980 lines
34 KiB
C
980 lines
34 KiB
C
/*********************************************************************************/
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/* */
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/* Animation of particles in billiard */
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/* */
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/* N. Berglund, december 2012, april 2021 */
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/* UPDATE 14 April 21 : graphics files go to subfolder, */
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/* Switch MOVIE to decide whether to create a movie */
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/* UPDATE 3 May 21 : new domains */
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/* */
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/* Feel free to reuse, but if doing so it would be nice to drop a */
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/* line to nils.berglund@univ-orleans.fr - Thanks! */
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/* */
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/* compile with */
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/* gcc -o particle_billiard particle_billiard.c */
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/* -O3 -L/usr/X11R6/lib -ltiff -lm -lGL -lGLU -lX11 -lXmu -lglut */
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/* */
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/* To make a video, set MOVIE to 1 and create subfolder tif_part */
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/* It may be possible to increase parameter PAUSE */
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/* */
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/* create movie using */
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/* ffmpeg -i part.%05d.tif -vcodec libx264 part.mp4 */
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/* */
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/*********************************************************************************/
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#include <math.h>
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#include <string.h>
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#include <GL/glut.h>
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#include <GL/glu.h>
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#include <unistd.h>
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#include <sys/types.h>
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#include <tiffio.h> /* Sam Leffler's libtiff library. */
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#define MOVIE 0 /* set to 1 to generate movie */
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#define WINWIDTH 1280 /* window width */
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#define WINHEIGHT 720 /* window height */
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#define XMIN -4.0
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#define XMAX 4.0 /* x interval */
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#define YMIN -1.25
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#define YMAX 3.25 /* y interval for 9/16 aspect ratio */
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// #define XMIN -2.0
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// #define XMAX 2.0 /* x interval */
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// #define YMIN -1.125
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// #define YMAX 1.125 /* y interval for 9/16 aspect ratio */
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#define BOXYMIN -1.0
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#define BOXYMAX 1.0 /* y dimensions of box (for circles in rectangle) */
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#define SCALING_FACTOR 1.0 /* scaling factor of drawing, needed for flower billiards, otherwise set to 1.0 */
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/* Choice of the billiard table, see global_particles.c */
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#define B_DOMAIN 23 /* choice of domain shape */
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#define CIRCLE_PATTERN 7 /* pattern of circles */
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#define POLYLINE_PATTERN 1 /* pattern of polyline */
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// #define CIRCLE_PATTERN 21 /* pattern of circles */
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#define ABSORBING_CIRCLES 0 /* set to 1 for circular scatterers to be absorbing */
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#define NMAXCIRCLES 5000 /* total number of circles (must be at least NCX*NCY for square grid) */
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#define NMAXPOLY 1000 /* total number of sides of polygonal line */
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#define NCX 44 /* number of circles in x direction */
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#define NCY 10 /* number of circles in y direction */
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#define NPOISSON 350 /* number of points for Poisson C_RAND_POISSON arrangement */
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#define NGOLDENSPIRAL 2000 /* max number of points for C_GOLDEN_SPIRAL arrandement */
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#define SDEPTH 1 /* Sierpinski gastket depth */
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#define LAMBDA 3.8 /* parameter controlling shape of domain */
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// #define MU 0.1 /* second parameter controlling shape of billiard */
