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nilsberglund-orleans 2021-09-26 16:47:29 +02:00 committed by GitHub
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commit c73cbe10a0
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10 changed files with 2597 additions and 79 deletions
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49
drop_billiard.c
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@ -30,23 +30,22 @@
#define MOVIE 0 /* set to 1 to generate movie */
// #define WINWIDTH 720 /* window width */
#define WINWIDTH 1280 /* window width */
#define WINHEIGHT 720 /* window height */
#define XMIN -2.0
#define XMAX 2.0 /* x interval */
// #define XMIN -1.125
// #define XMAX 1.125 /* x interval */
#define YMIN -1.125
#define YMAX 1.125 /* y interval for 9/16 aspect ratio */
// #define XMIN -1.8
// #define XMAX 1.8 /* x interval */
// #define YMIN -0.91
// #define YMAX 1.115 /* y interval for 9/16 aspect ratio */
#define 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 13 /* choice of domain shape */
#define B_DOMAIN 15 /* choice of domain shape */
#define CIRCLE_PATTERN 0 /* pattern of circles */
@ -57,30 +56,32 @@
// #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 LAMBDA 1.0 /* parameter controlling shape of billiard */
#define LAMBDA 1.124950941 /* sin(36°)/sin(31.5°) for 5-star shape with 45° angles */
#define LAMBDA 0.0 /* parameter controlling shape of billiard */
// #define LAMBDA 1.124950941 /* sin(36°)/sin(31.5°) for 5-star shape with 45° angles */
// #define LAMBDA 1.445124904 /* sin(36°)/sin(24°) for 5-star shape with 60° angles */
// #define LAMBDA 3.75738973 /* sin(36°)/sin(9°) for 5-star shape with 90° angles */
// #define LAMBDA -1.73205080756888 /* -sqrt(3) for Reuleaux triangle */
// #define LAMBDA 1.73205080756888 /* sqrt(3) for triangle tiling plane */
#define MU 0.1 /* second parameter controlling shape of billiard */
#define MU 0.9 /* second parameter controlling shape of billiard */
#define FOCI 1 /* set to 1 to draw focal points of ellipse */
#define NPOLY 5 /* number of sides of polygon */
#define APOLY -1.0 /* angle by which to turn polygon, in units of Pi/2 */
#define 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 RESAMPLE 0 /* set to 1 if particles should be added when dispersion too large */
#define NPART 50000 /* number of particles */
#define NPART 10000 /* number of particles */
#define NPARTMAX 100000 /* maximal number of particles after resampling */
#define NSTEPS 5500 /* number of frames of movie */
#define TIME 40 /* time between movie frames, for fluidity of real-time simulation */
#define NSTEPS 4200 /* number of frames of movie */
#define TIME 100 /* time between movie frames, for fluidity of real-time simulation */
#define DPHI 0.0001 /* integration step */
#define NVID 20 /* number of iterations between images displayed on screen */
#define NVID 50 /* 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 */
@ -98,9 +99,9 @@
/* color and other graphical parameters */
#define NCOLORS 16 /* number of colors */
#define COLORSHIFT 200 /* hue of initial color */
#define RAINBOW_COLOR 1 /* set to 1 to use different colors for all particles */
#define NCOLORS 12 /* 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 NSEG 100 /* number of segments of boundary */
#define BILLIARD_WIDTH 4 /* width of billiard */
#define FRONT_WIDTH 3 /* width of wave front */
@ -109,12 +110,14 @@
#define COLOR_OUTSIDE 0 /* set to 1 for colored outside */
#define OUTER_COLOR 300.0 /* color outside billiard */
#define PAINT_INT 1 /* set to 1 to paint interior in other color (for polygon) */
#define PAINT_EXT 0 /* 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 PSLEEP 1 /* sleep time during pause */
#define SLEEP1 1 /* initial sleeping time */
#define SLEEP2 100 /* final sleeping time */
#define END_FRAMES 0 /* number of frames at end of movie */
#define PI 3.141592654
#define DPI 6.283185307
@ -442,7 +445,9 @@ void animation()
for (i=0; i<NPARTMAX; i++)
configs[i] = (double *)malloc(8*sizeof(double));
init_drop_config(-1.0 + 0.3*sqrt(2.0), -1.0 + 0.5*sqrt(2.0), 0.0, DPI, configs);
// init_drop_config(0.1, 0.1, 0.0, DPI, configs);
init_drop_config(0.0, 0.0, 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);
@ -495,7 +500,7 @@ void animation()
if (MOVIE)
{
for (i=0; i<20; i++) save_frame();
for (i=0; i<END_FRAMES; i++) save_frame();
s = system("mv part*.tif tif_drop/");
}

13
global_particles.c
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@ -1,7 +1,10 @@
double circlex[NMAXCIRCLES], circley[NMAXCIRCLES], circlerad[NMAXCIRCLES]; /* position and radius of circular scatters */
short int circleactive[NMAXCIRCLES]; /* tells which circular scatters are active */
short int circleactive[NMAXCIRCLES]; /* tells which circular scatters are active */
short int newcircle[NMAXCIRCLES]; /* takes value 1 when circle has just been hit */
int circlecolor[NMAXCIRCLES]; /* color of circular scatterer */
int ncircles = NMAXCIRCLES; /* actual number of circles, can be decreased e.g. for random patterns */
double x_shooter = -0.2, y_shooter = -0.6, x_target = 0.4, y_target = 0.7;
/* shooter and target positions for "laser in room of mirrors" simulations, with default values for square domain */
@ -27,6 +30,8 @@ double x_shooter = -0.2, y_shooter = -0.6, x_target = 0.4, y_target = 0.7;
#define D_ANGLE 12 /* angular sector */
#define D_LSHAPE 13 /* L-shaped billiard for conical singularity */
#define D_GENUSN 14 /* polygon with identifies opposite sides */
#define D_PARABOLAS 15 /* polygon with parabolic sides */
#define D_PENROSE 16 /* Penrose solution to illumination problem */
#define D_CIRCLES 20 /* several circles */
#define D_CIRCLES_IN_RECT 21 /* several circles inside a rectangle */
@ -35,7 +40,13 @@ double x_shooter = -0.2, y_shooter = -0.6, x_target = 0.4, y_target = 0.7;
#define C_FOUR_CIRCLES 0 /* four circles almost touching each other */
#define C_SQUARE 1 /* square grid of circles */
#define C_HEX 2 /* hexagonal/triangular grid of circles */
#define C_TRI 21 /* equilateral triangular grid of circles */
#define C_GOLDEN_MEAN 3 /* golden mean grid */
#define C_GOLDEN_SPIRAL 4 /* golden spiral (sunflower) grid */
#define C_RAND_DISPLACED 5 /* randomly displaced square grid */
#define C_RAND_POISSON 6 /* random Poisson point process */
#define C_POISSON_DISC 7 /* Poisson disc sampling */
#define C_LASER 11 /* laser fight in a room of mirrors */
#define C_LASER_GENUSN 12 /* laser fight in a translation surface */

6
global_pdes.c
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@ -34,6 +34,11 @@
#define D_CIRCLES 20 /* several circles */
#define D_FOUR_PARABOLAS 31 /* four parabolas with axes in NSEW directions */
#define D_POLY_PARABOLAS 32 /* polygon with parabolic sides */
#define D_PENROSE 33 /* Penrose illumination problem */
#define D_HYPERBOLA 34 /* one branch of hyperbola */
#define NMAXCIRCLES 1000 /* total number of circles (must be at least NCX*NCY for square grid) */
#define C_SQUARE 0 /* square grid of circles */
@ -83,6 +88,7 @@
#define P_AMPLITUDE 0 /* plot amplitude of wave */
#define P_ENERGY 1 /* plot energy of wave */
#define P_MIXED 2 /* plot amplitude in upper half, energy in lower half */
#define P_MEAN_ENERGY 3 /* energy averaged over time */
/* For Schrodinger equation */
#define P_MODULE 10 /* plot module of wave function squared */

