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YouTube-simulations/drop_billiard.c

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/*********************************************************************************/
/* */
/* Animation of wave front in billiard */
/* */
/* N. Berglund, december 2012, april 2021 */
/* */
/* Feel free to reuse, but if doing so it would be nice to drop a */
/* line to nils.berglund@univ-orleans.fr - Thanks! */
/* */
/* compile with */
/* gcc -o drop_billiard drop_billiard.c */
/* -O3 -L/usr/X11R6/lib -ltiff -lm -lGL -lGLU -lX11 -lXmu -lglut */
/* */
/* */
/* To make a video, set MOVIE to 1 and create subfolder tif_drop */
/* It may be possible to increase parameter PAUSE */
/* */
/* create movie using */
/* ffmpeg -i part.%05d.tif -vcodec libx264 drop.mp4 */
/* */
/*********************************************************************************/
#include <math.h>
#include <string.h>
#include <GL/glut.h>
#include <GL/glu.h>
#include <unistd.h>
#include <sys/types.h>
#include <tiffio.h> /* Sam Leffler's libtiff library. */
#define MOVIE 0 /* set to 1 to generate movie */
#define SAVE_MEMORY 1 /* set to 1 to save memory when writing tiff images */
#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 SCALING_FACTOR 1.0 /* scaling factor of drawing, needed for flower billiards, otherwise set to 1.0 */
/* Choice of the billiard table, see global_particles.c */
#define B_DOMAIN 1 /* choice of domain shape */
#define CIRCLE_PATTERN 0 /* pattern of circles */
#define POLYLINE_PATTERN 1 /* pattern of polyline */
#define ABSORBING_CIRCLES 0 /* set to 1 for circular scatterers to be absorbing */
#define NMAXCIRCLES 1000 /* total number of circles (must be at least NCX*NCY for square grid) */
#define NMAXPOLY 1000 /* total number of sides of polygonal line */
// #define NCX 10 /* number of circles in x direction */
// #define NCY 15 /* number of circles in y direction */
#define NCX 15 /* number of circles in x direction */
#define NCY 20 /* number of circles in y direction */
#define NPOISSON 500 /* number of points for Poisson C_RAND_POISSON arrangement */
#define NGOLDENSPIRAL 2000 /* max number of points for C_GOLDEN_SPIRAL arrandement */
#define SDEPTH 1 /* Sierpinski gastket depth */
#define LAMBDA 1.5 /* parameter controlling the dimensions of domain */
// #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 0.7 /* parameter controlling the dimensions of domain */
#define FOCI 1 /* set to 1 to draw focal points of ellipse */
#define NPOLY 4 /* number of sides of polygon */
#define APOLY 0.0 /* angle by which to turn polygon, in units of Pi/2 */
#define DRAW_BILLIARD 1 /* set to 1 to draw billiard */
#define DRAW_CONSTRUCTION_LINES 1 /* set to 1 to draw additional construction lines for billiard */
#define PERIODIC_BC 0 /* set to 1 to enforce periodic boundary conditions when drawing particles */
#define PENROSE_RATIO 2.5 /* parameter controlling the shape of small ellipses in Penrose room */
#define RESAMPLE 1 /* set to 1 if particles should be added when dispersion too large */
#define NPART 20000 /* number of particles */
#define NPARTMAX 100000 /* maximal number of particles after resampling */
#define NSTEPS 5250 /* number of frames of movie */