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#define MU 0.07 /* second parameter controlling shape of billiard */
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// #define MU 0.085 /* second parameter controlling shape of billiard */
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// #define MU 0.09 /* second parameter controlling shape of billiard */
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// #define MU 0.034 /* second parameter controlling shape of billiard */
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#define FOCI 1 /* set to 1 to draw focal points of ellipse */
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#define NPOLY 4 /* number of sides of polygon */
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#define APOLY 0.5 /* angle by which to turn polygon, in units of Pi/2 */
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#define DRAW_BILLIARD 1 /* set to 1 to draw billiard */
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#define DRAW_CONSTRUCTION_LINES 0 /* set to 1 to draw additional construction lines for billiard */
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#define PERIODIC_BC 0 /* set to 1 to enforce periodic boundary conditions when drawing particles */
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#define RESAMPLE 0 /* set to 1 if particles should be added when dispersion too large */
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#define DEBUG 0 /* draw trajectories, for debugging purposes */
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/* Simulation parameters */
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#define NPART 1 /* number of particles */
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#define NPARTMAX 100000 /* maximal number of particles after resampling */
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#define LMAX 0.01 /* minimal segment length triggering resampling */
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#define DMIN 0.02 /* minimal distance to boundary for triggering resampling */
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#define CYCLE 1 /* set to 1 for closed curve (start in all directions) */
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#define SHOWTRAILS 0 /* set to 1 to keep trails of the particles */
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#define TEST_ACTIVE 0 /* set to 1 to test whether particle is in billiard */
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#define NSTEPS 10400 /* number of frames of movie */
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// #define NSTEPS 1000 /* number of frames of movie */
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// #define TIME 1500 /* time between movie frames, for fluidity of real-time simulation */
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#define TIME 4000 /* time between movie frames, for fluidity of real-time simulation */
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// #define DPHI 0.0001 /* integration step */
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// #define DPHI 0.00002 /* integration step */
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#define DPHI 0.00007 /* integration step */
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// #define DPHI 0.000035 /* integration step */
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#define NVID 150 /* number of iterations between images displayed on screen */
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/* Decreasing TIME accelerates the animation and the movie */
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/* For constant speed of movie, TIME*DPHI should be kept constant */
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/* However, increasing DPHI too much deterioriates quality of simulation */
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/* NVID tells how often a picture is drawn in the animation, increase it for faster anim */
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/* For a good quality movie, take for instance TIME = 400, DPHI = 0.00005, NVID = 100 */
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/* Colors and other graphical parameters */
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#define COLOR_PALETTE 1 /* Color palette, see list in global_pdes.c */
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// #define NCOLORS 256 /* number of colors */
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#define NCOLORS 48 /* number of colors */
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#define COLORSHIFT 2 /* hue of initial color */
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#define RAINBOW_COLOR 1 /* set to 1 to use different colors for all particles */
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#define SINGLE_COLOR 1 /* set to 1 to make all particles a single color */
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#define FLOWER_COLOR 0 /* set to 1 to adapt initial colors to flower billiard (tracks vs core) */
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#define NSEG 100 /* number of segments of boundary */
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#define LENGTH 0.1 /* length of velocity vectors */
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#define BILLIARD_WIDTH 2 /* width of billiard */
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#define PARTICLE_WIDTH 4 /* width of particles */
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#define FRONT_WIDTH 3 /* width of wave front */
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// #define COLOR_TRAJECTORY 0 /* hue for single color */
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#define COLOR_TRAJECTORY 8 /* hue for single color */