758
mangrove.c Normal file
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@ -0,0 +1,758 @@
/*********************************************************************************/
/* */
/* Animation of wave equation in a planar domain */
/* */
/* N. Berglund, december 2012, may 2021 */
/* */
/* UPDATE 24/04: distinction between damping and "elasticity" parameters */
/* UPDATE 27/04: new billiard shapes, bug in color scheme fixed */
/* UPDATE 28/04: code made more efficient, with help of Marco Mancini */
/* */
/* 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 wave_billiard wave_billiard.c */
/* -L/usr/X11R6/lib -ltiff -lm -lGL -lGLU -lX11 -lXmu -lglut -O3 -fopenmp */
/* */
/* OMP acceleration may be more effective after executing */
/* export OMP_NUM_THREADS=2 in the shell before running the program */
/* */
/* To make a video, set MOVIE to 1 and create subfolder tif_wave */
/* It may be possible to increase parameter PAUSE */
/* */
/* create movie using */
/* ffmpeg -i wave.%05d.tif -vcodec libx264 wave.mp4 */
/* */
/*********************************************************************************/
/*********************************************************************************/
/* */
/* NB: The algorithm used to simulate the wave equation is highly paralellizable */
/* One could make it much faster by using a GPU */
/* */
/*********************************************************************************/
#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. */
#include <omp.h>
#define MOVIE 0 /* set to 1 to generate movie */
/* General geometrical parameters */
#define WINWIDTH 1280 /* window width */
#define WINHEIGHT 720 /* window height */
#define NX 1280 /* number of grid points on x axis */
#define NY 720 /* number of grid points on y axis */
#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 JULIA_SCALE 1.0 /* scaling for Julia sets */
/* Choice of the billiard table */
#define B_DOMAIN 20 /* choice of domain shape, see list in global_pdes.c */
#define CIRCLE_PATTERN 8 /* pattern of circles, see list in global_pdes.c */
#define P_PERCOL 0.25 /* probability of having a circle in C_RAND_PERCOL arrangement */
#define NPOISSON 340 /* number of points for Poisson C_RAND_POISSON arrangement */
#define LAMBDA 0.85 /* parameter controlling the dimensions of domain */
#define MU 0.03 /* parameter controlling the dimensions of domain */
#define NPOLY 3 /* number of sides of polygon */
#define APOLY 1.0 /* angle by which to turn polygon, in units of Pi/2 */
#define MDEPTH 4 /* depth of computation of Menger gasket */
#define MRATIO 3 /* ratio defining Menger gasket */
#define MANDELLEVEL 1000 /* iteration level for Mandelbrot set */
#define MANDELLIMIT 10.0 /* limit value for approximation of Mandelbrot set */
#define FOCI 1 /* set to 1 to draw focal points of ellipse */
#define NGRIDX 15 /* number of grid point for grid of disks */
#define NGRIDY 20 /* number of grid point for grid of disks */
/* You can add more billiard tables by adapting the functions */
/* xy_in_billiard and draw_billiard below */
/* Physical parameters of wave equation */
#define TWOSPEEDS 1 /* set to 1 to replace hardcore boundary by medium with different speed */
#define OSCILLATE_LEFT 1 /* set to 1 to add oscilating boundary condition on the left */
#define OSCILLATE_TOPBOT 1 /* set to 1 to enforce a planar wave on top and bottom boundary */
#define X_SHIFT -0.9 /* x range on which to apply OSCILLATE_TOPBOT */
#define OMEGA 0.002 /* frequency of periodic excitation */
#define K_BC 3.0 /* spatial period of periodic excitation in y direction */
#define KX_BC 30.0 /* spatial period of periodic excitation in x direction */
#define KY_BC 10.0 /* spatial period of periodic excitation in y direction */
#define AMPLITUDE 1.0 /* amplitude of periodic excitation */
#define COURANT 0.02 /* Courant number */
#define COURANTB 0.01 /* Courant number in medium B */
// #define COURANTB 0.00666 /* Courant number in medium B */
#define GAMMA 2.0e-6 /* damping factor in wave equation */
#define GAMMAB 2.5e-4 /* damping factor in wave equation */
// #define GAMMAB 5.0e-4 /* damping factor in wave equation */
// #define GAMMAB 1.0e-4 /* damping factor in wave equation */
#define GAMMA_SIDES 1.0e-4 /* damping factor on boundary */
#define GAMMA_TOPBOT 1.0e-6 /* damping factor on boundary */
#define KAPPA 0.0 /* "elasticity" term enforcing oscillations */
#define KAPPAB 1.0e-6 /* "elasticity" term enforcing oscillations */
#define KAPPA_SIDES 5.0e-4 /* "elasticity" term on absorbing boundary */
#define KAPPA_TOPBOT 0.0 /* "elasticity" term on absorbing boundary */
/* The Courant number is given by c*DT/DX, where DT is the time step and DX the lattice spacing */
/* The physical damping coefficient is given by GAMMA/(DT)^2 */
/* Increasing COURANT speeds up the simulation, but decreases accuracy */
/* For similar wave forms, COURANT^2*GAMMA should be kept constant */
/* Boundary conditions, see list in global_pdes.c */
#define B_COND 3
/* Parameters for length and speed of simulation */
// #define NSTEPS 1000 /* number of frames of movie */
#define NSTEPS 4500 /* number of frames of movie */
#define NVID 60 /* number of iterations between images displayed on screen */
#define NSEG 100 /* number of segments of boundary */
#define INITIAL_TIME 100 /* time after which to start saving frames */
#define BOUNDARY_WIDTH 2 /* width of billiard boundary */
#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 1 /* final sleeping time */
#define END_FRAMES 100 /* number of still frames at end of movie */
/* Parameters of initial condition */
#define INITIAL_AMP 0.2 /* amplitude of initial condition */
#define INITIAL_VARIANCE 0.002 /* variance of initial condition */
#define INITIAL_WAVELENGTH 0.1 /* wavelength of initial condition */
/* Plot type, see list in global_pdes.c */
#define PLOT 0
/* Color schemes */
#define BLACK 1 /* background */
#define COLOR_SCHEME 1 /* choice of color scheme, see list in global_pdes.c */
#define SCALE 0 /* set to 1 to adjust color scheme to variance of field */
#define SLOPE 1.0 /* sensitivity of color on wave amplitude */
#define ATTENUATION 0.0 /* exponential attenuation coefficient of contrast with time */
#define E_SCALE 2500.0 /* scaling factor for energy representation */
#define COLORHUE 260 /* initial hue of water color for scheme C_LUM */
#define COLORDRIFT 0.0 /* how much the color hue drifts during the whole simulation */
#define LUMMEAN 0.5 /* amplitude of luminosity variation for scheme C_LUM */
#define LUMAMP 0.3 /* amplitude of luminosity variation for scheme C_LUM */
#define HUEMEAN 220.0 /* mean value of hue for color scheme C_HUE */
#define HUEAMP -50.0 /* amplitude of variation of hue for color scheme C_HUE */
/* mangrove properties */
#define MANGROVE_HUE_MIN 180.0 /* color of original mangrove */
#define MANGROVE_HUE_MAX -50.0 /* color of saturated mangrove */
// #define MANGROVE_EMAX 5.0e-3 /* max energy for mangrove to survive */
#define MANGROVE_EMAX 1.1e-3 /* max energy for mangrove to survive */
#define RANDOM_RADIUS 1 /* set to 1 for random circle radius */
#define ERODE_MANGROVES 0 /* set to 1 for mangroves to be eroded */
#define MOVE_MANGROVES 1 /* set to 1 for mobile mangroves */
#define DETACH_MANGROVES 1 /* set to 1 for mangroves to be able to detach */
#define INERTIA 1 /* set to 1 for taking inertia into account */
#define DT_MANGROVE 0.1 /* time step for mangrove displacement */
#define KSPRING 0.25 /* spring constant of mangroves */
