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YouTube-simulations/particle_billiard.c

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/*********************************************************************************/
/* */
/* Animation of particles in billiard */
/* */
/* N. Berglund, december 2012, april 2021 */
/* UPDATE 14 April 21 : graphics files go to subfolder, */
/* Switch MOVIE to decide whether to create a movie */
/* UPDATE 3 May 21 : new domains */
/* */
/* 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 particle_billiard particle_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_part */
/* It may be possible to increase parameter PAUSE */
/* */
/* create movie using */
/* ffmpeg -i part.%05d.tif -vcodec libx264 part.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 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 20 /* choice of domain shape */
#define CIRCLE_PATTERN 2 /* pattern of circles */
#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 NCX 15 /* number of circles in x direction */
#define NCY 20 /* number of circles in y direction */
#define LAMBDA 0.75 /* parameter controlling shape of billiard */
#define MU 0.035 /* second parameter controlling shape of billiard */
#define FOCI 1 /* set to 1 to draw focal points of ellipse */
#define NPOLY 8 /* number of sides of polygon */
#define APOLY 0.25 /* 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 RESAMPLE 0 /* set to 1 if particles should be added when dispersion too large */
#define DEBUG 0 /* draw trajectories, for debugging purposes */
/* Simulation parameters */
#define NPART 30000 /* number of particles */
#define NPARTMAX 100000 /* maximal number of particles after resampling */
#define LMAX 0.01 /* minimal segment length triggering resampling */
#define DMIN 0.02 /* minimal distance to boundary for triggering resampling */
#define CYCLE 1 /* set to 1 for closed curve (start in all directions) */
#define SHOWTRAILS 0 /* set to 1 to keep trails of the particles */
#define NSTEPS 3000 /* number of frames of movie */
#define TIME 1000 /* time between movie frames, for fluidity of real-time simulation */
#define DPHI 0.000005 /* integration step */
#define NVID 150 /* 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 */
/* NVID tells how often a picture is drawn in the animation, increase it for faster anim */
/* For a good quality movie, take for instance TIME = 400, DPHI = 0.00005, NVID = 100 */
/* Colors and other graphical parameters */
#define NCOLORS 32 /* number of colors */
#define COLORSHIFT 0 /* hue of initial color */
#define RAINBOW_COLOR 0 /* set to 1 to use different colors for all particles */
#define FLOWER_COLOR 0 /* set to 1 to adapt initial colors to flower billiard (tracks vs core) */
#define NSEG 100 /* number of segments of boundary */
#define LENGTH 0.02 /* length of velocity vectors */
#define BILLIARD_WIDTH 2 /* width of billiard */
#define PARTICLE_WIDTH 2 /* width of particles */
#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 270.0 /* color outside billiard */
#define PAINT_INT 0 /* set to 1 to paint interior in other color (for polygon/Reuleaux) */
#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 1000 /* final sleeping time */
#include "global_particles.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 */
/* WORKS FOR ELLIPSE, HAS TO BE ADAPTED TO GENERAL BILLIARD */
{
int i;
double ds, da, s, angle, theta, alpha, pos[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),
pos[0] = LAMBDA*cos(s);
pos[1] = sin(s);
theta = argument(-LAMBDA*pos[1], pos[0]/LAMBDA);
alpha = theta + angle;
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;
double conf[2], pos[2];
while (angle2 < angle1) angle2 += DPI;