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#define BLACK 1 /* set to 1 for black background */
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#define COLOR_OUTSIDE 0 /* set to 1 for colored outside */
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#define OUTER_COLOR 270.0 /* color outside billiard */
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#define PAINT_INT 0 /* set to 1 to paint interior in other color (for polygon/Reuleaux) */
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#define PAINT_EXT 0 /* set to 1 to paint exterior in other color */
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#define ERASE_OUTSIDE 1 /* set to 1 to erase outside of rectangular billiard (beta) */
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#define PAUSE 500 /* number of frames after which to pause */
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#define PSLEEP 5 /* sleep time during pause */
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#define SLEEP1 1 /* initial sleeping time */
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#define SLEEP2 1000 /* final sleeping time */
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#define END_FRAMES 100 /* number of still frames at end of movie */
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#define NPATHBINS 200 /* number of bins for path length histogramm */
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#define PATHLMAX 1.8 /* max free path on graph */
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#include "global_particles.c"
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#include "sub_part_billiard.c"
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#include "sub_part_pinball.c"
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int ncol = 0, nobst = 0, nmaxpeg = 0;
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int npath[NPATHBINS];
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double max_free_path = 0.0;
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/*********************/
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/* animation part */
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/*********************/
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void init_boundary_config(double smin, double smax, double anglemin, double anglemax, double *configs[NPARTMAX])
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/* initialize configuration: drop on the boundary, beta version */
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/* WORKS FOR ELLIPSE, HAS TO BE ADAPTED TO GENERAL BILLIARD */
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{
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int i;
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double ds, da, s, angle, theta, alpha, pos[2];
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if (anglemin <= 0.0) anglemin = PI/((double)NPART);
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if (anglemax >= PI) anglemax = PI*(1.0 - 1.0/((double)NPART));
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ds = (smax - smin)/((double)NPART);
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da = (anglemax - anglemin)/((double)NPART);
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for (i=0; i<NPART; i++)
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{
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s = smin + ds*((double)i);
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angle = anglemin + da*((double)i),
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pos[0] = LAMBDA*cos(s);
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pos[1] = sin(s);
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theta = argument(-LAMBDA*pos[1], pos[0]/LAMBDA);
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alpha = theta + angle;
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vbilliard_xy(configs[i], alpha, pos);
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}
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}
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void init_drop_config(double x0, double y0, double angle1, double angle2, double *configs[NPARTMAX])
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/* initialize configuration: drop at (x0,y0) */
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{
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int i;
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double dalpha, alpha;
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double conf[2], pos[2];
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while (angle2 < angle1) angle2 += DPI;
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if (NPART > 1) dalpha = (angle2 - angle1)/((double)(NPART-1));
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else dalpha = 0.0;
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for (i=0; i<NPART; i++)
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{
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alpha = angle1 + dalpha*((double)i);
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// printf("alpha=%.5lg\n", alpha);
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pos[0] = x0;
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pos[1] = y0;
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vbilliard_xy(configs[i], alpha, pos);
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}
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}
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void init_sym_drop_config(double x0, double y0, double angle1, double angle2, double *configs[NPARTMAX])
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/* initialize configuration with two symmetric partial drops */