// #define KSPRING 0.75 /* spring constant of mangroves */
// #define KSPRING 0.15 /* spring constant of mangroves */
#define KWAVE 2.0 /* constant in force due to wave gradient */
#define DXMAX 0.02 /* max displacement of mangrove in one time step */
#define L_DETACH 0.2 /* spring length beyond which mangroves detach */
#define DAMP_MANGROVE 0.2 /* damping coefficient of mangroves */
#define MANGROVE_MASS 1.5 /* mass of mangrove of radius MU */
// #define MANGROVE_MASS 2.0 /* mass of mangrove of radius MU */
// #define KSPRING 0.5 /* spring constant of mangroves */
// #define KWAVE 2.0 /* constant in force due to wave gradient */
// #define DXMAX 0.02 /* max displacement of mangrove in one time step */
// #define L_DETACH 0.4 /* spring length beyond which mangroves detach */
// #define DAMP_MANGROVE 0.3 /* damping coefficient of mangroves */
//
// #define KSPRING 1.0 /* spring constant of mangroves */
// #define KWAVE 2.0 /* constant in force due to wave gradient */
// #define DXMAX 0.02 /* max displacement of mangrove in one time step */
// #define L_DETACH 0.4 /* spring length beyond which mangroves detach */
// #define DAMP_MANGROVE 0.3 /* damping coefficient of mangroves */
//
// #define KSPRING 2.0 /* spring constant of mangroves */
// #define KWAVE 5.0 /* constant in force due to wave gradient */
// #define DXMAX 0.02 /* max displacement of mangrove in one time step */
// #define L_DETACH 0.2 /* spring length beyond which mangroves detach */
// #define DAMP_MANGROVE 0.2 /* damping coefficient of mangroves */
/* For debugging purposes only */
#define FLOOR 1 /* set to 1 to limit wave amplitude to VMAX */
#define VMAX 10.0 /* max value of wave amplitude */
#include "global_pdes.c"
#include "sub_wave.c"
#include "wave_common.c"
double courant2, courantb2; /* Courant parameters squared */
double circle_energy[NMAXCIRCLES]; /* energy dissipated by the circles */
double circley_wrapped[NMAXCIRCLES]; /* position of circle centers wrapped vertically */
double anchor_x[NMAXCIRCLES]; /* points moving circles are attached to */
double anchor_y[NMAXCIRCLES]; /* points moving circles are attached to */
double vx[NMAXCIRCLES]; /* x velocity of circles */
double vy[NMAXCIRCLES]; /* y velocity of circles */
double circlerad_initial[NMAXCIRCLES]; /* initial circle radii */
double mass_inverse[NMAXCIRCLES]; /* inverse of mangrove mass */
short int circle_attached[NMAXCIRCLES]; /* has value 1 if the circle is attached to its anchor */
/*********************/
/* animation part */
/*********************/
void init_bc_phase(double left_bc[NY], double top_bc[NX], double bot_bc[NX])
/* initialize boundary condition phase KX*x + KY*y */
{
int i, j;
double xy[2];
for (j=0; j<NY; j++)
{
ij_to_xy(0, j, xy);
left_bc[j] = KX_BC*XMIN + KY_BC*xy[1];
}
for (i=0; i<NX; i++)
{
ij_to_xy(i, 0, xy);
bot_bc[i] = KX_BC*xy[0] + KY_BC*YMIN;
top_bc[i] = KX_BC*xy[0] + KY_BC*YMAX;
}
}
void evolve_wave_half(double *phi_in[NX], double *psi_in[NX], double *phi_out[NX], double *psi_out[NX],
short int *xy_in[NX])
// void evolve_wave_half(phi_in, psi_in, phi_out, psi_out, xy_in)
/* time step of field evolution */
/* phi is value of field at time t, psi at time t-1 */
{
int i, j, iplus, iminus, jplus, jminus, tb_shift;
double delta, x, y, c, cc, gamma, kappa, phase, phasemin;
static long time = 0;
static int init_bc = 1;
static double left_bc[NY], top_bc[NX], bot_bc[NX];
time++;
/* initialize boundary condition phase KX*x + KY*y */
if ((OSCILLATE_LEFT)&&(init_bc))
{
init_bc_phase(left_bc, top_bc, bot_bc);
tb_shift = (int)((X_SHIFT - XMIN)*(double)NX/(XMAX - XMIN));
printf("tb_shift %i\n", tb_shift);
init_bc = 0;
}
#pragma omp parallel for private(i,j,iplus,iminus,jplus,jminus,delta,x,y,c,cc,gamma,kappa)
for (i=0; i<NX; i++){
for (j=0; j<NY; j++){
if (xy_in[i][j])
{
c = COURANT;
cc = courant2;
gamma = GAMMA;
kappa = KAPPA;
}
else if (TWOSPEEDS)
{
c = COURANTB;
cc = courantb2;
gamma = GAMMAB;
kappa = KAPPAB;
}
if ((TWOSPEEDS)||(xy_in[i][j])){
/* discretized Laplacian for various boundary conditions */
if ((B_COND == BC_DIRICHLET)||(B_COND == BC_ABSORBING))
{
iplus = (i+1); if (iplus == NX) iplus = NX-1;
iminus = (i-1); if (iminus == -1) iminus = 0;
jplus = (j+1); if (jplus == NY) jplus = NY-1;
jminus = (j-1); if (jminus == -1) jminus = 0;
}
else if (B_COND == BC_PERIODIC)
{
iplus = (i+1) % NX;
iminus = (i-1) % NX;
if (iminus < 0) iminus += NX;
jplus = (j+1) % NY;
jminus = (j-1) % NY;
if (jminus < 0) jminus += NY;
}
else if (B_COND == BC_VPER_HABS)
{
iplus = (i+1); if (iplus == NX) iplus = NX-1;
iminus = (i-1); if (iminus == -1) iminus = 0;
jplus = (j+1) % NY;
jminus = (j-1) % NY;
if (jminus < 0) jminus += NY;
}
/* imposing linear wave on top and bottom by making Laplacian 1d */
if ((OSCILLATE_TOPBOT)&&(i < tb_shift))
{
if (j == NY-1)
{
jminus = NY-1;
jplus = NY-1;
}
else if (j == 0)
{
jminus = 0;
jplus = 0;
}
}
delta = phi_in[iplus][j] + phi_in[iminus][j] + phi_in[i][jplus] + phi_in[i][jminus] - 4.0*phi_in[i][j];
x = phi_in[i][j];
y = psi_in[i][j];
/* evolve phi */
if ((B_COND == BC_PERIODIC)||(B_COND == BC_DIRICHLET))
phi_out[i][j] = -y + 2*x + cc*delta - kappa*x - gamma*(x-y);
else if (B_COND == BC_ABSORBING)
{
if ((i>0)&&(i<NX-1)&&(j>0)&&(j<NY-1))
phi_out[i][j] = -y + 2*x + cc*delta - kappa*x - gamma*(x-y);
/* upper border */
else if (j==NY-1)
phi_out[i][j] = x - c*(x - phi_in[i][NY-2]) - KAPPA_TOPBOT*x - GAMMA_TOPBOT*(x-y);
/* lower border */
else if (j==0)
phi_out[i][j] = x - c*(x - phi_in[i][1]) - KAPPA_TOPBOT*x - GAMMA_TOPBOT*(x-y);
/* right border */
if (i==NX-1)
phi_out[i][j] = x - c*(x - phi_in[NX-2][j]) - KAPPA_SIDES*x - GAMMA_SIDES*(x-y);
/* left border */
else if (i==0)
phi_out[i][j] = x - c*(x - phi_in[1][j]) - KAPPA_SIDES*x - GAMMA_SIDES*(x-y);
}
else if (B_COND == BC_VPER_HABS)
{
if ((i>0)&&(i<NX-1))
phi_out[i][j] = -y + 2*x + cc*delta - kappa*x - gamma*(x-y);
/* right border */
else if (i==NX-1)
phi_out[i][j] = x - c*(x - phi_in[NX-2][j]) - KAPPA_SIDES*x - GAMMA_SIDES*(x-y);
/* left border */
else if (i==0)
phi_out[i][j] = x - c*(x - phi_in[1][j]) - KAPPA_SIDES*x - GAMMA_SIDES*(x-y);
}
psi_out[i][j] = x;
/* add oscillating boundary condition on the left */
// if ((i == 0)&&(OSCILLATE_LEFT))
// {
// phase = (double)time*OMEGA - DPI*K_BC*(double)j/(double)NY;
// if (phase < 0.0) phase = 0.0;
// phi_out[i][j] = AMPLITUDE*sin(phase);
// }
/* add oscillating boundary condition on the left */
if (OSCILLATE_LEFT)
{
phasemin = left_bc[0];
if (i == 0)
{
phase = (double)time*OMEGA - left_bc[j] + phasemin;
if (phase < 0.0) phase = 0.0;
phi_out[i][j] = AMPLITUDE*sin(phase);
}
if ((j == 0)&&(i < tb_shift))
{
phase = (double)time*OMEGA - bot_bc[i] + phasemin;
if (phase < 0.0) phase = 0.0;
phi_out[i][j] = AMPLITUDE*sin(phase);
}
else if ((j == NY-1)&&(i < tb_shift))
{
phase = (double)time*OMEGA - top_bc[i] + phasemin;
if (phase < 0.0) phase = 0.0;
phi_out[i][j] = AMPLITUDE*sin(phase);
}
}
if (FLOOR)
{
if (phi_out[i][j] > VMAX) phi_out[i][j] = VMAX;
if (phi_out[i][j] < -VMAX) phi_out[i][j] = -VMAX;
if (psi_out[i][j] > VMAX) psi_out[i][j] = VMAX;
if (psi_out[i][j] < -VMAX) psi_out[i][j] = -VMAX;
}
}
}
}
// printf("phi(0,0) = %.3lg, psi(0,0) = %.3lg\n", phi[NX/2][NY/2], psi[NX/2][NY/2]);
}
void evolve_wave(double *phi[NX], double *psi[NX], double *phi_tmp[NX], double *psi_tmp[NX], short int *xy_in[NX])
/* time step of field evolution */
/* phi is value of field at time t, psi at time t-1 */
{
evolve_wave_half(phi, psi, phi_tmp, psi_tmp, xy_in);
