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YouTube-simulations/wave_sphere.c

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/*********************************************************************************/
/* */
/* Animation of wave equation on a sphere */
/* */
/* N. Berglund, july 2023 */
/* */
/* 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_sphere wave_sphere.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>
#include <time.h>
#define MOVIE 0 /* set to 1 to generate movie */
#define DOUBLE_MOVIE 1 /* set to 1 to produce movies for wave height and energy simultaneously */
#define SAVE_MEMORY 1 /* set to 1 to save memory when writing tiff images */
#define NO_EXTRA_BUFFER_SWAP 1 /* some OS require one less buffer swap when recording images */
/* General geometrical parameters */
#define WINWIDTH 1920 /* window width */
#define WINHEIGHT 1150 /* window height */
#define NX 2560 /* number of grid points on x axis */
#define NY 1280 /* number of grid points on y axis */
#define DPOLE 20 /* safety distance to poles */
#define SMOOTHPOLE 0.1 /* smoothing coefficient at poles */
#define XMIN -2.0
#define XMAX 2.0 /* x interval */
#define YMIN -1.041666667
#define YMAX 1.041666667 /* y interval for 9/16 aspect ratio */
#define HIGHRES 0 /* set to 1 if resolution of grid is double that of displayed image */
#define JULIA_SCALE 0.25 /* scaling for Julia sets */
#define JULIA_ROT 90.0 /* rotation of Julia set, in degrees */
#define JULIA_RE -0.77145
#define JULIA_IM -0.10295 /* parameters for Julia sets */
/* Choice of the billiard table */
#define B_DOMAIN 84 /* choice of domain shape, see list in global_pdes.c */
#define CIRCLE_PATTERN 33 /* pattern of circles or polygons, see list in global_pdes.c */
#define COMPARISON 0 /* set to 1 to compare two different patterns */
#define B_DOMAIN_B 20 /* second domain shape, for comparisons */
#define CIRCLE_PATTERN_B 0 /* second pattern of circles or polygons */
#define VARIABLE_IOR 0 /* set to 1 for a variable index of refraction */
#define IOR 9 /* choice of index of refraction, see list in global_pdes.c */
#define IOR_TOTAL_TURNS 1.0 /* total angle of rotation for IOR_PERIODIC_WELLS_ROTATING */
#define MANDEL_IOR_SCALE -0.05 /* parameter controlling dependence of IoR on Mandelbrot escape speed */
#define P_PERCOL 0.25 /* probability of having a circle in C_RAND_PERCOL arrangement */
#define NPOISSON 1000 /* number of points for Poisson C_RAND_POISSON arrangement */
#define RANDOM_POLY_ANGLE 1 /* set to 1 to randomize angle of polygons */
#define LAMBDA 0.75 /* parameter controlling the dimensions of domain */
#define MU 0.1 /* parameter controlling the dimensions of domain */
#define NPOLY 6 /* number of sides of polygon */
#define APOLY 0.0 /* angle by which to turn polygon, in units of Pi/2 */
#define MDEPTH 7 /* depth of computation of Menger gasket */
#define MRATIO 3 /* ratio defining Menger gasket */
#define MANDELLEVEL 2000 /* iteration level for Mandelbrot set */
#define MANDELLIMIT 20.0 /* limit value for approximation of Mandelbrot set */
#define FOCI 1 /* set to 1 to draw focal points of ellipse */
#define NGRIDX 30 /* number of grid point for grid of disks */
#define NGRIDY 18 /* number of grid point for grid of disks */
#define X_SHOOTER -0.2
#define Y_SHOOTER -0.6
#define X_TARGET 0.4
#define Y_TARGET 0.7 /* shooter and target positions in laser fight */
#define ISO_XSHIFT_LEFT -2.9
#define ISO_XSHIFT_RIGHT 1.4