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{
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int i;
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double dalpha, alpha, meanangle;
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double conf[2], pos[2];
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while (angle2 < angle1) angle2 += DPI;
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meanangle = 0.5*(angle1 + angle2);
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dalpha = (angle2 - angle1)/((double)(NPART-1));
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for (i=0; i<NPART/2; i++)
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{
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alpha = meanangle + dalpha*((double)i);
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pos[0] = x0;
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pos[1] = y0;
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vbilliard_xy(configs[i], alpha, pos);
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}
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for (i=0; i<NPART/2; i++)
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{
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alpha = meanangle - dalpha*((double)i);
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pos[0] = x0;
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pos[1] = y0;
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vbilliard_xy(configs[NPART/2 + i], alpha, pos);
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}
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}
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void init_line_config(double x0, double y0, double x1, double y1, double angle, double *configs[NPARTMAX])
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/* initialize configuration: line (x0,y0)-(x1,y1) in direction alpha */
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{
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int i;
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double dx, dy;
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double conf[2], pos[2];
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dx = (x1-x0)/((double)(NPART));
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dy = (y1-y0)/((double)(NPART));
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// dx = (x1-x0)/((double)(NPART-1));
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// dy = (y1-y0)/((double)(NPART-1));
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for (i=0; i<NPART; i++)
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{
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pos[0] = x0 + ((double)i)*dx;
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pos[1] = y0 + ((double)i)*dy;
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vbilliard_xy(configs[i], angle, pos);
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}
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}
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void draw_config_showtrails(int color[NPARTMAX], double *configs[NPARTMAX], int active[NPARTMAX])
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/* draw the particles */
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{
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int i;
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double x0, y0, x1, y1, x2, y2, cosphi, sinphi, rgb[3], len;
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glutSwapBuffers();
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if (PAINT_INT) paint_billiard_interior();
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glLineWidth(PARTICLE_WIDTH);
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glEnable(GL_LINE_SMOOTH);
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for (i=0; i<nparticles; i++)
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{
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// if (configs[i][2]<0.0)
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// {
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// vbilliard(configs[i]);
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// if (!RAINBOW_COLOR)
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// {
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// color[i]++;
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// if (color[i] >= NCOLORS) color[i] -= NCOLORS;
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// }
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// }
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configs[i][2] += DPHI;
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cosphi = (configs[i][6] - configs[i][4])/configs[i][3];
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sinphi = (configs[i][7] - configs[i][5])/configs[i][3];
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len = configs[i][2] + LENGTH;
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if (len > configs[i][3]) len = configs[i][3];
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x0 = configs[i][4];
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y0 = configs[i][5];
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x1 = configs[i][4] + configs[i][2]*cosphi;
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y1 = configs[i][5] + configs[i][2]*sinphi;
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x2 = configs[i][4] + len*cosphi;
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y2 = configs[i][5] + len*sinphi;
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/* test whether particle does not escape billiard */
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if ((TEST_ACTIVE)&&(active[i])) active[i] = xy_in_billiard(x1, y1);
