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This commit is contained in:
nilsberglund-orleans
2021-05-29 16:50:49 +02:00
committed by GitHub
parent c5137a51c5
commit bd6aa073a7
6 changed files with 2319 additions and 855 deletions
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195
drop_billiard.c
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@@ -33,14 +33,18 @@
#define WINWIDTH 1280 /* window width */
#define WINHEIGHT 720 /* window height */
#define XMIN -2.0
#define XMAX 2.0 /* x interval */
#define YMIN -1.125
#define YMAX 1.125 /* y interval for 9/16 aspect ratio */
#define XMIN -1.8
#define XMAX 1.8 /* x interval */
#define YMIN -0.91
#define YMAX 1.115 /* y interval for 9/16 aspect ratio */
// #define XMIN -2.0
// #define XMAX 2.0 /* x interval */
// #define YMIN -1.125
// #define YMAX 1.125 /* y interval for 9/16 aspect ratio */
/* Choice of the billiard table */
#define B_DOMAIN 5 /* choice of domain shape */
#define B_DOMAIN 9 /* choice of domain shape */
#define D_RECTANGLE 0 /* rectangular domain */
#define D_ELLIPSE 1 /* elliptical domain */
@@ -48,36 +52,59 @@
#define D_SINAI 3 /* Sinai billiard */
#define D_DIAMOND 4 /* diamond-shaped billiard */
#define D_TRIANGLE 5 /* triangular billiard */
#define D_ANNULUS 7 /* annulus */
#define D_POLYGON 8 /* polygon */
#define D_REULEAUX 9 /* Reuleaux and star shapes */
// #define LAMBDA 1.5 /* parameter controlling shape of billiard */
#define LAMBDA 1.73205080756888 /* sqrt(3) for triangle tiling plane */
// #define LAMBDA 1.0 /* parameter controlling shape of billiard */
#define LAMBDA 1.124950941 /* sin(36°)/sin(31.5°) for 5-star shape with 45° angles */
// #define LAMBDA 1.445124904 /* sin(36°)/sin(24°) for 5-star shape with 60° angles */
// #define LAMBDA 3.75738973 /* sin(36°)/sin(9°) for 5-star shape with 90° angles */
// #define LAMBDA -1.73205080756888 /* -sqrt(3) for Reuleaux triangle */
// #define LAMBDA 1.73205080756888 /* sqrt(3) for triangle tiling plane */
#define MU 0.1 /* second parameter controlling shape of billiard */
#define FOCI 1 /* set to 1 to draw focal points of ellipse */
#define NPOLY 5 /* number of sides of polygon */
#define APOLY -1.0 /* angle by which to turn polygon, in units of Pi/2 */
#define RESAMPLE 0 /* set to 1 if particles should be added when dispersion too large */
#define NPART 10000 /* number of particles */
#define NPARTMAX 20000 /* maximal number of particles after resampling */
#define LMAX 0.01 /* minimal segment length triggering resampling */
#define LPERIODIC 2.0 /* lines longer than this are not drawn (useful for Sinai billiard) */
#define DMIN 0.02 /* minimal distance to boundary for triggering resampling */
#define MARGIN 1.0 /* distance above which points of curve are not drawn */
#define CYCLE 0 /* set to 1 for closed curve (start in all directions) */
#define NPART 100000 /* number of particles */
#define NPARTMAX 100000 /* maximal number of particles after resampling */
#define NSTEPS 10000 /* number of frames of movie */
#define TIME 100 /* time between movie frames, for fluidity of real-time simulation */
#define DPHI 0.0001 /* integration step */
#define NVID 50 /* number of iterations between images displayed on screen */
#define NCOLORS 10 /* number of colors */
#define COLORSHIFT 200 /* hue of initial color */
#define NSEG 100 /* number of segments of boundary */
#define BLACK 1 /* set to 1 for black background */
#define NSTEPS 4000 /* number of frames of movie */
#define TIME 15 /* time between movie frames, for fluidity of real-time simulation */
#define DPHI 0.0001 /* integration step */