#define ISO_YSHIFT_LEFT -0.15
#define ISO_YSHIFT_RIGHT -0.15
#define ISO_SCALE 0.5 /* coordinates for isospectral billiards */
/* You can add more billiard tables by adapting the functions */
/* xy_in_billiard and draw_billiard below */
/* Physical parameters of wave equation */
#define TWOSPEEDS 0 /* set to 1 to replace hardcore boundary by medium with different speed */
#define OSCILLATE_LEFT 0 /* set to 1 to add oscilating boundary condition on the left */
#define OSCILLATE_TOPBOT 0 /* set to 1 to enforce a planar wave on top and bottom boundary */
#define OSCILLATION_SCHEDULE 3 /* oscillation schedule, see list in global_pdes.c */
#define OMEGA 0.001 /* frequency of periodic excitation */
#define AMPLITUDE 0.8 /* amplitude of periodic excitation */
#define ACHIRP 0.2 /* acceleration coefficient in chirp */
#define DAMPING 0.0 /* damping of periodic excitation */
#define COURANT 0.05 /* Courant number */
#define COURANTB 0.01 /* Courant number in medium B */
#define GAMMA 0.0 /* damping factor in wave equation */
#define GAMMAB 1.0e-6 /* damping factor in wave equation */
#define GAMMA_SIDES 1.0e-4 /* damping factor on boundary */
#define GAMMA_TOPBOT 1.0e-7 /* damping factor on boundary */
#define KAPPA 0.0 /* "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 */
#define OSCIL_LEFT_YSHIFT 0.0 /* y-dependence of left oscillation (for non-horizontal waves) */
/* 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 */
#define ADD_OSCILLATING_SOURCE 0 /* set to 1 to add an oscillating wave source */
#define OSCILLATING_SOURCE_PERIOD 30 /* period of oscillating source */
#define ALTERNATE_OSCILLATING_SOURCE 1 /* set to 1 to alternate sign of oscillating source */
#define ADD_WAVE_PACKET_SOURCES 0 /* set to 1 to add several sources emitting wave packets */
#define WAVE_PACKET_SOURCE_TYPE 1 /* type of wave packet sources */
#define N_WAVE_PACKETS 15 /* number of wave packets */
#define WAVE_PACKET_RADIUS 20 /* radius of wave packets */
/* Boundary conditions, see list in global_pdes.c */
#define B_COND 2
#define PRECOMPUTE_BC 0 /* set to 1 to compute neighbours for Laplacian in advance */
/* Parameters for length and speed of simulation */
#define NSTEPS 3600 /* number of frames of movie */
#define NVID 4 /* number of iterations between images displayed on screen */
#define NSEG 1000 /* number of segments of boundary */
#define INITIAL_TIME 0 /* time after which to start saving frames */
#define BOUNDARY_WIDTH 2 /* width of billiard boundary */
#define PRINT_SPEED 0 /* set to 1 to print speed of moving source */
#define PAUSE 100 /* number of frames after which to pause */
#define PSLEEP 3 /* sleep time during pause */
#define SLEEP1 1 /* initial sleeping time */
#define SLEEP2 1 /* final sleeping time */
#define MID_FRAMES 100 /* number of still frames between parts of two-part movie */
#define END_FRAMES 100 /* number of still frames at end of movie */
#define FADE 1 /* set to 1 to fade at end of movie */
#define ROTATE_VIEW_WHILE_FADE 1 /* set to 1 to keep rotating viewpoint during fade */
/* Parameters of initial condition */
#define INITIAL_AMP 0.75 /* amplitude of initial condition */
#define INITIAL_VARIANCE 0.0005 /* variance of initial condition */
#define INITIAL_WAVELENGTH 0.025 /* wavelength of initial condition */
/* Plot type, see list in global_pdes.c */
#define ZPLOT 103 /* wave height */
#define CPLOT 103 /* color scheme */
#define ZPLOT_B 108