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if (active[i])
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{
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rgb_color_scheme(color[i], rgb);
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glColor3f(rgb[0], rgb[1], rgb[2]);
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glBegin(GL_LINE_STRIP);
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glVertex2d(SCALING_FACTOR*x0, SCALING_FACTOR*y0);
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glVertex2d(SCALING_FACTOR*x2, SCALING_FACTOR*y2);
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glEnd ();
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}
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// if (configs[i][2] > configs[i][3] - DPHI)
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// {
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// glBegin(GL_LINE_STRIP);
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// glVertex2d(SCALING_FACTOR*x0, SCALING_FACTOR*y0);
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// glVertex2d(SCALING_FACTOR*configs[i][6], SCALING_FACTOR*configs[i][7]);
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// glEnd ();
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// }
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}
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if (DRAW_BILLIARD) draw_billiard();
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}
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void draw_config(int color[NPARTMAX], double *configs[NPARTMAX], int active[NPARTMAX])
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/* draw the particles */
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{
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int i;
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double x0, y0, x1, y1, x2, y2, cosphi, sinphi, rgb[3];
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glutSwapBuffers();
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if (!SHOWTRAILS) blank();
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if (PAINT_INT) paint_billiard_interior();
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glLineWidth(PARTICLE_WIDTH);
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glEnable(GL_LINE_SMOOTH);
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for (i=0; i<nparticles; i++)
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{
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// if (configs[i][2]<0.0)
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// {
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// vbilliard(configs[i]);
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// if (!RAINBOW_COLOR)
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// {
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// color[i]++;
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// if (color[i] >= NCOLORS) color[i] -= NCOLORS;
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// }
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// }
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configs[i][2] += DPHI;
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cosphi = (configs[i][6] - configs[i][4])/configs[i][3];
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sinphi = (configs[i][7] - configs[i][5])/configs[i][3];
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x1 = configs[i][4] + configs[i][2]*cosphi;
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y1 = configs[i][5] + configs[i][2]*sinphi;
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x2 = configs[i][4] + (configs[i][2] + LENGTH)*cosphi;
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y2 = configs[i][5] + (configs[i][2] + LENGTH)*sinphi;
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/* test whether particle does not escape billiard */
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if ((TEST_ACTIVE)&&(active[i])) active[i] = xy_in_billiard(x1, y1);
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if (active[i])
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{
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rgb_color_scheme(color[i], rgb);
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glColor3f(rgb[0], rgb[1], rgb[2]);
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glBegin(GL_LINE_STRIP);
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glVertex2d(SCALING_FACTOR*x1, SCALING_FACTOR*y1);
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glVertex2d(SCALING_FACTOR*x2, SCALING_FACTOR*y2);
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glEnd ();
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/* taking care of boundary conditions - only needed for periodic boundary conditions */
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if (PERIODIC_BC)
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{
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if (SCALING_FACTOR*x2 > XMAX)
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{
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glBegin(GL_LINE_STRIP);
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glVertex2d(SCALING_FACTOR*(x1+XMIN-XMAX), SCALING_FACTOR*y1);
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glVertex2d(SCALING_FACTOR*(x2+XMIN-XMAX), SCALING_FACTOR*y2);
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glEnd ();
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}
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if (SCALING_FACTOR*x2 < XMIN)
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{
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glBegin(GL_LINE_STRIP);