evolve_wave_half(phi_tmp, psi_tmp, phi, psi, xy_in);
}
void animation()
{
double time, scale, diss, rgb[3], hue, y, dissip, ej, gradient[2], dx, dy, dt, xleft, xright, length;
double *phi[NX], *psi[NX], *phi_tmp[NX], *psi_tmp[NX];
short int *xy_in[NX], redraw = 0;
int i, j, s, ij[2];
static int imin, imax;
static short int first = 1;
/* Since NX and NY are big, it seemed wiser to use some memory allocation here */
for (i=0; i<NX; i++)
{
phi[i] = (double *)malloc(NY*sizeof(double));
psi[i] = (double *)malloc(NY*sizeof(double));
phi_tmp[i] = (double *)malloc(NY*sizeof(double));
psi_tmp[i] = (double *)malloc(NY*sizeof(double));
xy_in[i] = (short int *)malloc(NY*sizeof(short int));
}
/* initialise positions and radii of circles */
if (B_DOMAIN == D_CIRCLES) init_circle_config();
courant2 = COURANT*COURANT;
courantb2 = COURANTB*COURANTB;
// dt = 0.01;
/* initialize wave with a drop at one point, zero elsewhere */
init_wave_flat(phi, psi, xy_in);
// init_planar_wave(XMIN + 0.01, 0.0, phi, psi, xy_in);
// init_planar_wave(XMIN + 0.02, 0.0, phi, psi, xy_in);
// init_planar_wave(XMIN + 1.0, 0.0, phi, psi, xy_in);
// init_wave(-1.5, 0.0, phi, psi, xy_in);
// init_wave(0.0, 0.0, phi, psi, xy_in);
/* add a drop at another point */
// add_drop_to_wave(1.0, 0.7, 0.0, phi, psi);
// add_drop_to_wave(1.0, -0.7, 0.0, phi, psi);
// add_drop_to_wave(1.0, 0.0, -0.7, phi, psi);
/* initialise mangroves */
for (i=0; i < ncircles; i++)
{
circle_energy[i] = 0.0;
y = circley[i];
if (y >= YMAX) y -= circlerad[i];
if (y <= YMIN) y += circlerad[i];
// if (y >= YMAX) y -= (YMAX - YMIN);
// if (y <= YMIN) y += (YMAX - YMIN);
circley_wrapped[i] = y;
if (RANDOM_RADIUS) circlerad[i] = circlerad[i]*(0.75 + 0.5*((double)rand()/RAND_MAX));
circlerad_initial[i] = circlerad[i];
circle_attached[i] = 1;
mass_inverse[i] = MU*MU/(MANGROVE_MASS*circlerad[i]*circlerad[i]);
if (MOVE_MANGROVES)
{
anchor_x[i] = circlex[i];
anchor_y[i] = circley_wrapped[i];
// anchor_y[i] = circley[i];
}
if (INERTIA)
{
vx[i] = 0.0;
vy[i] = 0.0;
}
}
if (first) /* compute box limits where circles are reset */
{
/* find leftmost and rightmost circle */
for (i=0; i<ncircles; i++)
if ((circleactive[i])&&(circlex[i] - circlerad[i] < xleft)) xleft = circlex[i] - circlerad[i];
for (i=0; i<ncircles; i++)
if ((circleactive[i])&&(circlex[i] + circlerad[i] > xright)) xright = circlex[i] + circlerad[i];
xy_to_ij(xleft, 0.0, ij);
imin = ij[0] - 10;
if (imin < 0) imin = 0;
xy_to_ij(xright, 0.0, ij);
imax = ij[0];
if (imax >= NX) imax = NX-1;
first = 0;
printf("xleft = %.3lg, xright = %.3lg, imin = %i, imax = %i\n", xleft, xright, imin, imax);
}
blank();
glColor3f(0.0, 0.0, 0.0);
draw_wave(phi, psi, xy_in, 1.0, 0, PLOT);
draw_billiard();
glutSwapBuffers();
sleep(SLEEP1);
for (i=0; i<=INITIAL_TIME + NSTEPS; i++)
{
//printf("%d\n",i);
/* compute the variance of the field to adjust color scheme */
/* the color depends on the field divided by sqrt(1 + variance) */
if (SCALE)
{
scale = sqrt(1.0 + compute_variance(phi,psi, xy_in));
// printf("Scaling factor: %5lg\n", scale);
}
else scale = 1.0;
draw_wave(phi, psi, xy_in, scale, i, PLOT);
for (j=0; j<NVID; j++)
{
evolve_wave(phi, psi, phi_tmp, psi_tmp, xy_in);
// if (i % 10 == 9) oscillate_linear_wave(0.2*scale, 0.15*(double)(i*NVID + j), -1.5, YMIN, -1.5, YMAX, phi, psi);
}
/* compute energy dissipated in obstacles */
if (ERODE_MANGROVES) for (j=0; j<ncircles; j++)
{
dissip = compute_dissipation(phi, psi, xy_in, circlex[j], circley_wrapped[j]);
/* make sure the dissipation does not grow too fast because of round-off/blow-up */
if (dissip > 0.1*MANGROVE_EMAX)
{
dissip = 0.1*MANGROVE_EMAX;
printf("Flooring dissipation!\n");
}
if (circleactive[j])
{
circle_energy[j] += dissip;
ej = circle_energy[j];
if (ej <= MANGROVE_EMAX)
{
if (ej > 0.0)
{
hue = MANGROVE_HUE_MIN + (MANGROVE_HUE_MAX - MANGROVE_HUE_MIN)*ej/MANGROVE_EMAX;
if (hue < 0.0) hue += 360.0;
}
else hue = MANGROVE_HUE_MIN;
hsl_to_rgb(hue, 0.9, 0.5, rgb);
if (j%NGRIDY == 0) printf("Circle %i, energy %.5lg, hue %.5lg\n", j, ej, hue);
draw_colored_circle(circlex[j], circley[j], circlerad[j], NSEG, rgb);
/* shrink mangrove */
if (ej > 0.0)
{
// circlerad[j] -= MU*ej*ej/(MANGROVE_EMAX*MANGROVE_EMAX);
// if (circlerad[j] < 0.0) circlerad[j] = 0.0;
circlerad[j] = circlerad_initial[j]*(1.0 - ej*ej/(MANGROVE_EMAX*MANGROVE_EMAX));
redraw = 1;
}
else circlerad[j] = circlerad_initial[j];
}
else /* remove mangrove */
{
circleactive[j] = 0;
/* reinitialize table xy_in */
redraw = 1;
}
}
else /* allow disabled mangroves to recover */
{
circle_energy[j] -= 0.15*dissip;
// circlerad[j] += 0.005*MU;
// if (circlerad[j] > MU) circlerad[j] = MU;
// if ((circle_energy[j] < 0.0)&&(circlerad[j] > 0.0))
if (circle_energy[j] < 0.0)
{
circleactive[j] = 1;
// circlerad[j] = circlerad[j]*(0.75 + 0.5*((double)rand()/RAND_MAX));
circlerad[j] = circlerad_initial[j];
circle_energy[j] = -MANGROVE_EMAX;
/* reinitialize table xy_in */
redraw = 1;
}
}
// printf("Circle %i, energy %.5lg\n", j, circle_energy[j]);
}
/* move mangroves */
if (MOVE_MANGROVES) for (j=0; j<ncircles; j++) if (circleactive[j])
{
compute_gradient(phi, psi, circlex[j], circley_wrapped[j], gradient);
// if (j%NGRIDY == 0) printf("gradient (%.3lg, %.3lg)\n", gradient[0], gradient[1]);
// if (j%NGRIDY == 0) printf("circle %i (%.3lg, %.3lg) -> ", j, circlex[j], circley[j]);
/* compute force of wave */
dx = DT_MANGROVE*KWAVE*gradient[0];
dy = DT_MANGROVE*KWAVE*gradient[1];
/* compute force of spring */
if (circle_attached[j])
{
dx += DT_MANGROVE*(-KSPRING*(circlex[j] - anchor_x[j]));
dy += DT_MANGROVE*(-KSPRING*(circley_wrapped[j] - anchor_y[j]));
}
/* detach mangrove if spring is too long */
if (DETACH_MANGROVES)
{
length = module2(circlex[j] - anchor_x[j], circley_wrapped[j] - anchor_y[j]);
if (j%NGRIDY == 0) printf("spring length %.i: %.3lg\n", j, length);
// if (length > L_DETACH) circle_attached[j] = 0;
if (length*mass_inverse[j] > L_DETACH) circle_attached[j] = 0;
}
if (dx > DXMAX) dx = DXMAX;
if (dx < -DXMAX) dx = -DXMAX;
if (dy > DXMAX) dy = DXMAX;
if (dy < -DXMAX) dy = -DXMAX;
if (INERTIA)
{
vx[j] += (dx - DAMP_MANGROVE*vx[j])*mass_inverse[j];
vy[j] += (dy - DAMP_MANGROVE*vy[j])*mass_inverse[j];
circlex[j] += vx[j]*DT_MANGROVE;
circley[j] += vy[j]*DT_MANGROVE;
circley_wrapped[j] += vy[j]*DT_MANGROVE;
if (j%NGRIDY == 0)
printf("circle %.i: (dx,dy) = (%.3lg,%.3lg), (vx,vy) = (%.3lg,%.3lg)\n",
j, circlex[j]-anchor_x[j], circley[j]-anchor_y[j], vx[j], vy[j]);
}
else
{
circlex[j] += dx*mass_inverse[j]*DT_MANGROVE;
circley[j] += dy*mass_inverse[j]*DT_MANGROVE;
circley_wrapped[j] += dy*mass_inverse[j]*DT_MANGROVE;
}
if (circlex[j] <= XMIN) circlex[j] = XMIN;
if (circlex[j] >= XMAX) circlex[j] = XMAX;
if (circley_wrapped[j] <= YMIN) circley_wrapped[j] = YMIN;
if (circley_wrapped[j] >= YMAX) circley_wrapped[j] = YMAX;
// if (j%NGRIDY == 0) printf("(%.3lg, %.3lg)\n", circlex[j], circley[j]);
redraw = 1;
}
draw_billiard();
glutSwapBuffers();
if (redraw)
{
printf("Reinitializing xy_in\n");
init_xyin_xrange(xy_in, imin, NX-1);
// init_xyin_xrange(xy_in, imin, imax);
}
redraw = 0;
if (MOVIE)
{
if (i >= INITIAL_TIME) save_frame();
else printf("Initial phase time %i of %i\n", i, INITIAL_TIME);
/* 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/");
}
}
}
if (MOVIE)
{
for (i=0; i<END_FRAMES; i++) save_frame();
s = system("mv wave*.tif tif_wave/");
}
for (i=0; i<NX; i++)
{
free(phi[i]);
free(psi[i]);
free(phi_tmp[i]);
free(psi_tmp[i]);
free(xy_in[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;
}