#define CPLOT_B 108 /* plot type for second movie */
#define CHANGE_LUMINOSITY 1 /* set to 1 to let luminosity depend on energy flux intensity */
#define FLUX_WINDOW 30 /* size of averaging window of flux intensity */
#define AMPLITUDE_HIGH_RES 1 /* set to 1 to increase resolution of plot */
#define SHADE_3D 1 /* set to 1 to change luminosity according to normal vector */
#define SHADE_2D 0 /* set to 1 to change luminosity according to normal vector to plane */
#define SHADE_WAVE 1 /* set to 1 to have luminosity depend on wave height */
#define NON_DIRICHLET_BC 0 /* set to 1 to draw only facets in domain, if field is not zero on boundary */
#define FLOOR_ZCOORD 1 /* set to 1 to draw only facets with z not too negative */
#define DRAW_BILLIARD 0 /* set to 1 to draw boundary */
#define DRAW_BILLIARD_FRONT 0 /* set to 1 to draw front of boundary after drawing wave */
#define DRAW_CONSTRUCTION_LINES 0 /* set to 1 to draw construction lines of certain domains */
#define FADE_IN_OBSTACLE 1 /* set to 1 to fade color inside obstacles */
#define DRAW_OUTSIDE_GRAY 0 /* experimental, draw outside of billiard in gray */
#define SHADE_SCALE_2D 10.0 /* controls "depth" of 2D shading */
#define COS_LIGHT_MIN 0.0 /* controls angle-dependence of 2D shading */
#define COS_LIGHT_MAX 0.8 /* controls angle-dependence of 2D shading */
#define PLOT_SCALE_ENERGY 0.4 /* vertical scaling in energy plot */
#define PLOT_SCALE_LOG_ENERGY 0.5 /* vertical scaling in log energy plot */
/* 3D representation */
#define REPRESENTATION_3D 1 /* choice of 3D representation */
#define PLOT_2D 0 /* switch to 2D representation, equirectangular projection */
#define PHISHIFT 0.0 /* shift of phi in 2D plot (in degrees) */
#define REP_AXO_3D 0 /* linear projection (axonometry) */
#define REP_PROJ_3D 1 /* projection on plane orthogonal to observer line of sight */
#define ROTATE_VIEW 1 /* set to 1 to rotate position of observer */
#define ROTATE_ANGLE -360.0 /* total angle of rotation during simulation */
#define VIEWPOINT_TRAJ 1 /* type of viewpoint trajectory */
/* Color schemes */
#define COLOR_PALETTE 11 /* Color palette, see list in global_pdes.c */
#define COLOR_PALETTE_B 16 /* Color palette, see list in global_pdes.c */
#define BLACK 1 /* background */
#define COLOR_OUT_R 1.0 /* color outside domain */
#define COLOR_OUT_G 1.0
#define COLOR_OUT_B 1.0
#define COLOR_SCHEME 3 /* 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 VSCALE_AMPLITUDE 1.0 /* additional scaling factor for color scheme P_3D_AMPLITUDE */
#define VSCALE_ENERGY 10.0 /* additional scaling factor for color scheme P_3D_ENERGY */
#define PHASE_FACTOR 20.0 /* factor in computation of phase in color scheme P_3D_PHASE */
#define PHASE_SHIFT 0.0 /* shift of phase in color scheme P_3D_PHASE */
#define ATTENUATION 0.0 /* exponential attenuation coefficient of contrast with time */
#define E_SCALE 100.0 /* scaling factor for energy representation */
#define LOG_SCALE 0.75 /* scaling factor for energy log representation */
#define LOG_SHIFT 0.5 /* shift of colors on log scale */
#define LOG_ENERGY_FLOOR -10.0 /* floor value for log of (total) energy */
#define LOG_MEAN_ENERGY_SHIFT 1.0 /* additional shift for log of mean energy */
#define FLUX_SCALE 600.0 /* scaling factor for energy flux representation */
#define FLUX_CSCALE 5.0 /* scaling factor for color in energy flux representation */
#define RESCALE_COLOR_IN_CENTER 0 /* set to 1 to decrease color intentiy in the center (for wave escaping ring) */