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glVertex2d(SCALING_FACTOR*(x1-XMIN+XMAX), SCALING_FACTOR*y1);
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glVertex2d(SCALING_FACTOR*(x2-XMIN+XMAX), SCALING_FACTOR*y2);
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glEnd ();
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}
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if (SCALING_FACTOR*y2 > YMAX)
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{
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glBegin(GL_LINE_STRIP);
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glVertex2d(SCALING_FACTOR*x1, SCALING_FACTOR*(y1+YMIN-YMAX));
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glVertex2d(SCALING_FACTOR*x2, SCALING_FACTOR*(y2+YMIN-YMAX));
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glEnd ();
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}
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if (SCALING_FACTOR*y2 < YMIN)
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{
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glBegin(GL_LINE_STRIP);
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glVertex2d(SCALING_FACTOR*x1, SCALING_FACTOR*(y1+YMAX-YMIN));
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glVertex2d(SCALING_FACTOR*x2, SCALING_FACTOR*(y2+YMAX-YMIN));
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glEnd ();
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}
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}
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}
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/* draw trajectories, for debugging purpose */
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if (DEBUG)
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{
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glLineWidth(1.0);
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glBegin(GL_LINES);
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glVertex2d(SCALING_FACTOR*configs[i][4], SCALING_FACTOR*configs[i][5]);
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glVertex2d(SCALING_FACTOR*configs[i][6], SCALING_FACTOR*configs[i][7]);
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glEnd ();
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glLineWidth(3.0);
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}
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// if (configs[i][2] > configs[i][3] - DPHI) configs[i][2] -= configs[i][3];
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}
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if (DRAW_BILLIARD) draw_billiard();
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}
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void graph_movie(int time, int color[NPARTMAX], double *configs[NPARTMAX], int active[NPARTMAX])
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/* compute next movie frame */
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{
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int i, j, k, c;
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double rgb[3];
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static double total_pathlength = 0.0;
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for (j=0; j<time; j++)
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{
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for (i=0; i<nparticles; i++)
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{
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if (configs[i][2]<0.0)
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{
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// printf("reflecting particle %i\n", i);
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if ((SHOWTRAILS)&&(active[i]))
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{
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glLineWidth(PARTICLE_WIDTH);
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rgb_color_scheme(color[i], rgb);
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glColor3f(rgb[0], rgb[1], rgb[2]);
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glBegin(GL_LINE_STRIP);
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glVertex2d(SCALING_FACTOR*configs[i][4], SCALING_FACTOR*configs[i][5]);
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glVertex2d(SCALING_FACTOR*configs[i][6], SCALING_FACTOR*configs[i][7]);
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glEnd ();
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}
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total_pathlength += configs[i][3];
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c = vbilliard(configs[i]);
|
|
|
|
/* update number of collisions, not counting boundary for periodic b.c. */
|
|
if (B_DOMAIN != D_CIRCLES_IN_TORUS) ncol++;
|
|
else if (c >= 0) ncol++;
|
|
|
|
if ((c >= 0)&&(circles[c].color == 0)) nobst++;
|
|
circles[c].color++;
|
|
|
|
/* take care of circles doubled because of periodic boundary conditions */
|
|
if ((circles[c].active)&&(B_DOMAIN == D_CIRCLES_IN_TORUS)&&(circles[c].partner != c)) circles[circles[c].partner].color++;
|
|
|
|
circles[c].new = 10;
|
|
|
|
/* update free path statistics */
|
|
if (ncol > 1) /* disregard very first collision */
|
|
{
|
|
if (B_DOMAIN != D_CIRCLES_IN_TORUS)
|
|
{
|
|
k = (int)((double)NPATHBINS*configs[i][3]/PATHLMAX);
|
|
if (k < NPATHBINS) npath[k]++;
|
|
if (total_pathlength > max_free_path) max_free_path = total_pathlength;
|
|
total_pathlength = 0.0;
|
|
}
|
|
else /* case with periodic boundary conditions */
|
|
{
|
|
if (c >= 0) /* a circle is hit, update histogram */
|
|
{
|
|
// printf("total path length %.3lg\n", total_pathlength);
|
|
k = (int)((double)NPATHBINS*total_pathlength/PATHLMAX);
|
|
if (k < NPATHBINS) npath[k]++;