#define TIME 150 /* time between movie frames, for fluidity of real-time simulation */
#define DPHI 0.0001 /* integration step */
#define NVID 75 /* 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 0.1 /* minimal segment length triggering resampling */
#define LPERIODIC 0.5 /* lines longer than this are not drawn (useful for Sinai billiard) */
#define LCUT 10000000.0 /* controls the max size of segments not considered as being cut */
#define DMIN 0.1 /* minimal distance to boundary for triggering resampling */
#define CYCLE 0 /* set to 1 for closed curve (start in all directions) */
#define ORDER_COLORS 0 /* set to 1 if colors should be drawn in order */
/* color and other graphical parameters */
#define COLOR_PALETTE 14 /* Color palette, see list in global_pdes.c */
#define NCOLORS 16 /* number of colors */
#define COLORSHIFT 3 /* hue of initial color */
#define COLOR_HUEMIN 0 /* minimal color hue */
#define COLOR_HUEMAX 360 /* maximal color hue */
#define RAINBOW_COLOR 0 /* set to 1 to use different colors for all particles */
#define NSEG 100 /* number of segments of boundary */
#define BILLIARD_WIDTH 4 /* width of billiard */
#define FRONT_WIDTH 4 /* 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 0 /* set to 1 to paint interior in other color (for polygon) */
#define PAINT_EXT 1 /* set to 1 to paint exterior of billiard */
#define PAUSE 1000 /* number of frames after which to pause */
#define PSLEEP 1 /* sleep time during pause */
#define SLEEP1 1 /* initial sleeping time */
#define SLEEP2 100 /* final sleeping time */
#define END_FRAMES 25 /* number of frames at end of movie */
#define NXMAZE 8 /* width of maze */
#define NYMAZE 8 /* height of maze */
#define MAZE_MAX_NGBH 4 /* max number of neighbours of maze cell */
#define RAND_SHIFT 58 /* seed of random number generator */
#define MAZE_XSHIFT 0.0 /* horizontal shift of maze */
#define MAZE_RANDOM_FACTOR 0.1 /* randomization factor for S_MAZE_RANDOM */
#define MAZE_CORNER_RADIUS 0.5 /* radius of tounded corners in maze */
#define CLOSE_MAZE 0 /* set to 1 to close maze exits */
#define PI 3.141592654
#define DPI 6.283185307
#define PID 1.570796327
#include "global_particles.c"
#include "sub_maze.c"
#include "sub_part_billiard.c"
/*********************/
/* animation part */
/*********************/
void init_boundary_config(double smin, double smax, double anglemin, double anglemax, double *configs[NPARTMAX])
/* initialize configuration: drop on the boundary, beta version */
{
int i;
double ds, da, s, angle, alpha, pos[2], conf[2];
if (anglemin <= 0.0) anglemin = PI/((double)NPART);
if (anglemax >= PI) anglemax = PI*(1.0 - 1.0/((double)NPART));
ds = (smax - smin)/((double)NPART);
da = (anglemax - anglemin)/((double)NPART);
for (i=0; i<NPART; i++)
{
s = smin + ds*((double)i);
angle = anglemin + da*((double)i);
conf[0] = s;
conf[1] = angle;
pos_billiard(conf, pos, &alpha);
vbilliard_xy(configs[i], alpha, pos);
}
}
void init_drop_config(double x0, double y0, double angle1, double angle2, double *configs[NPARTMAX])
/* initialize configuration: drop at (x0,y0) */
{
int i;
double dalpha, alpha, pos[2];
while (angle2 < angle1) angle2 += DPI;
dalpha = (angle2 - angle1)/((double)(NPART));
// dalpha = (angle2 - angle1)/((double)(NPART-1));
for (i=0; i<NPART; i++)
{