#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 240.0 /* mean value of hue for color scheme C_HUE */
#define HUEAMP -200.0 /* amplitude of variation of hue for color scheme C_HUE */
#define NXMAZE 8 /* width of maze */
#define NYMAZE 32 /* height of maze */
#define MAZE_MAX_NGBH 5 /* max number of neighbours of maze cell */
#define RAND_SHIFT 5 /* seed of random number generator */
#define MAZE_XSHIFT 0.0 /* horizontal shift of maze */
#define MAZE_WIDTH 0.02 /* half width of maze walls */
#define DRAW_COLOR_SCHEME 1 /* set to 1 to plot the color scheme */
#define COLORBAR_RANGE 3.0 /* scale of color scheme bar */
#define COLORBAR_RANGE_B 2.0 /* scale of color scheme bar for 2nd part */
#define ROTATE_COLOR_SCHEME 0 /* set to 1 to draw color scheme horizontally */
#define CIRC_COLORBAR 0 /* set to 1 to draw circular color scheme */
#define CIRC_COLORBAR_B 0 /* set to 1 to draw circular color scheme */
#define DRAW_WAVE_PROFILE 0 /* set to 1 to draw a profile of the wave */
#define SAVE_TIME_SERIES 0 /* set to 1 to save wave time series at a point */
#define ADD_POTENTIAL 0 /* set to 1 to add potential to z coordinate */
#define POTENTIAL 10
#define POT_FACT 20.0
/* end of constants only used by sub_wave and sub_maze */
/* 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 */
/* Parameters controlling 3D projection */
double u_3d[2] = {0.75, -0.45}; /* projections of basis vectors for REP_AXO_3D representation */
double v_3d[2] = {-0.75, -0.45};
double w_3d[2] = {0.0, 0.015};
double light[3] = {0.816496581, -0.40824829, 0.40824829}; /* vector of "light" direction for P_3D_ANGLE color scheme */
double observer[3] = {6.0, 8.0, 2.5}; /* location of observer for REP_PROJ_3D representation */
int reset_view = 0; /* switch to reset 3D view parameters (for option ROTATE_VIEW) */
#define RSCALE 0.01 /* scaling factor of radial component */
#define RMAX 10.0 /* max value of radial component */
#define Z_SCALING_FACTOR 0.8 /* overall scaling factor of z axis for REP_PROJ_3D representation */
#define XY_SCALING_FACTOR 2.0 /* overall scaling factor for on-screen (x,y) coordinates after projection */
#define ZMAX_FACTOR 1.0 /* max value of z coordinate for REP_PROJ_3D representation */
#define XSHIFT_3D 0.0 /* overall x shift for REP_PROJ_3D representation */
#define YSHIFT_3D 0.0 /* overall y shift for REP_PROJ_3D representation */
#define COS_VISIBLE -0.75 /* limit on cosine of normal to shown facets */
#include "global_pdes.c" /* constants and global variables */
#include "global_3d.c" /* constants and global variables */
#include "sub_maze.c" /* support for generating mazes */
#include "sub_wave.c" /* common functions for wave_billiard, heat and schrodinger */
#include "wave_common.c" /* common functions for wave_billiard, wave_comparison, etc */
#include "sub_wave_3d.c" /* graphical functions specific to wave_3d */
#include "sub_sphere.c" /* graphical functions specific to wave_sphere */
FILE *time_series_left, *time_series_right, *image_file;
double courant2, courantb2; /* Courant parameters squared */
void evolve_wave_half(double phi_in[NX*NY], double psi_in[NX*NY], double phi_out[NX*NY],
short int xy_in[NX*NY], double tc[NX*NY], double tcc[NX*NY], double tgamma[NX*NY])
/* time step of field evolution */
/* phi is value of field at time t, psi at time t-1 */
/* this version of the function has been rewritten in order to minimize the number of if-branches */
{