|
|
if (total_pathlength > max_free_path) max_free_path = total_pathlength;
|
|
total_pathlength = 0.0;
|
|
}
|
|
}
|
|
}
|
|
|
|
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 print_particle_numbers(double *configs[NPARTMAX])
|
|
{
|
|
char message[50], message1[50];
|
|
double cosphi, x1;
|
|
static double rgb[3], xleft, xright;
|
|
static short int first = 1;
|
|
int i, nleft = 0, nmid = 0, nright = 0;
|
|
|
|
rgb[0] = 0.0; rgb[1] = 0.0; rgb[2] = 0.0;
|
|
|
|
if (first) /* compute box limits */
|
|
{
|
|
/* find leftmost and rightmost circle */
|
|
for (i=0; i<ncircles; i++)
|
|
if ((circles[i].active)&&(circles[i].xc - circles[i].radius < xleft)) xleft = circles[i].xc - circles[i].radius;
|
|
for (i=0; i<ncircles; i++)
|
|
if ((circles[i].active)&&(circles[i].xc + circles[i].radius > xright)) xright = circles[i].xc + circles[i].radius;
|
|
|
|
first = 0;
|
|
|
|
printf("xleft = %.3lg, xright = %.3lg", xleft, xright);
|
|
}
|
|
|
|
for (i=0; i<nparticles; i++)
|
|
{
|
|
cosphi = (configs[i][6] - configs[i][4])/configs[i][3];
|
|
x1 = configs[i][4] + configs[i][2]*cosphi;
|
|
|
|
if (x1 > xright) nright++;
|
|
else if (x1 < xleft) nleft++;
|
|
else nmid++;
|
|
|
|
// if (i == nparticles-1) printf("x1 = %.3lg, nleft = %i, nright = %i\n", x1, nleft, nright);
|
|
}
|
|
|
|
erase_area(XMIN + 0.31, YMIN + 0.07, 0.24, 0.05, rgb);
|
|
sprintf(message, "%4d particles", nleft);
|
|
glColor3f(1.0, 1.0, 1.0);
|
|
write_text_fixedwidth(XMIN + 0.1, YMIN + 0.04, message);
|
|
|
|
erase_area(0.0, YMIN + 0.07, 0.24, 0.05, rgb);
|
|
sprintf(message, "%4d particles", nmid);
|
|
glColor3f(1.0, 1.0, 1.0);
|
|
write_text_fixedwidth(-0.21, YMIN + 0.04, message);
|
|
|
|
erase_area(XMAX - 0.29, YMIN + 0.07, 0.24, 0.05, rgb);
|
|
sprintf(message, "%4d particles", nright);
|
|
glColor3f(1.0, 1.0, 1.0);
|
|
write_text_fixedwidth(XMAX - 0.5, YMIN + 0.04, message);
|
|
}
|
|
|
|
void draw_statistics()
|
|
{
|
|
int i, n, colmax = 55, pegcollisions[90], nypegs = 70, meanpegs = 0, meansquarepegs = 0, total_coll = 0, ymax = 0,
|
|
meanbins = 0, meansquarebins, total_bin = 0, stephits = 10, tickstephits = 1;
|
|
double x, y, yscale = 110.0, y0, dx, rgb[3], xshift, coll_mean, coll_stdv, path_mean, path_stdv, ebin, len_over_bin,
|
|
steppath = 0.5;
|
|
char message[50];
|
|
|
|
glLineWidth(1);
|
|
|
|
y0 = 0.5*(YMAX + YMIN) + 0.2;
|
|
dx = (XMAX-0.6)/(double)colmax;
|
|
xshift = XMIN + 0.3;
|
|
rgb[0] = 0.0; rgb[1] = 0.0; rgb[2] = 1.0;
|
|
|
|
/* histogram of number of collisions per peg */
|
|
for (i=0; i<colmax; i++) pegcollisions[i] = 0;
|
|
|
|
for (i=0; i<ncircles; i++) if ((circles[i].active)&&(!circles[i].double_circle))
|
|
{
|
|
n = circles[i].color;
|
|
if (n < colmax) pegcollisions[n]++;
|
|
}
|
|
for (i=1; i<colmax; i++)
|
|
{
|
|
total_coll += pegcollisions[i];
|
|
meanpegs += i*pegcollisions[i];
|
|
meansquarepegs += i*i*pegcollisions[i];
|
|
}
|
|
|
|
for (i=1; i<colmax; i++)
|
|
{
|
|
x = xshift + (double)i*dx;
|
|
y = y0 + (double)pegcollisions[i]*YMAX/yscale;
|
|
|
|
rgb_color_scheme(i, rgb);
|
|
erase_rectangle(x, y0, x+dx, y, rgb);
|
|
}
|
|
|
|
glColor3f(1.0, 1.0, 1.0);
|
|
glBegin(GL_LINE_STRIP);
|
|
/* histogram */
|
|
for (i=0; i<colmax; i++)
|
|
{
|
|
x = xshift + (double)i*dx;
|
|
y = y0 + (double)pegcollisions[i]*YMAX/yscale;
|
|
glVertex2d(x, y0);
|
|
glVertex2d(x, y);
|
|
glVertex2d(x+dx, y);
|
|
glVertex2d(x+dx, y0);
|
|
glVertex2d(x, y0);
|
|
}
|
|
glVertex2d(xshift, y0);
|
|
glVertex2d(xshift, y0 + (double)nypegs*YMAX/yscale);
|
|
glEnd ();
|
|
|
|
/* graduation and labels */
|
|
for (i=10; i<nypegs; i+=10)
|
|
{
|
|
glBegin(GL_LINE_STRIP);
|
|
glVertex2d(xshift - 0.025, y0 + (double)i*YMAX/yscale);
|
|
glVertex2d(xshift + 0.025, y0 + (double)i*YMAX/yscale);
|
|
glEnd ();
|
|
}
|
|
|
|
for (i=tickstephits; i<colmax; i+=tickstephits)
|
|
{
|
|
glBegin(GL_LINE_STRIP);
|
|
glVertex2d(xshift + (double)i*dx, y0 - 0.025);
|
|
glVertex2d(xshift + (double)i*dx, y0 + 0.025);
|
|
glEnd ();
|
|
}
|
|
|
|
for (i=stephits; i<nypegs - stephits; i+=stephits)
|
|
{
|
|
sprintf(message, "%4d", i);
|
|
write_text_fixedwidth(xshift + (double)i*dx - 0.15, y0 - 0.12, message);
|
|
}
|
|
|
|
for (i=10; i<nypegs; i+=10)
|
|
{
|
|
sprintf(message, "%4d", i);
|
|
write_text_fixedwidth(xshift - 0.3, y0 - 0.025 + (double)i*YMAX/yscale, message);
|
|
}
|
|
|
|
coll_mean = (double)meanpegs/(double)total_coll;
|
|
coll_stdv = sqrt((double)meansquarepegs/(double)total_coll - coll_mean*coll_mean);
|
|
|
|
|
|
sprintf(message, "hits");
|
|
write_text_fixedwidth(xshift + (double)(colmax-3)*dx, y0 - 0.12, message);
|
|
sprintf(message, "pegs");
|
|
write_text_fixedwidth(xshift - 0.25, y0 - 0.025 + (double)(nypegs - 3)*YMAX/yscale, message);
|
|
// sprintf(message, "Mean %.4lg", (double)meanpegs/(double)total_coll);
|
|
|
|
sprintf(message, "Max hits/peg %d", nmaxpeg);
|
|
write_text(-1.5, YMAX - 0.3, message);
|
|
|
|
sprintf(message, "Mean hits/peg %.4lg", coll_mean);
|
|
write_text(-1.5, YMAX - 0.5, message);
|
|
|
|
sprintf(message, "Stdv hits/peg %.4lg", coll_stdv);
|
|
write_text(-1.5, YMAX - 0.7, message);
|
|
|
|
|
|
/* histogram of path lengths */
|
|
|
|
for (i=1; i<NPATHBINS; i++)
|
|
{
|
|
if (npath[i] > ymax) ymax = npath[i];
|
|
total_bin += npath[i];
|
|
meanbins += i*npath[i];
|
|
meansquarebins += i*i*npath[i];
|
|
}
|
|
|
|
yscale = 0.9*(YMAX-y0)*(double)ymax;
|
|
dx = (XMAX-0.6)/(double)NPATHBINS;
|
|
xshift = 0.3;
|
|
rgb[0] = 1.0; rgb[1] = 0.0; rgb[2] = 0.0;
|
|
|
|
for (i=1; i<NPATHBINS; i++)
|
|
{
|
|
x = xshift + (double)i*dx;
|
|
y = y0 + (double)npath[i]*YMAX/yscale;
|
|
|
|
if (y > y0) erase_rectangle(x, y0, x+dx, y, rgb);
|
|
}
|
|
|
|
glColor3f(1.0, 1.0, 1.0);
|
|
glBegin(GL_LINE_STRIP);
|
|
/* histogram */
|
|
for (i=1; i<NPATHBINS; i++) if (npath[i] > 0)
|
|
{
|
|