alpha = angle1 + dalpha*((double)i);
pos[0] = x0;
pos[1] = y0;
vbilliard_xy(configs[i], alpha, pos);
}
}
void init_partial_drop_config(int i1, int i2, double x0, double y0, double angle1, double angle2, double *configs[NPARTMAX])
/* initialize configuration: drop at (x0,y0) */
{
int i;
double dalpha, alpha, pos[2];
while (angle2 < angle1) angle2 += DPI;
dalpha = (angle2 - angle1)/((double)(i2 - i1));
if (i2 >= NPART) i2 = NPART;
for (i=i1; i<i2; i++)
{
alpha = angle1 + dalpha*((double)i);
pos[0] = x0;
pos[1] = y0;
vbilliard_xy(configs[i], alpha, pos);
}
}
int resample(int color[NPARTMAX], double *configs[NPARTMAX])
/* add particles where the front is stretched too thin */
{
int len, i, j, k, iplus, newnparticles=nparticles, *newcolor;
double dx, dy, pos[2], s1, s2, s, x, y, x1, y1, theta, alpha, beta, length2;
double *newconfigs[NPARTMAX];
/* Since NPARTMAX can be big, it seemed wiser to use some memory allocation here */
newcolor = malloc(sizeof(int)*(NPARTMAX));
for (i=0; i<NPARTMAX; i++)
newconfigs[i] = (double *)malloc(8*sizeof(double));
printf("resampling, %i particles\n", nparticles);
newnparticles=nparticles;
j = 0;
for (i=0; i<nparticles; i++)
{
iplus = i+1;
if (iplus==nparticles)
if (CYCLE) iplus = 0;
else iplus = nparticles - 1;
for (k=0; k<8; k++) newconfigs[j][k] = configs[i][k];
newcolor[j] = color[i];
dx = configs[iplus][4] - configs[i][4];
dy = configs[iplus][5] - configs[i][5];
length2 = dx*dx + dy*dy;
/* add a particle if length too big, but only if particles are of the same color,
and not too close to the boundary, to avoid problems due to roundoff */
if ((color[i]==color[iplus])&&(length2 > LMAX*LMAX)&&(configs[i][2] < configs[i][3] - DMIN))
{
// print_config(configs[i]);
if (newnparticles < NPARTMAX)
{
j++;
newnparticles++;
// printf("Adding one point at %i, %i particles \n", j, newnparticles);
newcolor[j] = color[i];
s1 = configs[i][0];
s2 = configs[iplus][0];
s = 0.5*(s1 + s2);
if (vabs(s-s1) > PID) s += PI; /* needed if s1, s2 close to 0 and Pi */
while (s<0) s += DPI;
while (s>DPI) s -= DPI;
x1 = LAMBDA*cos(s);
y1 = sin(s);
x = 0.5*(configs[i][4] + configs[iplus][4]);
y = 0.5*(configs[i][5] + configs[iplus][5]);
theta = argument(-LAMBDA*y1,x1/LAMBDA);
alpha = argument(x1-x,y1-y);
beta = theta-alpha;
while (beta<0) beta += PI;
while (beta>PI) beta -= PI;
newconfigs[j][0] = s;
newconfigs[j][1] = theta - alpha;
newconfigs[j][2] = 0.5*(configs[i][2] + configs[iplus][2]);
newconfigs[j][3] = module2(x-x1,y-y1);
newconfigs[j][4] = x;
newconfigs[j][5] = y;
newconfigs[j][6] = x1;
newconfigs[j][7] = y1;
// print_config(newconfigs[j]);
}
}
j++;
}
if ((newnparticles > nparticles)&&(newnparticles < NPARTMAX))
{
for (i=0; i<newnparticles; i++)
{
for (k=0; k<8; k++)
configs[i][k] = newconfigs[i][k];
color[i] = newcolor[i];
}
}
// if (newnparticles == NPARTMAX) printf("Warning: Cannot add more particles\n");
nparticles = newnparticles;
free(newcolor);
for (i=0; i<NPARTMAX; i++) free(newconfigs[i]);
if (newnparticles == NPARTMAX) return(0);
else return(1);
}
void draw_config(int color[NPARTMAX], double *configs[NPARTMAX])
/* draw the particles */
{
int i;
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);
if (CYCLE) glBegin (GL_LINE_LOOP);
else glBegin(GL_LINE_STRIP);
for (i=0; i<nparticles; i++)
{