45
particle_billiard.c
View File

@ -44,23 +44,29 @@
/* Choice of the billiard table, see global_particles.c */
#define B_DOMAIN 20 /* choice of domain shape */
#define B_DOMAIN 16 /* 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 NCX 10 /* number of circles in x direction */
// #define NCY 10 /* number of circles in y direction */
#define NCX 30 /* 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 LAMBDA 0.75 /* parameter controlling shape of billiard */
#define MU 0.035 /* second parameter controlling shape of billiard */
// #define LAMBDA 1.4 /* parameter controlling shape of domain */
// #define MU 0.2 /* second parameter controlling shape of billiard */
#define LAMBDA 1.5 /* parameter controlling shape of domain */
#define MU 0.3 /* 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 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 DRAW_CONSTRUCTION_LINES 0 /* 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 */
@ -68,16 +74,16 @@
/* Simulation parameters */
#define NPART 30000 /* number of particles */
#define NPART 10000 /* 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 NSTEPS 3500 /* number of frames of movie */
#define TIME 1200 /* time between movie frames, for fluidity of real-time simulation */
#define DPHI 0.00001 /* integration step */
#define NVID 150 /* number of iterations between images displayed on screen */
/* Decreasing TIME accelerates the animation and the movie */
@ -88,12 +94,12 @@
/* Colors and other graphical parameters */
#define NCOLORS 32 /* number of colors */
#define NCOLORS 16 /* 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 LENGTH 0.01 /* 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 */
@ -102,7 +108,7 @@
#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 PAINT_EXT 1 /* set to 1 to paint exterior */
#define PAUSE 1000 /* number of frames after which to pause */
#define PSLEEP 1 /* sleep time during pause */
@ -326,7 +332,7 @@ void graph_movie(int time, int color[NPARTMAX], double *configs[NPARTMAX], int a
{
// printf("reflecting particle %i\n", i);
c = vbilliard(configs[i]);
// if (c>=0) color[i]++;
if (c>=0) color[i]++;
if (!RAINBOW_COLOR)
{
color[i]++;
@ -368,14 +374,17 @@ void animation()
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, 0.7, 0.0, DPI, configs);
// init_drop_config(-1.3, -0.1, 0.0, DPI, configs);
init_drop_config(1.4, 0.1, 0.0, DPI, 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(-1.3, -0.3, -1.2, -0.3, PID, configs);
// init_line_config(0.0, 0.0, 0.5, 0.0, PID, configs);
// init_line_config(0.0, 0.0, 0.0, -0.5, PI, 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);

