Pi,0), sign(y1-y0)*Pi/2)); 
      img2  =  [round((x1-XMIN)*gxden)*gxden1 + XMIN, round((y1-YMIN)*gyden)*gyden1 + YMIN]; 
      img1  =  concat( img1, img2); 
    );
  img  =  concat(img, [mattranspose(img1)]); 
 steps;
}

draw_main( dt)  = 
{ local(x0, y0, px0, py0, px1, py1, px2, py2, px3, py3,
   step1, step2); 
  x0 = 0; y0 = 0;
  draw_init();
  test  =  0; test1  =  0;
  while(test  >=  0 && test1 < LIM,
   test1 ++;
   step1 = do_loop(x0, y0, dt);
   step2 = do_loop(x0, y0, -dt);
   if (step1 >= MIN_STEP+1 && step2 >= MIN_STEP, /* draw an arrow */
    px0 = round((x0-XMIN)*gxden)*gxden1 + XMIN;
    py0 = round((y0-YMIN)*gyden)*gyden1 + YMIN;
    px1 = px0+round(ARROW_LEN*cos(dir_angle))*gxden1;
    py1 = py0+round(ARROW_LEN*sin(dir_angle))*gyden1;
          ARROW  =  concat(ARROW, [arrow; px0;py0;px1;py1;ARROW_WIDTH;color])
   );
  test  =  get_point(); 
  );
 ARROW;
}

draw_main(get_dt());