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 ((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 draw_ordered_config(int color[NPARTMAX], double *configs[NPARTMAX])
/* draw the wave front, one color after the other */
{
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(int time, int color[NPARTMAX], double *configs[NPARTMAX])
/* compute next movie frame */
{
int i, j;
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]);
if (!RAINBOW_COLOR)
{
color[i]++;
if (color[i] >= NCOLORS) color[i] -= NCOLORS;
}
}
configs[i][2] += DPHI;
if (configs[i][2] > configs[i][3] - DPHI) configs[i][2] -= configs[i][3];
}
}
}
void graph_no_movie(int time, int color[NPARTMAX], double *configs[NPARTMAX])
/* plot next image without making a movie */
{
int i, j;
for (j=0; j<time; j++)
{
global_time++;
for (i=0; i<nparticles; i++)
{
if (configs[i][2]<0.0)
{
vbilliard(configs[i]);
// print_config(configs[i]);
color[i]++;
if (color[i] >= NCOLORS) color[i] -= NCOLORS;
}
configs[i][2] += DPHI;
if (configs[i][2] > configs[i][3] - DPHI) configs[i][2] -= configs[i][3];
}
}
}
void animation()
{
// double time, dt;
double *configs[NPARTMAX];
int i, resamp = 1, s;
int *color;
/* Since NPARTMAX can be big, it seemed wiser to use some memory allocation here */
color = malloc(sizeof(int)*(NPARTMAX));
for (i=0; i<NPARTMAX; i++)
configs[i] = (double *)malloc(8*sizeof(double));
init_drop_config(0.0, 0.0, 0.0, DPI, configs);
// init_partial_drop_config(0, NPART/4, LAMBDA, 0.0, 0.0, DPI, configs);
// init_partial_drop_config(NPART/4, NPART/2, -LAMBDA, 0.0, 0.0, DPI, configs);
// init_partial_drop_config(NPART/2, 3*NPART/4, 0.0, LAMBDA, 0.0, DPI, configs);
// init_partial_drop_config(3*NPART/4, NPART, 0.0, -LAMBDA, 0.0, DPI, configs);
// init_drop_config(-1.0 + 0.3*sqrt(2.0), -1.0 + 0.5*sqrt(2.0), 0.0, DPI, configs);
// init_drop_config(-0.5, -0.5, 0.0, DPI, configs);
// init_boundary_config(1.5, 1.5, 0.0, PI, configs);
blank();
glColor3d(0.0, 0.0, 0.0);
draw_billiard(LAMBDA);
if (PAINT_INT) paint_billiard_interior();
glutSwapBuffers();
for (i=0; i<NPARTMAX; i++) color[i] = 0;
if (RAINBOW_COLOR) /* rainbow color scheme */
for (i=0; i<NPART; i++) color[i] = (i*NCOLORS)/NPART;
sleep(SLEEP1);
for (i=0; i<=NSTEPS; i++)
{
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);
if (!resamp) printf("Warning: Cannot add more particles\n");
if (MOVIE)
{
save_frame();
/* it seems that saving too many files too fast can cause trouble with the file system */
/* so this is to make a pause from time to time - parameter PAUSE may need adjusting */
if (i % PAUSE == PAUSE - 1)
{
printf("Making a short pause\n");
sleep(PSLEEP);
s = system("mv part*.tif tif_drop/");
}
}
}
if (MOVIE)
{
for (i=0; i<END_FRAMES; i++) save_frame();
s = system("mv part*.tif tif_drop/");
}
free(color);
for (i=0; i<NPARTMAX; i++) free(configs[i]);
}
void display(void)
{
glPushMatrix();
blank();
glutSwapBuffers();
blank();
glutSwapBuffers();
animation();
sleep(SLEEP2);
glPopMatrix();
}
int main(int argc, char** argv)
{
glutInit(&argc, argv);
glutInitDisplayMode(GLUT_RGB | GLUT_DOUBLE | GLUT_DEPTH);
glutInitWindowSize(WINWIDTH,WINHEIGHT);
glutCreateWindow("Wave front in billiard");
init();
glutDisplayFunc(display);
glutMainLoop();
return 0;
}
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