if (NPART > 1) dalpha = (angle2 - angle1)/((double)(NPART-1));
else dalpha = 0.0;
for (i=0; i<NPART; i++)
{
alpha = angle1 + dalpha*((double)i);
// printf("alpha=%.5lg\n", alpha);
pos[0] = x0;
pos[1] = y0;
vbilliard_xy(configs[i], alpha, pos);
}
}
void init_sym_drop_config(double x0, double y0, double angle1, double angle2, double *configs[NPARTMAX])
/* initialize configuration with two symmetric partial drops */
{
int i;
double dalpha, alpha, meanangle;
double conf[2], pos[2];
while (angle2 < angle1) angle2 += DPI;
meanangle = 0.5*(angle1 + angle2);
dalpha = (angle2 - angle1)/((double)(NPART-1));
for (i=0; i<NPART/2; i++)
{
alpha = meanangle + dalpha*((double)i);
pos[0] = x0;
pos[1] = y0;
vbilliard_xy(configs[i], alpha, pos);
}
for (i=0; i<NPART/2; i++)
{
alpha = meanangle - dalpha*((double)i);
pos[0] = x0;
pos[1] = y0;
vbilliard_xy(configs[NPART/2 + i], alpha, pos);
}
}
void init_line_config(double x0, double y0, double x1, double y1, double angle, double *configs[NPARTMAX])
/* initialize configuration: line (x0,y0)-(x1,y1) in direction alpha */
{
int i;
double dx, dy;
double conf[2], pos[2];
dx = (x1-x0)/((double)(NPART));
dy = (y1-y0)/((double)(NPART));
// dx = (x1-x0)/((double)(NPART-1));
// dy = (y1-y0)/((double)(NPART-1));
for (i=0; i<NPART; i++)
{
pos[0] = x0 + ((double)i)*dx;
pos[1] = y0 + ((double)i)*dy;
vbilliard_xy(configs[i], angle, pos);
}
}
void draw_config(int color[NPARTMAX], double *configs[NPARTMAX], int active[NPARTMAX])
/* draw the particles */
{
int i;
double x1, y1, x2, y2, cosphi, sinphi, rgb[3];
glutSwapBuffers();
if (!SHOWTRAILS) blank();
if (PAINT_INT) paint_billiard_interior();
glLineWidth(PARTICLE_WIDTH);
glEnable(GL_LINE_SMOOTH);
for (i=0; i<nparticles; 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;
cosphi = (configs[i][6] - configs[i][4])/configs[i][3];
sinphi = (configs[i][7] - configs[i][5])/configs[i][3];
x1 = configs[i][4] + configs[i][2]*cosphi;
y1 = configs[i][5] + configs[i][2]*sinphi;
x2 = configs[i][4] + (configs[i][2] + LENGTH)*cosphi;
y2 = configs[i][5] + (configs[i][2] + LENGTH)*sinphi;
/* test whether particle does not escape billiard */
if (active[i]) active[i] = xy_in_billiard(x1, y1);
if (active[i])
{
rgb_color_scheme(color[i], rgb);
glColor3f(rgb[0], rgb[1], rgb[2]);
glBegin(GL_LINE_STRIP);
glVertex2d(SCALING_FACTOR*x1, SCALING_FACTOR*y1);
glVertex2d(SCALING_FACTOR*x2, SCALING_FACTOR*y2);
glEnd ();
/* taking care of boundary conditions - only needed for periodic boundary conditions */
if (PERIODIC_BC)
{
if (SCALING_FACTOR*x2 > XMAX)
{
glBegin(GL_LINE_STRIP);
glVertex2d(SCALING_FACTOR*(x1+XMIN-XMAX), SCALING_FACTOR*y1);
glVertex2d(SCALING_FACTOR*(x2+XMIN-XMAX), SCALING_FACTOR*y2);
glEnd ();
}
if (SCALING_FACTOR*x2 < XMIN)
{
glBegin(GL_LINE_STRIP);
glVertex2d(SCALING_FACTOR*(x1-XMIN+XMAX), SCALING_FACTOR*y1);
glVertex2d(SCALING_FACTOR*(x2-XMIN+XMAX), SCALING_FACTOR*y2);
glEnd ();
}
if (SCALING_FACTOR*y2 > YMAX)
{
glBegin(GL_LINE_STRIP);
glVertex2d(SCALING_FACTOR*x1, SCALING_FACTOR*(y1+YMIN-YMAX));
glVertex2d(SCALING_FACTOR*x2, SCALING_FACTOR*(y2+YMIN-YMAX));
glEnd ();
}
if (SCALING_FACTOR*y2 < YMIN)
{
glBegin(GL_LINE_STRIP);
glVertex2d(SCALING_FACTOR*x1, SCALING_FACTOR*(y1+YMAX-YMIN));
glVertex2d(SCALING_FACTOR*x2, SCALING_FACTOR*(y2+YMAX-YMIN));
glEnd ();
}
}
}
/* draw trajectories, for debugging purpose */
if (DEBUG)
{
glLineWidth(1.0);
glBegin(GL_LINES);
glVertex2d(SCALING_FACTOR*configs[i][4], SCALING_FACTOR*configs[i][5]);
glVertex2d(SCALING_FACTOR*configs[i][6], SCALING_FACTOR*configs[i][7]);
glEnd ();
glLineWidth(3.0);
}
if (configs[i][2] > configs[i][3] - DPHI) configs[i][2] -= configs[i][3];
}
if (DRAW_BILLIARD) draw_billiard();
}
