2021-05-05 22:05:38 +02:00
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/*********************************************************************************/
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/* */
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/* Animation of wave equation in a planar domain */
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/* */
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2021-05-29 16:50:49 +02:00
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/* N. Berglund, december 2012, may 2021 */
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2021-05-05 22:05:38 +02:00
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/* */
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/* UPDATE 24/04: distinction between damping and "elasticity" parameters */
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/* UPDATE 27/04: new billiard shapes, bug in color scheme fixed */
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/* UPDATE 28/04: code made more efficient, with help of Marco Mancini */
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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 wave_billiard wave_billiard.c */
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/* -L/usr/X11R6/lib -ltiff -lm -lGL -lGLU -lX11 -lXmu -lglut -O3 -fopenmp */
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/* */
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/* To make a video, set MOVIE to 1 and create subfolder tif_wave */
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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 wave.%05d.tif -vcodec libx264 wave.mp4 */
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/* */
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/*********************************************************************************/
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/*********************************************************************************/
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/* */
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/* NB: The algorithm used to simulate the wave equation is highly paralellizable */
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/* One could make it much faster by using a GPU */
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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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#include <omp.h>
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#define MOVIE 0 /* set to 1 to generate movie */
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/* General geometrical parameters */
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#define WINWIDTH 1280 /* window width */
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#define WINHEIGHT 720 /* window height */
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#define NX 640 /* number of grid points on x axis */
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#define NY 360 /* number of grid points on y axis */
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/* setting NX to WINWIDTH and NY to WINHEIGHT increases resolution */
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/* but will multiply run time by 4 */
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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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/* Choice of the billiard table */
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#define B_DOMAIN 8 /* choice of domain shape */
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#define D_RECTANGLE 0 /* rectangular domain */
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#define D_ELLIPSE 1 /* elliptical domain */
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#define D_STADIUM 2 /* stadium-shaped domain */
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#define D_SINAI 3 /* Sinai billiard */
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#define D_DIAMOND 4 /* diamond-shaped billiard */
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#define D_TRIANGLE 5 /* triangular billiard */
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#define D_FLAT 6 /* flat interface */
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#define D_ANNULUS 7 /* annulus */
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#define D_POLYGON 8 /* polygon */
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2021-05-29 16:50:49 +02:00
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#define D_YOUNG 9 /* Young diffraction slits */
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#define D_GRATING 10 /* diffraction grating */
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#define D_EHRENFEST 11 /* Ehrenfest urn type geometry */
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2021-05-05 22:05:38 +02:00
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2021-05-29 16:50:49 +02:00
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#define LAMBDA 1.0 /* parameter controlling the dimensions of domain */
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#define MU 0.05 /* parameter controlling the dimensions of domain */
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#define NPOLY 8 /* number of sides of polygon */
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2021-05-05 22:05:38 +02:00
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#define APOLY 1.0 /* angle by which to turn polygon, in units of Pi/2 */
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#define FOCI 1 /* set to 1 to draw focal points of ellipse */
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/* You can add more billiard tables by adapting the functions */
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/* xy_in_billiard and draw_billiard below */
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/* Physical patameters of wave equation */
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#define COURANT 0.01 /* Courant number */
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#define GAMMA 0.0 /* damping factor in wave equation */
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// #define GAMMA 5.0e-10 /* damping factor in wave equation */
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2021-05-29 16:50:49 +02:00
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#define KAPPA 5.0e-6 /* "elasticity" term enforcing oscillations */
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2021-05-05 22:05:38 +02:00
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// #define KAPPA 5.0e-9 /* "elasticity" term enforcing oscillations */
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// #define KAPPA 5.0e-8 /* "elasticity" term enforcing oscillations */
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/* The Courant number is given by c*DT/DX, where DT is the time step and DX the lattice spacing */
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/* The physical damping coefficient is given by GAMMA/(DT)^2 */
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/* Increasing COURANT speeds up the simulation, but decreases accuracy */
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/* For similar wave forms, COURANT^2*GAMMA should be kept constant */
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/* For debugging purposes only */
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#define FLOOR 0 /* set to 1 to limit wave amplitude to VMAX */
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#define VMAX 10.0 /* max value of wave amplitude */
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/* Parameters for length and speed of simulation */
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2021-05-29 16:50:49 +02:00
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#define NSTEPS 5000 /* number of frames of movie */
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#define NVID 25 /* number of iterations between images displayed on screen */
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2021-05-05 22:05:38 +02:00
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#define NSEG 100 /* number of segments of boundary */
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#define PAUSE 1000 /* number of frames after which to pause */