1287
sub_part_billiard.c
View File

File diff suppressed because it is too large Load Diff

294
sub_wave.c
View File

@ -150,6 +150,41 @@ void color_scheme(int scheme, double value, double scale, int time, double rgb[3
}
void color_scheme_lum(int scheme, double value, double scale, int time, double lum, double rgb[3]) /* color scheme */
{
double hue, y, r, amplitude;
int intpart;
/* saturation = r, luminosity = y */
switch (scheme) {
case (C_LUM):
{
hue = COLORHUE + (double)time*COLORDRIFT/(double)NSTEPS;
if (hue < 0.0) hue += 360.0;
if (hue >= 360.0) hue -= 360.0;
r = 0.9;
amplitude = color_amplitude(value, scale, time);
y = LUMMEAN + amplitude*LUMAMP;
intpart = (int)y;
y -= (double)intpart;
hsl_to_rgb(hue, r, y, rgb);
break;
}
case (C_HUE):
{
r = 0.9;
amplitude = color_amplitude(value, scale, time);
y = lum;
hue = HUEMEAN + amplitude*HUEAMP;
if (hue < 0.0) hue += 360.0;
if (hue >= 360.0) hue -= 360.0;
hsl_to_rgb(hue, r, y, rgb);
break;
}
}
}
void blank()
{
if (BLACK) glClearColor(0.0, 0.0, 0.0, 1.0);
@ -191,6 +226,20 @@ void save_frame_counter(int counter)
}
void write_text_fixedwidth( double x, double y, char *st)
{
int l, i;
l=strlen( st ); // see how many characters are in text string.
glRasterPos2d( x, y); // location to start printing text
for( i=0; i < l; i++) // loop until i is greater then l
{
// glutBitmapCharacter(GLUT_BITMAP_TIMES_ROMAN_24, st[i]); // Print a character on the screen
// glutBitmapCharacter(GLUT_BITMAP_8_BY_13, st[i]); // Print a character on the screen
glutBitmapCharacter(GLUT_BITMAP_9_BY_15, st[i]); // Print a character on the screen
}
}
void write_text( double x, double y, char *st)
{
@ -739,7 +788,7 @@ int xy_in_billiard(double x, double y)
/* returns 1 if (x,y) represents a point in the billiard */
// double x, y;
{
double l2, r2, r2mu, omega, c, angle, z, x1, y1, x2, y2, u, v, u1, v1, dx, dy, width;
double l2, r2, r2mu, omega, b, c, angle, z, x1, y1, x2, y2, u, v, u1, v1, dx, dy, width;
int i, j, k, k1, k2, condition;
switch (B_DOMAIN) {
@ -876,6 +925,48 @@ int xy_in_billiard(double x, double y)
else if ((x > x1)&&(x < x2)) return(1);
else return(0);
}
case (D_FOUR_PARABOLAS):
{
x1 = MU + LAMBDA - 0.25*y*y/MU;
y1 = MU + LAMBDA - 0.25*x*x/MU;
return((vabs(x) < x1)&&(vabs(y) < y1));
}
case (D_POLY_PARABOLAS):
{
condition = 1;
omega = DPI/((double)NPOLY);
for (k=0; k<NPOLY; k++)
{
angle = APOLY*PID + (k+0.5)*omega;
x1 = x*cos(angle) + y*sin(angle);
y1 = -x*sin(angle) + y*cos(angle);
condition = condition*(x1 < LAMBDA + MU - 0.25*y1*y1/MU);
}
return(condition);
}
case (D_PENROSE):
{
c = sqrt(LAMBDA*LAMBDA - (1.0 - MU)*(1.0 - MU));
width = 0.1*MU;
x1 = vabs(x);
y1 = vabs(y);
/* sides */
if (vabs(x) >= LAMBDA) return(0);
/* upper and lower ellipse */
else if ((vabs(y) >= MU)&&(x*x/(LAMBDA*LAMBDA) + (y1-MU)*(y1-MU)/((1.0-MU)*(1.0-MU)) >= 1.0)) return(0);
/* small ellipses */
else if ((vabs(x) <= c)&&(4.0*(x1-c)*(x1-c)/(MU*MU) + y*y/(MU*MU) <= 1.0)) return(0);
/* straight parts */
else if ((vabs(x) >= c)&&(vabs(y) <= width)) return(0);
else return(1);
}
case (D_HYPERBOLA):
{
b = MU*sqrt(1.0 + x*x/(LAMBDA*LAMBDA - MU*MU));
if (y > 1.02*b) return(1);
else if (y < 0.98*b) return (1);
else return(0);
}
case (D_CIRCLES):
{
for (i = 0; i < ncircles; i++)
@ -1046,7 +1137,7 @@ int ij_in_billiard(int i, int j)
void draw_billiard() /* draws the billiard boundary */
{
double x0, x, y, x1, y1, dx, dy, phi, r = 0.01, pos[2], pos1[2], alpha, dphi, omega, z, l, width;
double x0, x, y, x1, y1, dx, dy, phi, r = 0.01, pos[2], pos1[2], alpha, dphi, omega, z, l, width, a, b, c, ymax;
int i, j, k, k1, k2, mr2;
if (BLACK) glColor3f(1.0, 1.0, 1.0);
@ -1376,6 +1467,205 @@ void draw_billiard() /* draws the billiard boundary */
break;
}
case (D_FOUR_PARABOLAS):
{
x1 = 2.0*(sqrt(MU*(2.0*MU + LAMBDA)) - MU);
dy = 2.0*x1/(double)NSEG;
glBegin(GL_LINE_LOOP);
for (i = 0; i < NSEG+1; i++)
{
y = -x1 + dy*(double)i;
x = MU + LAMBDA - 0.25*y*y/MU;
xy_to_pos(x, y, pos);
glVertex2d(pos[0], pos[1]);
}
for (i = 0; i < NSEG+1; i++)
{
x = x1 - dy*(double)i;
y = MU + LAMBDA - 0.25*x*x/MU;
xy_to_pos(x, y, pos);
glVertex2d(pos[0], pos[1]);
}
for (i = 0; i < NSEG+1; i++)
{
y = x1 - dy*(double)i;
x = -MU - LAMBDA + 0.25*y*y/MU;
xy_to_pos(x, y, pos);
glVertex2d(pos[0], pos[1]);
}
for (i = 0; i < NSEG+1; i++)
{
x = -x1 + dy*(double)i;
y = -MU - LAMBDA + 0.25*x*x/MU;
xy_to_pos(x, y, pos);
glVertex2d(pos[0], pos[1]);
}
glEnd ();
if (FOCI)
{
glColor3f(0.3, 0.3, 0.3);
draw_circle(-LAMBDA, 0.0, r, NSEG);
draw_circle(LAMBDA, 0.0, r, NSEG);
draw_circle(0.0, -LAMBDA, r, NSEG);
draw_circle(0.0, LAMBDA, r, NSEG);
}
break;
}
case (D_POLY_PARABOLAS):
{
omega = PI/((double)NPOLY);
a = 0.25/MU;
b = 1.0/tan(omega);
c = LAMBDA + MU;
ymax = (-b + sqrt(b*b + 4.0*a*c))/(2.0*a);
dy = 2.0*ymax/(double)NSEG;
// printf("a = %.3lg, b = %.3lg, ymax = %.3lg\n", a, b,ymax);
glBegin(GL_LINE_LOOP);
for (k=0; k<NPOLY; k++)
{
alpha = APOLY*PID + (2.0*(double)k+1.0)*omega;
for (i = 0; i < NSEG+1; i++)
{
y1 = -ymax + dy*(double)i;
x1 = MU + LAMBDA - 0.25*y1*y1/MU;
x = x1*cos(alpha) - y1*sin(alpha);
y = x1*sin(alpha) + y1*cos(alpha);
xy_to_pos(x, y, pos);
glVertex2d(pos[0], pos[1]);
}
}
glEnd ();
if (FOCI)
{
glColor3f(0.3, 0.3, 0.3);
for (k=0; k<NPOLY; k++)
{
alpha = APOLY*PID + (k+0.5)*omega;
draw_circle(LAMBDA*cos(alpha), LAMBDA*sin(alpha), r, NSEG);
}
}
break;
}
case (D_PENROSE):
{
c = sqrt(LAMBDA*LAMBDA - (1.0 - MU)*(1.0 - MU));
width = 0.1*MU;
x1 = vabs(x);
y1 = vabs(y);
dphi = PI/(double)NSEG;
glBegin(GL_LINE_LOOP);
/* upper half ellipse */
for (i=0; i<=NSEG; i++)
{
phi = (double)i*dphi;
x = LAMBDA*cos(phi);
y = MU + (1.0-MU)*sin(phi);
xy_to_pos(x, y, pos);
glVertex2d(pos[0], pos[1]);
}
/* straight parts */
xy_to_pos(-LAMBDA, width, pos);
glVertex2d(pos[0], pos[1]);
xy_to_pos(-c, width, pos);
glVertex2d(pos[0], pos[1]);
xy_to_pos(-c, MU, pos);
glVertex2d(pos[0], pos[1]);
/* left half ellipse */
for (i=0; i<=NSEG; i++)
{
phi = (double)i*dphi;
x = -c + 0.5*MU*sin(phi);
y = MU*cos(phi);
xy_to_pos(x, y, pos);
glVertex2d(pos[0], pos[1]);
}
/* straight parts */
xy_to_pos(-c, -width, pos);
glVertex2d(pos[0], pos[1]);
xy_to_pos(-LAMBDA, -width, pos);
glVertex2d(pos[0], pos[1]);
xy_to_pos(-LAMBDA, -MU, pos);
glVertex2d(pos[0], pos[1]);
/* lower half ellipse */
for (i=0; i<=NSEG; i++)
{
phi = (double)i*dphi;
x = -LAMBDA*cos(phi);
y = -MU - (1.0-MU)*sin(phi);
xy_to_pos(x, y, pos);
glVertex2d(pos[0], pos[1]);
}
/* straight parts */
xy_to_pos(LAMBDA, -width, pos);
glVertex2d(pos[0], pos[1]);
xy_to_pos(c, -width, pos);
glVertex2d(pos[0], pos[1]);
xy_to_pos(c, -MU, pos);
glVertex2d(pos[0], pos[1]);
/* right half ellipse */
for (i=0; i<=NSEG; i++)
{
phi = (double)i*dphi;
x = c - 0.5*MU*sin(phi);
y = -MU*cos(phi);
xy_to_pos(x, y, pos);
glVertex2d(pos[0], pos[1]);
}
/* straight parts */
xy_to_pos(c, width, pos);
glVertex2d(pos[0], pos[1]);
xy_to_pos(LAMBDA, width, pos);
glVertex2d(pos[0], pos[1]);
xy_to_pos(LAMBDA, MU, pos);
glVertex2d(pos[0], pos[1]);
glEnd ();
break;
}
case (D_HYPERBOLA):
{
dx = (XMAX - XMIN)/(double)NSEG;
glBegin(GL_LINE_STRIP);
for (i = 0; i < NSEG+1; i++)
{
x = XMIN + dx*(double)i;
y = MU*1.02*sqrt(1.0 + x*x/(LAMBDA*LAMBDA - MU*MU));
xy_to_pos(x, y, pos);
glVertex2d(pos[0], pos[1]);
}
glEnd ();
glBegin(GL_LINE_STRIP);
for (i = 0; i < NSEG+1; i++)
{
x = XMIN + dx*(double)i;
y = MU*0.98*sqrt(1.0 + x*x/(LAMBDA*LAMBDA - MU*MU));
xy_to_pos(x, y, pos);
glVertex2d(pos[0], pos[1]);
}
glEnd ();
if (FOCI)
{
glColor3f(0.3, 0.3, 0.3);
draw_circle(0.0, LAMBDA, r, NSEG);
draw_circle(0.0, -LAMBDA, r, NSEG);
}
break;
}
case (D_CIRCLES):
{
glLineWidth(BOUNDARY_WIDTH);