void graph_movie(int time, int color[NPARTMAX], double *configs[NPARTMAX], int active[NPARTMAX])
/* compute next movie frame */
{
int i, j, c;
for (j=0; j<time; j++)
{
for (i=0; i<nparticles; i++)
{
if (configs[i][2]<0.0)
{
// printf("reflecting particle %i\n", i);
c = vbilliard(configs[i]);
// if (c>=0) color[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];
}
}
}
// draw_config(color, configs);
}
void animation()
{
double time, dt, alpha, r;
double *configs[NPARTMAX];
int i, j, resamp = 1, s, i1, i2;
int *color, *newcolor, *active;
/* Since NPARTMAX can be big, it seemed wiser to use some memory allocation here */
color = malloc(sizeof(int)*(NPARTMAX));
newcolor = malloc(sizeof(int)*(NPARTMAX));
active = malloc(sizeof(int)*(NPARTMAX));
for (i=0; i<NPARTMAX; i++)
configs[i] = (double *)malloc(8*sizeof(double));
/* init circle configuration if the domain is D_CIRCLES */
if ((B_DOMAIN == D_CIRCLES)||(B_DOMAIN == D_CIRCLES_IN_RECT)||(B_DOMAIN == D_CIRCLES_IN_GENUSN)) init_circle_config();
/* initialize system by putting particles in a given point with a range of velocities */
r = cos(PI/(double)NPOLY)/cos(DPI/(double)NPOLY);
// init_line_config(-1.25, -0.5, -1.25, 0.5, 0.0, configs);
// init_drop_config(-0.75, 0.0, -0.1, 0.1, configs);
// init_drop_config(0.5, 0.5, -1.0, 1.0, configs);
// init_sym_drop_config(-1.0, 0.5, -PID, PID, configs);
// init_drop_config(-0.999, 0.0, -alpha, alpha, configs);
// other possible initial conditions :
init_line_config(-1.25, -0.5, -1.25, 0.5, 0.0, configs);
// init_line_config(0.0, -0.5, 0.0, 0.5, 0.0, configs);
// init_line_config(-1.25, -0.5, -1.25, 0.5, 0.0*PID, configs);
// init_line_config(-1.0, -0.3, -1.0, 0.3, 0.0, configs);
// init_line_config(-0.7, -0.45, -0.7, 0.45, 0.0, configs);
// init_line_config(-1.5, 0.1, -0.1, 1.0, -0.5*PID, configs);
if (!SHOWTRAILS) blank();
glColor3f(0.0, 0.0, 0.0);
if (DRAW_BILLIARD) draw_billiard();
glutSwapBuffers();
for (i=0; i<NPARTMAX; i++)
{
color[i] = 0;
newcolor[i] = 0;
active[i] = 1;
}
if (FLOWER_COLOR) /* adapt color scheme to flower configuration (beta implementation) */
{
// i1 = (int)((double)NPART*0.2538); /* the 0.27 is just a trial-and-error guess, to be improved */
// i1 = (int)((double)NPART*0.1971); /* the 0.27 is just a trial-and-error guess, to be improved */
i1 = (int)((double)NPART*0.3015); /* the 0.27 is just a trial-and-error guess, to be improved */
i2 = NPART-i1;
for (i=i1; i<i2; i++)
{
color[i] += NCOLORS/3;
newcolor[i] = NCOLORS/3;
}
for (i=i2; i<NPART; i++)
{
color[i] += 2*NCOLORS/3;
newcolor[i] = 2*NCOLORS/3;
}
}
if (RAINBOW_COLOR) /* rainbow color scheme */
for (i=0; i<NPART; i++)
{
color[i] = (i*NCOLORS)/NPART;
newcolor[i] = (i*NCOLORS)/NPART;
}
sleep(SLEEP1);
for (i=0; i<=NSTEPS; i++)
{
graph_movie(TIME, newcolor, configs, active);
draw_config(newcolor, configs, active);
if (DRAW_BILLIARD) draw_billiard();
for (j=0; j<NPARTMAX; j++) color[j] = newcolor[j];
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_part/");
}
}
}
if (MOVIE)
{
for (i=0; i<20; i++) save_frame();
s = system("mv part*.tif tif_part/");
}
free(color);
free(newcolor);
for (i=0; i<NPARTMAX; i++) free(configs[i]);
}
void display(void)
{
glPushMatrix();
blank();
if (!SHOWTRAILS)
{
glutSwapBuffers();
blank();
glutSwapBuffers();
}
animation();
sleep(SLEEP2);
glPopMatrix();
}
int main(int argc, char** argv)
{
glutInit(&argc, argv);
if (SHOWTRAILS) glutInitDisplayMode(GLUT_RGB | GLUT_SINGLE | GLUT_DEPTH);
else glutInitDisplayMode(GLUT_RGB | GLUT_DOUBLE | GLUT_DEPTH);
// glutInitDisplayMode(GLUT_RGB | GLUT_DOUBLE | GLUT_DEPTH);
glutInitWindowSize(WINWIDTH,WINHEIGHT);
glutCreateWindow("Billiard animation");
init();
glutDisplayFunc(display);
glutMainLoop();
return 0;
}
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