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#define PSLEEP 1 /* sleep time during pause */
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#define SLEEP1 1 /* initial sleeping time */
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#define SLEEP2 1 /* final sleeping time */
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/* Color schemes */
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2021-05-29 16:50:49 +02:00
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#define BLACK 1 /* background */
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2021-05-05 22:05:38 +02:00
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#define COLOR_SCHEME 1 /* choice of color scheme */
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#define C_LUM 0 /* color scheme modifies luminosity (with slow drift of hue) */
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#define C_HUE 1 /* color scheme modifies hue */
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#define SCALE 1 /* set to 1 to adjust color scheme to variance of field */
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#define SLOPE 1.0 /* sensitivity of color on wave amplitude */
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#define ATTENUATION 0.0 /* exponential attenuation coefficient of contrast with time */
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#define COLORHUE 260 /* initial hue of water color for scheme C_LUM */
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#define COLORDRIFT 0.0 /* how much the color hue drifts during the whole simulation */
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#define LUMMEAN 0.5 /* amplitude of luminosity variation for scheme C_LUM */
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#define LUMAMP 0.3 /* amplitude of luminosity variation for scheme C_LUM */
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2021-05-29 16:50:49 +02:00
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#define HUEMEAN 100.0 /* mean value of hue for color scheme C_HUE */
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#define HUEAMP 80.0 /* amplitude of variation of hue for color scheme C_HUE */
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2021-05-05 22:05:38 +02:00
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// #define HUEMEAN 320.0 /* mean value of hue for color scheme C_HUE */
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// #define HUEAMP 100.0 /* amplitude of variation of hue for color scheme C_HUE */
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/* Basic math */
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#define PI 3.141592654
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#define DPI 6.283185307
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#define PID 1.570796327
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2021-05-29 16:50:49 +02:00
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#include "sub_wave.c"
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2021-05-05 22:05:38 +02:00
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2021-05-29 16:50:49 +02:00
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double courant2; /* Courant parameter squared */
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2021-05-05 22:05:38 +02:00
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void init_wave(x, y, phi, psi, xy_in)
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/* initialise field with drop at (x,y) - phi is wave height, psi is phi at time t-1 */
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double x, y, *phi[NX], *psi[NX]; short int * xy_in[NX];
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{
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int i, j;
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double xy[2], dist2;
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for (i=0; i<NX; i++)
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for (j=0; j<NY; j++)
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{
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ij_to_xy(i, j, xy);
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dist2 = (xy[0]-x)*(xy[0]-x) + (xy[1]-y)*(xy[1]-y);
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xy_in[i][j] = xy_in_billiard(xy[0],xy[1]);
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phi[i][j] = 0.2*exp(-dist2/0.001)*cos(-sqrt(dist2)/0.01);
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psi[i][j] = 0.0;
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}
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}
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void add_drop_to_wave(factor, x, y, phi, psi)
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/* add drop at (x,y) to the field with given prefactor */
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double factor, x, y, *phi[NX], *psi[NX];
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{
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int i, j;
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double xy[2], dist2;
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for (i=0; i<NX; i++)
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for (j=0; j<NY; j++)
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{
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ij_to_xy(i, j, xy);
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dist2 = (xy[0]-x)*(xy[0]-x) + (xy[1]-y)*(xy[1]-y);
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phi[i][j] += 0.2*factor*exp(-dist2/0.001)*cos(-sqrt(dist2)/0.01);
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}
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}
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/*********************/
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/* animation part */
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/*********************/
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void draw_wave(phi, psi, xy_in, scale, time)
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/* draw the field */
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double *phi[NX], *psi[NX], scale;
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short int *xy_in[NX];
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int time;
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{
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int i, j;
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double rgb[3], xy[2], x1, y1, x2, y2;
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glBegin(GL_QUADS);
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for (i=0; i<NX; i++)
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for (j=0; j<NY; j++)
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{
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if (xy_in[i][j])
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{
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color_scheme(COLOR_SCHEME, phi[i][j], scale, time, rgb);
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glColor3f(rgb[0], rgb[1], rgb[2]);
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glVertex2i(i, j);
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glVertex2i(i+1, j);
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glVertex2i(i+1, j+1);
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glVertex2i(i, j+1);
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}
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}
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glEnd ();
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}
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void evolve_wave(phi, psi, xy_in)
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/* time step of field evolution */
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/* phi is value of field at time t, psi at time t-1 */
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double *phi[NX], *psi[NX]; short int *xy_in[NX];
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{
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int i, j, iplus, iminus, jplus, jminus;
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double delta, x, y;
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2021-05-29 16:50:49 +02:00
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#pragma omp parallel for private(i,j,iplus,iminus,jplus,jminus,delta,x,y)