#define NVID 10 /* number of iterations between images displayed on screen */
/* Decreasing TIME accelerates the animation and the movie */
/* For constant speed of movie, TIME*DPHI should be kept constant */
/* However, increasing DPHI too much deterioriates quality of simulation */
/* For a good quality movie, take for instance TIME = 50, DPHI = 0.0002 */
/* simulation parameters */
#define LMAX 0.01 /* minimal segment length triggering resampling */
#define LPERIODIC 1.0 /* lines longer than this are not drawn (useful for Sinai billiard) */
#define LCUT 1000.0 /* controls the max size of segments not considered as being cut */
#define DMIN 0.02 /* minimal distance to boundary for triggering resampling */
#define CYCLE 0 /* set to 1 for closed curve (start in all directions) */
#define ORDER_COLORS 1 /* set to 1 if colors should be drawn in order */
/* color and other graphical parameters */
#define NCOLORS 10 /* number of colors */
#define COLORSHIFT 200 /* hue of initial color */
#define NSEG 100 /* number of segments of boundary */
#define BILLIARD_WIDTH 4 /* width of billiard */
#define FRONT_WIDTH 3 /* width of wave front */
#define BLACK 1 /* set to 1 for black background */
#define COLOR_OUTSIDE 0 /* set to 1 for colored outside */
#define OUTER_COLOR 300.0 /* color outside billiard */
#define PAINT_INT 1 /* set to 1 to paint interior in other color (for polygon) */
#define PAUSE 1000 /* number of frames after which to pause */
#define PSLEEP 1 /* sleep time during pause */
#define SLEEP1 1 /* initial sleeping time */
@@ -89,6 +116,7 @@
#include "sub_part_billiard.c"
/*********************/
/* animation part */
/*********************/
@@ -126,7 +154,8 @@ double *configs[NPARTMAX];
double dalpha, alpha, pos[2];
while (angle2 < angle1) angle2 += DPI;
dalpha = (angle2 - angle1)/((double)(NPART-1));
dalpha = (angle2 - angle1)/((double)(NPART));
// dalpha = (angle2 - angle1)/((double)(NPART-1));
for (i=0; i<NPART; i++)
{
alpha = angle1 + dalpha*((double)i);
@@ -227,37 +256,26 @@ double *configs[NPARTMAX];
else return(1);
}
void draw_config(color, configs)
/* draw the wave front */
/* draw the wave front by ordering colors */
int color[NPARTMAX];
double *configs[NPARTMAX];
{
int i;
double x1, y1, x2, y2, cosphi, sinphi, rgb[3], dist;
double x1, y1, x2, y2, cosphi, sinphi, rgb[3], dist, dmax;
glutSwapBuffers();
blank();
if (PAINT_INT) paint_billiard_interior();
glLineWidth(5.0);
glLineWidth(FRONT_WIDTH);
glEnable(GL_LINE_SMOOTH);
if (CYCLE) glBegin (GL_LINE_LOOP);
else glBegin(GL_LINE_STRIP);
for (i=0; i<nparticles; i++)
{
// print_config(configs[i]);
if (configs[i][2]<0.0)
{
vbilliard(configs[i]);
color[i]++;
if (color[i] >= NCOLORS) color[i] -= NCOLORS;
}
configs[i][2] += DPHI;
{
cosphi = (configs[i][6] - configs[i][4])/configs[i][3];
sinphi = (configs[i][7] - configs[i][5])/configs[i][3];
x2 = configs[i][4] + configs[i][2]*cosphi;
@@ -266,18 +284,20 @@ double *configs[NPARTMAX];
/* determine length of segment to avoid drawing too long segments */
if (i>0) dist = module2(x2-x1,y2-y1);
else dist = 0.0;
dmax = DPI*((double)global_time)*DPHI/((double)nparticles);
/* expected maximal distance between points for growing circle */
rgb_color_scheme(color[i], rgb);
glColor3d(rgb[0], rgb[1], rgb[2]);
/* draw line only if it does not exceed */
if ((xy_in_billiard(x2, y2))&&(dist < LPERIODIC)) glVertex2d(x2, y2);
/* draw line only if it does not exceed LPERIODIC and 2*dmax */
if ((xy_in_billiard(x2, y2))&&(dist < LPERIODIC)&&(dist < LCUT*dmax)) glVertex2d(x2, y2);
else
{
glEnd();
glBegin (GL_LINE_STRIP);
