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YouTube-simulations/mangrove.c

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/*********************************************************************************/
/* */
/* 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 COLOR_PALETTE 0 /* Color palette, see list in global_pdes.c */
#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 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 */
/* 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 "hsluv.c"
#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;
}
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