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\\ Les variables commentes sont mis par defaut dans wims
\\color=red
\\LIM = 15;
\\NTEST = 50;
\\MINDIV = 2; \\
\\MAXCOUNT = 50; \\ ??
\\XDIV = 25; \\ on dcoupe le carr en petits carrs
\\YDIV = 25;
\\ zoom = 4.0;
\\XMIN = (-zoom);
\\YMIN = (-zoom);
\\XMAX = (zoom);
\\YMAX = (zoom);
\\dx(x,y) = funct[1];
\\dy(x,y) = funct[2];
program_gp=ARROW_LEN = 5; \\ taille de la flche\
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 rsultat n'en dpend. Dfinit plutot la precision\
en pixels*/\
height = 200; \\ mettre l'extrieur ?\
\
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());
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