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2021-05-05 22:05:38 +02:00
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for (i=0; i<NX; i++){
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for (j=0; j<NY; j++){
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if (xy_in[i][j]){
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/* discretized Laplacian */
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iplus = (i+1) % NX;
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iminus = (i-1) % NX;
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if (iminus < 0) iminus += NX;
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jplus = (j+1) % NY;
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jminus = (j-1) % NY;
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if (jminus < 0) jminus += NY;
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delta = phi[iplus][j] + phi[iminus][j] + phi[i][jplus] + phi[i][jminus] - 4.0*phi[i][j];
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x = phi[i][j];
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y = psi[i][j];
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/* evolve phi */
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phi[i][j] = -y + 2*x + courant2*delta - KAPPA*x - GAMMA*(x-y);
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/* Old versions of the simulation used this: */
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// phi[i][j] = (-psi[i][j] + 2*phi[i][j] + courant2*delta)*damping;
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// where damping = 1.0 - 0.0001;
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psi[i][j] = x;
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if (FLOOR)
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{
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if (phi[i][j] > VMAX) phi[i][j] = VMAX;
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if (phi[i][j] < -VMAX) phi[i][j] = -VMAX;
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if (psi[i][j] > VMAX) psi[i][j] = VMAX;
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if (psi[i][j] < -VMAX) psi[i][j] = -VMAX;
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}
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}
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}
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}
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// printf("phi(0,0) = %.3lg, psi(0,0) = %.3lg\n", phi[NX/2][NY/2], psi[NX/2][NY/2]);
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}
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double compute_variance(phi, psi, xy_in)
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/* compute the variance of the field, to adjust color scheme */
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double *phi[NX], *psi[NX]; short int * xy_in[NX];
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{
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int i, j, n = 0;
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double variance = 0.0;
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for (i=1; i<NX; i++)
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for (j=1; j<NY; j++)
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{
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if (xy_in[i][j])
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{
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n++;
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variance += phi[i][j]*phi[i][j];
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}
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}
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if (n==0) n=1;
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return(variance/(double)n);
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}
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void animation()
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{
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double time, scale;
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double *phi[NX], *psi[NX];
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short int *xy_in[NX];
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int i, j, s;
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/* Since NX and NY are big, it seemed wiser to use some memory allocation here */
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for (i=0; i<NX; i++)
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{
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phi[i] = (double *)malloc(NY*sizeof(double));
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psi[i] = (double *)malloc(NY*sizeof(double));
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xy_in[i] = (short int *)malloc(NY*sizeof(short int));
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}
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courant2 = COURANT*COURANT;
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/* initialize wave with a drop at one point, zero elsewhere */
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init_wave(0.0, 0.0, phi, psi, xy_in);
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/* add a drop at another point */
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// add_drop_to_wave(1.0, 0.7, 0.0, phi, psi);
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// add_drop_to_wave(1.0, -0.7, 0.0, phi, psi);
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// add_drop_to_wave(1.0, 0.0, -0.7, phi, psi);
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blank();
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glColor3f(0.0, 0.0, 0.0);
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draw_wave(phi, psi, xy_in, 1.0, 0);
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draw_billiard();
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glutSwapBuffers();
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sleep(SLEEP1);
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for (i=0; i<=NSTEPS; i++)
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{
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//printf("%d\n",i);
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/* compute the variance of the field to adjust color scheme */
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/* the color depends on the field divided by sqrt(1 + variance) */
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if (SCALE)
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{
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scale = sqrt(1.0 + compute_variance(phi,psi, xy_in));
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// printf("Scaling factor: %5lg\n", scale);
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}
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else scale = 1.0;
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draw_wave(phi, psi, xy_in, scale, i);
|
|
|
|
for (j=0; j<NVID; j++) evolve_wave(phi, psi, xy_in);
|
|
|
|
draw_billiard();
|
|
|
|
|
|
|
|
|
|
|
|
glutSwapBuffers();
|
|
|
|
|
|
|
|
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 wave*.tif tif_wave/");
|
|
|
|
}
|
|
|
|
}
|
|
|
|
|
|
|
|
}
|
|
|
|
|
2021-05-29 16:50:49 +02:00
|
|
|
if (MOVIE)
|
|
|
|
{
|
|
|
|
for (i=0; i<20; i++) save_frame();
|
|
|
|
s = system("mv wave*.tif tif_wave/");
|
|
|
|
}
|
2021-05-05 22:05:38 +02:00
|
|
|
for (i=0; i<NX; i++)
|
|
|
|
{
|
|
|
|
free(phi[i]);
|
|
|
|
free(psi[i]);
|
|
|
|
}
|
|
|
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
|
|
void display(void)
|
|
|
|
{
|
|
|
|
glPushMatrix();
|
|
|
|
|
|
|
|
blank();
|
|
|
|
glutSwapBuffers();
|
|
|
|
blank();
|
|
|
|
glutSwapBuffers();
|
|
|
|
|
|
|
|
animation();
|
|
|
|
sleep(SLEEP2);
|
|
|
|
|
|
|
|
glPopMatrix();
|
|
|
|
|
|
|
|
glutDestroyWindow(glutGetWindow());
|
|
|
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
|
|
int main(int argc, char** argv)
|
|
|
|
{
|
|
|
|
glutInit(&argc, argv);
|
|
|
|
glutInitDisplayMode(GLUT_RGB | GLUT_DOUBLE | GLUT_DEPTH);
|
|
|
|
glutInitWindowSize(WINWIDTH,WINHEIGHT);
|
|
|
|
glutCreateWindow("Wave equation in a planar domain");
|
|
|
|
|
|
|
|
init();
|
|
|
|
|
|
|
|
glutDisplayFunc(display);
|
|
|
|
|
|
|
|
glutMainLoop();
|
|
|
|
|
|
|
|
return 0;
|
|
|
|
}
|
|
|
|
|