x = xshift + (double)i*dx;
|
|
y = y0 + (double)npath[i]*YMAX/yscale;
|
|
glVertex2d(x, y0);
|
|
glVertex2d(x, y);
|
|
glVertex2d(x+dx, y);
|
|
glVertex2d(x+dx, y0);
|
|
glVertex2d(x, y0);
|
|
}
|
|
glEnd ();
|
|
|
|
glBegin(GL_LINE_STRIP);
|
|
glVertex2d(xshift, YMAX - 0.1);
|
|
glVertex2d(xshift, y0);
|
|
glVertex2d(xshift + (double)NPATHBINS*dx, y0);
|
|
glEnd ();
|
|
|
|
|
|
for (x = steppath; x < PATHLMAX; x+=steppath)
|
|
{
|
|
i = (int)(x*(double)NPATHBINS/PATHLMAX);
|
|
sprintf(message, "%.2f", x);
|
|
write_text_fixedwidth(xshift + (double)i*dx - 0.1, y0 - 0.12, message);
|
|
}
|
|
|
|
for (x = steppath; x < PATHLMAX; x+=steppath)
|
|
{
|
|
i = (int)(x*(double)NPATHBINS/PATHLMAX);
|
|
glBegin(GL_LINE_STRIP);
|
|
glVertex2d(xshift + (double)i*dx, y0 - 0.025);
|
|
glVertex2d(xshift + (double)i*dx, y0 + 0.025);
|
|
glEnd ();
|
|
}
|
|
|
|
|
|
ebin = (double)meanbins/(double)total_bin; /* mean bin */
|
|
len_over_bin = PATHLMAX/(double)NPATHBINS; /* conversion from bin to path length */
|
|
path_mean = ebin*len_over_bin; /* mean free path */
|
|
path_stdv = sqrt((double)meansquarebins/(double)total_bin - ebin*ebin)*len_over_bin;
|
|
|
|
sprintf(message, "free path");
|
|
write_text_fixedwidth(XMAX - 0.6, y0 - 0.12, message);
|
|
|
|
sprintf(message, "Max free path %.4lg", max_free_path);
|
|
write_text(2.2, YMAX - 0.3, message);
|
|
|
|
sprintf(message, "Mean free path %.4lg", path_mean);
|
|
write_text(2.2, YMAX - 0.5, message);
|
|
|
|
sprintf(message, "Stdv free path %.4lg", path_stdv);
|
|
write_text(2.2, YMAX - 0.7, message);
|
|
}
|
|
|
|
|
|
void animation(int circle_config)
|
|
{
|
|
double time, dt, alpha, r;
|
|
double *configs[NPARTMAX];
|
|
int i, j, resamp = 1, s, i1, i2;
|
|
int *color, *newcolor, *active;
|
|
char message[50];
|
|
|
|
/* 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)
|
|
// ||(B_DOMAIN == D_CIRCLES_IN_TORUS))
|
|
// init_circle_config_pinball(circle_config);
|
|
|
|
/* 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)
|
|
||(B_DOMAIN == D_CIRCLES_IN_TORUS)) init_circles_pinball(circle_config, circles);
|
|
|
|
|
|
/* remove discs that are not in domain */
|
|
if ((B_DOMAIN == D_CIRCLES_IN_RECT)||(B_DOMAIN == D_CIRCLES_IN_GENUSN))
|
|
// ||(B_DOMAIN == D_CIRCLES_IN_TORUS))
|
|
for (i=0; i<ncircles; i++)
|
|
{
|
|
if (vabs(circles[i].xc) + circles[i].radius > 0.99) circles[i].active = 0;
|
|
if (vabs(circles[i].xc) + circles[i].radius > 0.99*LAMBDA) circles[i].active = 0;
|
|
}
|
|
else if (B_DOMAIN == D_CIRCLES_IN_TORUS)
|
|
for (i=0; i<ncircles; i++)
|
|
{
|
|
if (vabs(circles[i].yc) - circles[i].radius > 1.0) circles[i].active = 0;
|
|
if (vabs(circles[i].xc) - circles[i].radius > LAMBDA) circles[i].active = 0;
|
|
}
|
|
|
|
// for (i=0; i<ncircles; i++)
|
|
// printf("Circle %i at (%.2f, %.2f), double %i, partner %i\n", i, circlex[i], circley[i], double_circle[i], partner_circle[i]);
|
|
|
|
// if (vabs(circley[i]) > 1.0) circleactive[i] = 0;
|
|
|
|
/* initialize system by putting particles in a given point with a range of velocities */
|
|
r = cos(PI/(double)NPOLY)/cos(DPI/(double)NPOLY);
|
|
|
|
// init_drop_config(0.4, 0.0, PID, 0.5*PID, configs);
|
|
init_drop_config(0.0, 0.0, -0.45*PID, 0.45*PID, configs);
|
|
|
|
// init_line_config(-1.25, -0.5, -1.25, 0.5, 0.0, configs);
|
|
// init_drop_config(0.5, 0.1, -0.5*PID, 0.5*PID, configs);
|
|
// init_drop_config(-1.4, 0.0, -0.5*PID, 0.5*PID, 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(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();
|
|
blank();
|
|
glColor3f(0.0, 0.0, 0.0);
|
|
if (DRAW_BILLIARD) draw_billiard();
|
|
if (ERASE_OUTSIDE) erase_rectangle_outside(270.0, 0.1, 0.15);
|
|
// print_particle_numbers(configs);
|
|
|
|
glutSwapBuffers();
|
|
|
|
// if (MOVIE)
|
|
// {
|
|
// for (i=0; i<20; i++) save_frame();
|
|
// s = system("mv part*.tif tif_part/");
|
|
// }
|
|
|
|
|
|
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;
|
|
}
|
|
|
|
if (SINGLE_COLOR)
|
|
for (i=0; i<NPART; i++)
|
|
{
|
|
color[i] = COLOR_TRAJECTORY;
|
|
newcolor[i] = COLOR_TRAJECTORY;
|
|
}
|
|
|
|
for (i=0; i<NPATHBINS; i++) npath[i] = 0;
|
|
|
|
sleep(SLEEP1);
|
|
|
|
for (i=0; i<=NSTEPS; i++)
|
|
{
|
|
graph_movie(TIME, newcolor, configs, active);
|
|
|
|
if (SHOWTRAILS) draw_config_showtrails(newcolor, configs, active);
|
|
else draw_config(newcolor, configs, active);
|
|
if (DRAW_BILLIARD) draw_billiard();
|
|
if (ERASE_OUTSIDE) erase_rectangle_outside(270.0, 0.1, 0.15);
|
|
// print_particle_numbers(configs);
|
|
|
|
sprintf(message, "%d collisions", ncol);
|
|
glColor3f(1.0, 1.0, 1.0);
|
|
write_text(XMIN + 0.6, YMIN + 0.08, message);
|
|
// write_text(XMIN + 0.3, YMIN + 0.04, message);
|
|
|
|
sprintf(message, "%d pegs hit", nobst);
|
|
glColor3f(1.0, 1.0, 1.0);
|
|
write_text(XMAX-1.4, YMIN + 0.08, message);
|
|
// write_text(XMAX-0.7, YMIN + 0.04, message);
|
|
|
|
/* count max number a peg is hit */
|
|
nmaxpeg = 0;
|
|
for (j=0; j<ncircles; j++)
|
|
if (circles[j].color > nmaxpeg) nmaxpeg = circles[j].color;
|
|
|
|
// sprintf(message, "max hits per peg: %d", nmaxpeg);
|
|
// glColor3f(1.0, 1.0, 1.0);
|
|
// write_text(-0.6, YMIN + 0.08, message);
|
|
// write_text(-0.3, YMIN + 0.04, message);
|
|
|
|
draw_statistics();
|
|
|
|
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<END_FRAMES; i++) save_frame();
|
|
printf("Making a short pause\n");
|
|
sleep(PSLEEP);
|
|
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(CIRCLE_PATTERN);
|
|
// animation(C_TRI);
|
|
|
|
// animation(C_GOLDEN_SPIRAL);
|
|
// animation(C_SQUARE);
|
|
// animation(C_HEX);
|
|
// animation(C_GOLDEN_MEAN);
|
|
// animation(C_RAND_DISPLACED);
|
|
// animation(C_POISSON_DISC);
|
|
// animation(C_RAND_POISSON);
|
|
|
|
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;
|
|
}
|
|
|
|
|