54
wave_billiard.c
View File

@ -42,37 +42,43 @@
#include <tiffio.h> /* Sam Leffler's libtiff library. */
#include <omp.h>
#define MOVIE 1 /* set to 1 to generate movie */
#define MOVIE 0 /* set to 1 to generate movie */
#define DOUBLE_MOVIE 0 /* set to 1 to produce movies for wave height and energy simultaneously */
/* General geometrical parameters */
#define WINWIDTH 1280 /* window width */
// #define WINWIDTH 720 /* window width */
#define WINHEIGHT 720 /* window height */
#define NX 1280 /* number of grid points on x axis */
// #define NX 720 /* number of grid points on x axis */
#define NY 720 /* number of grid points on y axis */
#define XMIN -2.0
#define XMAX 2.0 /* x interval */
#define YMIN -1.125
#define YMAX 1.125 /* y interval for 9/16 aspect ratio */
// #define XMIN -1.6
// #define XMAX 1.6 /* x interval */
// #define YMIN -1.6
// #define YMAX 1.6 /* y interval for 9/16 aspect ratio */
#define JULIA_SCALE 1.0 /* scaling for Julia sets */
/* Choice of the billiard table */
#define B_DOMAIN 19 /* choice of domain shape, see list in global_pdes.c */
#define B_DOMAIN 34 /* choice of domain shape, see list in global_pdes.c */
#define CIRCLE_PATTERN 8 /* pattern of circles, see list in global_pdes.c */
#define P_PERCOL 0.25 /* probability of having a circle in C_RAND_PERCOL arrangement */
#define NPOISSON 300 /* number of points for Poisson C_RAND_POISSON arrangement */
#define LAMBDA 0.0 /* parameter controlling the dimensions of domain */
#define MU 1.25 /* parameter controlling the dimensions of domain */
#define LAMBDA 0.6 /* parameter controlling the dimensions of domain */
#define MU 0.3 /* parameter controlling the dimensions of domain */
#define NPOLY 3 /* number of sides of polygon */
#define APOLY 1.0 /* angle by which to turn polygon, in units of Pi/2 */
#define APOLY 0.0 /* angle by which to turn polygon, in units of Pi/2 */
#define MDEPTH 4 /* depth of computation of Menger gasket */
#define MRATIO 3 /* ratio defining Menger gasket */
#define MANDELLEVEL 1000 /* iteration level for Mandelbrot set */
@ -112,8 +118,8 @@
/* Parameters for length and speed of simulation */
#define NSTEPS 5000 /* number of frames of movie */
#define NVID 25 /* number of iterations between images displayed on screen */
#define NSTEPS 4050 /* number of frames of movie */
#define NVID 32 /* number of iterations between images displayed on screen */
#define NSEG 100 /* number of segments of boundary */
#define INITIAL_TIME 0 /* time after which to start saving frames */
#define BOUNDARY_WIDTH 2 /* width of billiard boundary */
@ -125,6 +131,12 @@
#define MID_FRAMES 20 /* number of still frames between parts of two-part movie */
#define END_FRAMES 100 /* number of still frames at end of movie */
/* Parameters of initial condition */
#define INITIAL_AMP 0.2 /* amplitude of initial condition */
#define INITIAL_VARIANCE 0.002 /* variance of initial condition */
#define INITIAL_WAVELENGTH 0.1 /* wavelength of initial condition */
/* Plot type, see list in global_pdes.c */
#define PLOT 1
@ -138,9 +150,10 @@
#define COLOR_SCHEME 1 /* choice of color scheme, see list in global_pdes.c */
#define SCALE 0 /* set to 1 to adjust color scheme to variance of field */
#define SLOPE 1.0 /* sensitivity of color on wave amplitude */
#define SLOPE 0.08 /* sensitivity of color on wave amplitude */
// #define SLOPE 0.05 /* sensitivity of color on wave amplitude */
#define ATTENUATION 0.0 /* exponential attenuation coefficient of contrast with time */
#define E_SCALE 500.0 /* scaling factor for energy representation */
#define E_SCALE 200.0 /* scaling factor for energy representation */
// #define E_SCALE 2500.0 /* scaling factor for energy representation */
#define COLORHUE 260 /* initial hue of water color for scheme C_LUM */
@ -148,7 +161,7 @@
#define LUMMEAN 0.5 /* amplitude of luminosity variation for scheme C_LUM */
#define LUMAMP 0.3 /* amplitude of luminosity variation for scheme C_LUM */
#define HUEMEAN 220.0 /* mean value of hue for color scheme C_HUE */
#define HUEAMP -220.0 /* amplitude of variation of hue for color scheme C_HUE */
#define HUEAMP -230.0 /* amplitude of variation of hue for color scheme C_HUE */
/* For debugging purposes only */
#define FLOOR 0 /* set to 1 to limit wave amplitude to VMAX */
@ -327,9 +340,14 @@ void animation()
courantb2 = COURANTB*COURANTB;
/* initialize wave with a drop at one point, zero elsewhere */
init_circular_wave(0.0, -LAMBDA, phi, psi, xy_in);
// init_wave_flat(phi, psi, xy_in);
init_wave(-LAMBDA, 0.0, phi, psi, xy_in);
// init_wave_plus(LAMBDA - 0.3*MU, 0.5*MU, phi, psi, xy_in);
// init_wave(LAMBDA - 0.3*MU, 0.5*MU, phi, psi, xy_in);
// init_wave(0.0, 0.0, phi, psi, xy_in);
// init_planar_wave(XMIN + 0.015, 0.0, phi, psi, xy_in);
// init_planar_wave(XMIN + 0.02, 0.0, phi, psi, xy_in);
// init_planar_wave(XMIN + 0.8, 0.0, phi, psi, xy_in);
@ -372,7 +390,14 @@ void animation()
}
draw_billiard();
/* add oscillating waves */
// if (i%160 == 159)
if (i%150 == 149)
{
add_circular_wave(1.0, 0.0, LAMBDA, phi, psi, xy_in);
add_circular_wave(1.0, 0.0, -LAMBDA, phi, psi, xy_in);
}
glutSwapBuffers();
@ -416,9 +441,10 @@ void animation()
draw_wave(phi, psi, xy_in, scale, i, PLOT_B);
draw_billiard();
glutSwapBuffers();
for (i=0; i<END_FRAMES; i++) save_frame_counter(NSTEPS + MID_FRAMES + 1 + counter + i);
// for (i=0; i<END_FRAMES; i++) save_frame_counter(NSTEPS + MID_FRAMES + 1 + counter + i);
}
for (i=0; i<END_FRAMES; i++) save_frame_counter(NSTEPS + MID_FRAMES + 1 + counter + i);
s = system("mv wave*.tif tif_wave/");
}
for (i=0; i<NX; i++)