}
if (configs[i][2] > configs[i][3] - DPHI) configs[i][2] -= configs[i][3];
@@ -290,6 +310,67 @@ double *configs[NPARTMAX];
}
void draw_ordered_config(color, configs)
/* draw the wave front, one color after the other */
int color[NPARTMAX];
double *configs[NPARTMAX];
{
int i, col;
double x1, y1, x2, y2, cosphi, sinphi, rgb[3], dist, dmax;
glutSwapBuffers();
blank();
if (PAINT_INT) paint_billiard_interior();
glLineWidth(FRONT_WIDTH);
glEnable(GL_LINE_SMOOTH);
for (col=0; col<NCOLORS; col++)
{
glBegin(GL_LINE_STRIP);
for (i=0; i<nparticles; i++)
{
if (color[i] == col)
{
cosphi = (configs[i][6] - configs[i][4])/configs[i][3];
sinphi = (configs[i][7] - configs[i][5])/configs[i][3];
x2 = configs[i][4] + configs[i][2]*cosphi;
y2 = configs[i][5] + configs[i][2]*sinphi;
/* determine length of segment to avoid drawing too long segments */
if (i>0) dist = module2(x2-x1,y2-y1);
else dist = 0.0;
dmax = DPI*((double)global_time)*DPHI/((double)nparticles);
/* expected maximal distance between points for growing circle */
rgb_color_scheme(color[i], rgb);
glColor3d(rgb[0], rgb[1], rgb[2]);
/* draw line only if it does not exceed LPERIODIC and 2*dmax */
if ((i>0)&&(xy_in_billiard(x2, y2))&&(dist < LPERIODIC)&&(dist < LCUT*dmax)) glVertex2d(x2, y2);
else
{
glEnd();
glBegin (GL_LINE_STRIP);
}
if (configs[i][2] > configs[i][3] - DPHI) configs[i][2] -= configs[i][3];
/* keep track of previous point to determine segment length */
x1 = x2;
y1 = y2;
}
}
glEnd ();
}
draw_billiard(LAMBDA);
}
void graph_movie(time, color, configs)
/* compute next movie frame */
int time, color[NPARTMAX];
@@ -299,6 +380,7 @@ double *configs[NPARTMAX];
for (j=0; j<time; j++)
{
global_time++;
for (i=0; i<nparticles; i++)
{
// print_config(configs[i]);
@@ -315,9 +397,6 @@ double *configs[NPARTMAX];
if (configs[i][2] > configs[i][3] - DPHI) configs[i][2] -= configs[i][3];
}
}
draw_config(color, configs);
}
void graph_no_movie(time, color, configs)
@@ -329,10 +408,9 @@ double *configs[NPARTMAX];
for (j=0; j<time; j++)
{
global_time++;
for (i=0; i<nparticles; i++)
{
// print_config(configs[i]);
if (configs[i][2]<0.0)
{
vbilliard(configs[i]);
@@ -347,9 +425,6 @@ double *configs[NPARTMAX];
if (configs[i][2] > configs[i][3] - DPHI) configs[i][2] -= configs[i][3];
}
}
draw_config(color, configs);
draw_billiard(color, configs);
}
@@ -368,20 +443,15 @@ void animation()
for (i=0; i<NPARTMAX; i++)
configs[i] = (double *)malloc(8*sizeof(double));
init_drop_config(0.0, -0.5, 0.0, DPI, configs);
// init_drop_config(0.0, -1.0, 0.0, PI, configs);
// init_drop_config(0.95, 0.95, PI, 3.0*DPI, configs);
// init_drop_config(1.4, 0.9, DPI, configs);
init_drop_config(0.0, 0.1, 0.0, DPI, configs);
// init_boundary_config(1.5, 1.5, 0.0, PI, configs);
// other possible initial conditions :
// init_drop_config(sqrt(LAMBDA*LAMBDA-1.0) - 0.1,0.0, 0.0, DPI, configs); /* Start at focus */
// init_boundary_config(0.0, 0.0, 0.0, PI, configs);
// init_drop_config(LAMBDA-0.01, 0.0, PID, 3.0*PID, configs);
blank();
glColor3d(0.0, 0.0, 0.0);
draw_billiard(LAMBDA);
if (PAINT_INT) paint_billiard_interior();
glutSwapBuffers();
@@ -395,6 +465,11 @@ void animation()
if (MOVIE) graph_movie(TIME, color, configs);
else graph_no_movie(NVID, color, configs);
if (ORDER_COLORS) draw_ordered_config(color, configs);
else draw_config(color, configs);
draw_billiard();
/* for the ellipse, paths passing close to the foci are stronly divergent
* and the configurations may need to be resampled be adding extra points */
if ((RESAMPLE)&&(i % 5 == 0)&&(nparticles < NPARTMAX)) resamp = resample(color, configs);