int i, j, iplus, iminus, jplus, jminus, jtop, jbot;
double delta, x, y, c, cc, gamma, sintheta, cottheta, invstheta, sum, avrg;
static long time = 0;
static short int first = 1;
static double dphi, dtheta, cphiphi, ctheta;
if (first)
{
dphi = DPI/(double)NX;
dtheta = PI/(double)NY;
cphiphi = dphi*dphi/(dtheta*dtheta);
ctheta = dphi*dphi/(2.0*dtheta);
printf("dphi = %.5lg, dtheta = %.5lg, cphiphi = %.5lg, ctheta = %.5lg\n", dphi, dtheta, cphiphi, ctheta);
first = 0;
}
time++;
#pragma omp parallel for private(i,j,iplus,iminus,jplus,jminus,delta,x,y)
/* evolution in the bulk */
for (j=DPOLE; j<NY-DPOLE; j++){
sintheta = sin(j*dtheta);
// invstheta = 1.0/(sintheta*sintheta);
invstheta = 1.0/(sintheta*sintheta + SMOOTHPOLE*SMOOTHPOLE);
// cottheta = ctheta*cos(j*dtheta)/sintheta;
cottheta = ctheta*cos(j*dtheta)/(sintheta + SMOOTHPOLE);
for (i=1; i<NX-1; i++){
if ((TWOSPEEDS)||(xy_in[i*NY+j] != 0)){
x = phi_in[i*NY+j];
y = psi_in[i*NY+j];
/* discretized Laplacian */
/* 2nd phi derivative */
delta = invstheta*(phi_in[(i+1)*NY+j] + phi_in[(i-1)*NY+j] - 2.0*x);
/* 2nd theta derivative */
delta += cphiphi*(phi_in[i*NY+j+1] + phi_in[i*NY+j-1] - 2.0*x);
/* first theta derivative */
delta += cottheta*(phi_in[i*NY+j+1] - phi_in[i*NY+j-1]);
/* evolve phi */
phi_out[i*NY+j] = -y + 2*x + tcc[i*NY+j]*delta - KAPPA*x - tgamma[i*NY+j]*(x-y);
}
}
}
/* evolution at longitude zero */
for (j=DPOLE; j<NY-DPOLE; j++){
sintheta = sin(j*dtheta);
invstheta = 1.0/(sintheta*sintheta);
cottheta = ctheta*cos(j*dtheta)/sintheta;
/* i = 0 */
if ((TWOSPEEDS)||(xy_in[j] != 0)){
x = phi_in[j];
y = psi_in[j];
/* discretized Laplacian */
/* 2nd phi derivative */
delta = invstheta*(phi_in[NY+j] + phi_in[(NX-1)*NY+j] - 2.0*x);
/* 2nd theta derivative */
delta += cphiphi*(phi_in[j+1] + phi_in[j-1] - 2.0*x);
/* first theta derivative */
delta += cottheta*(phi_in[j+1] - phi_in[j-1]);
/* evolve phi */
phi_out[j] = -y + 2*x + tcc[j]*delta - KAPPA*x - tgamma[j]*(x-y);
}
/* i = NX-1 */
if ((TWOSPEEDS)||(xy_in[(NX-1)*NY+j] != 0)){
x = phi_in[(NX-1)*NY+j];
y = psi_in[(NX-1)*NY+j];
/* discretized Laplacian */
/* 2nd phi derivative */
delta = invstheta*(phi_in[j] + phi_in[(NX-2)*NY+j] - 2.0*x);
/* 2nd theta derivative */
delta += cphiphi*(phi_in[(NX-1)*NY+j+1] + phi_in[(NX-1)*NY+j-1] - 2.0*x);
/* first theta derivative */
delta += cottheta*(phi_in[(NX-1)*NY+j+1] - phi_in[(NX-1)*NY+j-1]);
/* evolve phi */
phi_out[(NX-1)*NY+j] = -y + 2*x + tcc[(NX-1)*NY+j]*delta - KAPPA*x - tgamma[(NX-1)*NY+j]*(x-y);
}
}
/* compute average at north pole */
sum = 0.0;
for (i=0; i<NX; i++) sum += phi_out[i*NY + DPOLE];
avrg = sum/(double)NX;
for (i=0; i<NX; i++) for (j=0; j<DPOLE; j++)
phi_out[i*NY + j] = avrg;
// {
// x = phi_in[(NX-1)*NY+j];
// y = psi_in[(NX-1)*NY+j];
// phi_out[(NX-1)*NY+j] = -y + 2*x + tcc[(NX-1)*NY+j]*avrg - KAPPA*x - tgamma[(NX-1)*NY+j]*(x-y);
// //
// }
/* compute average at south pole */
sum = 0.0;
for (i=0; i<NX; i++) sum += phi_out[i*NY + NY-1-DPOLE];
avrg = sum/(double)NX;
for (i=0; i<NX; i++) for (j=NY-DPOLE; j<NY; j++)
phi_out[i*NY + j] = avrg;
// {
// x = phi_in[(NX-1)*NY+j];
// y = psi_in[(NX-1)*NY+j];
// phi_out[(NX-1)*NY+j] = -y + 2*x + tcc[(NX-1)*NY+j]*avrg - KAPPA*x - tgamma[(NX-1)*NY+j]*(x-y);
// //
// }
// /* north pole, j = 0 */
// if ((TWOSPEEDS)||(xy_in[0] != 0)){
// x = phi_in[0];
// y = psi_in[0];
//
// /* discretized Laplacian */
// delta = cphiphi*(phi_in[1] + phi_in[(NX/4)*NY+1] + phi_in[(NX/2)*NY+1] + phi_in[(3*NX/4)*NY+1] - 4.0*x);