162
wave_common.c
View File

@ -16,6 +16,22 @@ void init_xyin(short int * xy_in[NX])
}
}
void init_xyin_xrange(short int * xy_in[NX], int imin, int imax)
/* initialise table xy_in, needed when obstacles are killed */
// short int * xy_in[NX];
//
{
int i, j;
double xy[2];
for (i=imin; i<imax; i++)
for (j=0; j<NY; j++)
{
ij_to_xy(i, j, xy);
xy_in[i][j] = xy_in_billiard(xy[0],xy[1]);
}
}
void init_wave(double x, double y, double *phi[NX], double *psi[NX], short int * xy_in[NX])
/* initialise field with drop at (x,y) - phi is wave height, psi is phi at time t-1 */
@ -30,12 +46,53 @@ void init_wave(double x, double y, double *phi[NX], double *psi[NX], short int *
dist2 = (xy[0]-x)*(xy[0]-x) + (xy[1]-y)*(xy[1]-y);
xy_in[i][j] = xy_in_billiard(xy[0],xy[1]);
if ((xy_in[i][j])||(TWOSPEEDS)) phi[i][j] = 0.2*exp(-dist2/0.001)*cos(-sqrt(dist2)/0.01);
if ((xy_in[i][j])||(TWOSPEEDS)) phi[i][j] = 0.2*exp(-dist2/0.005)*cos(-sqrt(dist2)/0.1);
// if ((xy_in[i][j])||(TWOSPEEDS)) phi[i][j] = 0.2*exp(-dist2/0.001)*cos(-sqrt(dist2)/0.01);
// if ((xy_in[i][j])||(TWOSPEEDS)) phi[i][j] = 0.2*exp(-dist2/0.00025)*cos(-sqrt(dist2)/0.005);
else phi[i][j] = 0.0;
psi[i][j] = 0.0;
}
}
void init_circular_wave(double x, double y, double *phi[NX], double *psi[NX], short int * xy_in[NX])
/* initialise field with drop at (x,y) - phi is wave height, psi is phi at time t-1 */
{
int i, j;
double xy[2], dist2;
for (i=0; i<NX; i++)
for (j=0; j<NY; j++)
{
ij_to_xy(i, j, xy);
dist2 = (xy[0]-x)*(xy[0]-x) + (xy[1]-y)*(xy[1]-y);
xy_in[i][j] = xy_in_billiard(xy[0],xy[1]);
if ((xy_in[i][j])||(TWOSPEEDS))
phi[i][j] = INITIAL_AMP*exp(-dist2/INITIAL_VARIANCE)*cos(-sqrt(dist2)/INITIAL_WAVELENGTH);
else phi[i][j] = 0.0;
psi[i][j] = 0.0;
}
}
void init_wave_plus(double x, double y, double *phi[NX], double *psi[NX], short int * xy_in[NX])
/* initialise field with drop at (x,y) for y > 0 - phi is wave height, psi is phi at time t-1 */
{
int i, j;
double xy[2], dist2;
for (i=0; i<NX; i++)
for (j=0; j<NY; j++)
{
ij_to_xy(i, j, xy);
dist2 = (xy[0]-x)*(xy[0]-x) + (xy[1]-y)*(xy[1]-y);
xy_in[i][j] = xy_in_billiard(xy[0],xy[1]);
if ((xy[1] > 0.0)&&((xy_in[i][j])||(TWOSPEEDS)))
phi[i][j] = INITIAL_AMP*exp(-dist2/INITIAL_VARIANCE)*cos(-sqrt(dist2)/INITIAL_WAVELENGTH);
else phi[i][j] = 0.0;
psi[i][j] = 0.0;
}
}
void init_planar_wave(double x, double y, double *phi[NX], double *psi[NX], short int * xy_in[NX])
/* initialise field with drop at (x,y) - phi is wave height, psi is phi at time t-1 */
@ -81,7 +138,7 @@ void init_wave_flat( double *phi[NX], double *psi[NX], short int * xy_in[NX])
void add_drop_to_wave(double factor, double x, double y, double *phi[NX], double *psi[NX])
/* add drop at (x,y) to the field with given prefactor */
/* OLD VERSION - add drop at (x,y) to the field with given prefactor */
{
int i, j;
double xy[2], dist2;
@ -95,6 +152,22 @@ void add_drop_to_wave(double factor, double x, double y, double *phi[NX], double
}
}
void add_circular_wave(double factor, double x, double y, double *phi[NX], double *psi[NX], short int * xy_in[NX])
/* add drop at (x,y) to the field with given prefactor */
{
int i, j;
double xy[2], dist2;
for (i=0; i<NX; i++)
for (j=0; j<NY; j++)
{
ij_to_xy(i, j, xy);
dist2 = (xy[0]-x)*(xy[0]-x) + (xy[1]-y)*(xy[1]-y);
if ((xy_in[i][j])||(TWOSPEEDS))
phi[i][j] += INITIAL_AMP*factor*exp(-dist2/INITIAL_VARIANCE)*cos(-sqrt(dist2)/INITIAL_WAVELENGTH);
}
}
void oscillate_linear_wave(double amplitude, double t, double x1, double y1, double x2, double y2, double *phi[NX],
double *psi[NX])
@ -123,6 +196,26 @@ void oscillate_linear_wave(double amplitude, double t, double x1, double y1, dou
}
}
void compute_gradient(double *phi[NX], double *psi[NX], double x, double y, double gradient[2])
{
double velocity;
int iplus, iminus, jplus, jminus, ij[2], i, j;
xy_to_ij(x, y, ij);
i = ij[0];
j = ij[1];
iplus = (i+1); if (iplus == NX) iplus = NX-1;
iminus = (i-1); if (iminus == -1) iminus = 0;
jplus = (j+1); if (jplus == NY) jplus = NY-1;
jminus = (j-1); if (jminus == -1) jminus = 0;
gradient[0] = (phi[iplus][j]-phi[i][j])*(phi[iplus][j]-phi[i][j])
+ (phi[i][j] - phi[iminus][j])*(phi[i][j] - phi[iminus][j]);
gradient[1] = (phi[i][jplus]-phi[i][j])*(phi[i][jplus]-phi[i][j])
+ (phi[i][j] - phi[i][jminus])*(phi[i][j] - phi[i][jminus]);
}
double compute_energy(double *phi[NX], double *psi[NX], short int *xy_in[NX], int i, int j)
{
@ -196,7 +289,11 @@ void draw_wave(double *phi[NX], double *psi[NX], short int *xy_in[NX], double sc
if ((TWOSPEEDS)||(xy_in[i][j]))
{
if (plot == P_AMPLITUDE)
color_scheme(COLOR_SCHEME, phi[i][j], scale, time, rgb);
{
/* make wave luminosity larger inside obstacles */
if (!(xy_in[i][j])) color_scheme_lum(COLOR_SCHEME, phi[i][j], scale, time, 0.7, rgb);
else color_scheme(COLOR_SCHEME, phi[i][j], scale, time, rgb);
}
else if (plot == P_ENERGY)
color_scheme(COLOR_SCHEME, compute_energy(phi, psi, xy_in, i, j), scale, time, rgb);
else if (plot == P_MIXED)
@ -216,6 +313,65 @@ void draw_wave(double *phi[NX], double *psi[NX], short int *xy_in[NX], double sc
glEnd ();
}
void draw_wave_e(double *phi[NX], double *psi[NX], double *total_energy[NX], short int *xy_in[NX], double scale, int time, int plot)
/* draw the field, new version with total energy option */
{
int i, j, iplus, iminus, jplus, jminus;
double rgb[3], xy[2], x1, y1, x2, y2, velocity, energy, gradientx2, gradienty2;
static double dtinverse = ((double)NX)/(COURANT*(XMAX-XMIN)), dx = (XMAX-XMIN)/((double)NX);
glBegin(GL_QUADS);
// printf("dtinverse = %.5lg\n", dtinverse);
for (i=0; i<NX; i++)
for (j=0; j<NY; j++)
{
if ((TWOSPEEDS)||(xy_in[i][j]))
{
switch (plot) {
case (P_AMPLITUDE):
{
/* make wave luminosity larger inside obstacles */
if (!(xy_in[i][j])) color_scheme_lum(COLOR_SCHEME, phi[i][j], scale, time, 0.7, rgb);
else color_scheme(COLOR_SCHEME, phi[i][j], scale, time, rgb);
break;
}
case (P_ENERGY):
{
color_scheme(COLOR_SCHEME, compute_energy(phi, psi, xy_in, i, j), scale, time, rgb);
break;
}
case (P_MIXED):
{
if (j > NY/2) color_scheme(COLOR_SCHEME, phi[i][j], scale, time, rgb);
else color_scheme(COLOR_SCHEME, compute_energy(phi, psi, xy_in, i, j), scale, time, rgb);
break;
}
case (P_MEAN_ENERGY):
{
energy = compute_energy(phi, psi, xy_in, i, j);
total_energy[i][j] += energy;
color_scheme(COLOR_SCHEME, total_energy[i][j]/(double)(time+1), scale, time, rgb);
break;
}
}
glColor3f(rgb[0], rgb[1], rgb[2]);
glVertex2i(i, j);
glVertex2i(i+1, j);
glVertex2i(i+1, j+1);
glVertex2i(i, j+1);
}
}
glEnd ();
}

8
wave_comparison.c
View File

@ -42,7 +42,7 @@
#include <tiffio.h> /* Sam Leffler's libtiff library. */
#include <omp.h>
#define MOVIE 1 /* set to 1 to generate movie */
#define MOVIE 0 /* set to 1 to generate movie */
#define WINWIDTH 1280 /* window width */
#define WINHEIGHT 720 /* window height */
@ -131,6 +131,12 @@
#define SLEEP2 1 /* final sleeping time */
#define END_FRAMES 100 /* number of still frames at end of movie */
/* Parameters of initial condition */
#define INITIAL_AMP 0.2 /* amplitude of initial condition */
#define INITIAL_VARIANCE 0.002 /* variance of initial condition */
#define INITIAL_WAVELENGTH 0.1 /* wavelength of initial condition */
/* Plot type, see list in global_pdes.c */
#define PLOT 0