//
// /* evolve phi */
// phi_out[0] = -y + 2*x + tcc[0]*delta - KAPPA*x - tgamma[0]*(x-y);
//
// /* set same values for all i */
// for (i=1; i<NX; i++) phi_out[i*NY] = phi_out[0];
// }
//
// /* south pole, j = NY-1 */
// if ((TWOSPEEDS)||(xy_in[NY-1] != 0)){
// x = phi_in[NY-1];
// y = psi_in[NY-1];
//
// /* discretized Laplacian */
// delta = cphiphi*(phi_in[NY-2] + phi_in[(NX/4)*NY+NY-2] + phi_in[(NX/2)*NY+NY-2] + phi_in[(3*NX/4)*NY+NY-2] - 4.0*x);
//
// /* evolve phi */
// phi_out[NY-1] = -y + 2*x + tcc[0]*delta - KAPPA*x - tgamma[0]*(x-y);
//
// /* set same values for all i */
// for (i=1; i<NX; i++) phi_out[i*NY+NY-1] = phi_out[NY-1];
// }
/* for debugging purposes/if there is a risk of blow-up */
if (FLOOR) for (i=0; i<NX; i++){
for (j=0; j<NY; j++){
if (xy_in[i*NY+j] != 0)
{
if (phi_out[i*NY+j] > VMAX) phi_out[i*NY+j] = VMAX;
if (phi_out[i*NY+j] < -VMAX) phi_out[i*NY+j] = -VMAX;
}
}
}
}
void evolve_wave(double phi[NX*NY], double psi[NX*NY], double tmp[NX*NY], short int xy_in[NX*NY],
double tc[NX*NY], double tcc[NX*NY], double tgamma[NX*NY], t_laplacian laplace[NX*NY], t_laplacian laplace1[NX*NY],
t_laplacian laplace2[NX*NY])
/* time step of field evolution */
/* phi is value of field at time t, psi at time t-1 */
{
evolve_wave_half(phi, psi, tmp, xy_in, tc, tcc, tgamma);
evolve_wave_half(tmp, phi, psi, xy_in, tc, tcc, tgamma);
evolve_wave_half(psi, tmp, phi, xy_in, tc, tcc, tgamma);
}
void draw_color_bar_palette(int plot, double range, int palette, int circular, int fade, double fade_value)
{
// double width = 0.2;
double width = 0.14;
// double width = 0.2;
width *= (double)NX/(double)WINWIDTH;
if (ROTATE_COLOR_SCHEME)
draw_color_scheme_palette_3d(-1.0, -0.8, XMAX - 0.1, -1.0, plot, -range, range, palette, fade, fade_value);
else if (circular)
draw_circular_color_scheme_palette_3d(XMAX - 2.0*width, YMIN + 2.0*width, 1.5*width, 1.3*width, plot, -range, range, palette, fade, fade_value);
else
draw_color_scheme_palette_3d(XMAX - 1.5*width, YMIN + 0.1, XMAX - 0.5*width, YMAX - 0.1, plot, -range, range, palette, fade, fade_value);
}
void viewpoint_schedule(int i)
/* change position of observer */
{
int j;
double angle, ca, sa, r1;
static double observer_initial[3], r, ratio;
static int first = 1;
if (first)
{
for (j=0; j<3; j++) observer_initial[j] = observer[j];
r1 = observer[0]*observer[0] + observer[1]*observer[1];
r = sqrt(r1 + observer[2]*observer[2]);
ratio = r/sqrt(r1);
first = 0;
}
angle = (ROTATE_ANGLE*DPI/360.0)*(double)i/(double)NSTEPS;
ca = cos(angle);
sa = sin(angle);
switch (VIEWPOINT_TRAJ)
{
case (VP_HORIZONTAL):
{
observer[0] = ca*observer_initial[0] - sa*observer_initial[1];
observer[1] = sa*observer_initial[0] + ca*observer_initial[1];
break;
}
case (VP_ORBIT):
{
observer[0] = ca*observer_initial[0] - sa*observer_initial[1]*ratio;
observer[1] = ca*observer_initial[1] + sa*observer_initial[0]*ratio;
observer[2] = ca*observer_initial[2];
break;
}
}
printf("Angle %.3lg, Observer position (%.3lg, %.3lg, %.3lg)\n", angle, observer[0], observer[1], observer[2]);
}
void animation()
{
double time, scale, ratio, startleft[2], startright[2], sign = 1.0, r2, xy[2], fade_value, yshift, speed = 0.0, a, b, c, angle = 0.0, lambda1, y, x1, sign1, omega, phase_shift, theta, amp;
double *phi, *psi, *tmp, *color_scale, *tc, *tcc, *tgamma;
// double *total_energy;
short int *xy_in;
int i, j, s, sample_left[2], sample_right[2], period = 0, fade, source_counter = 0, k, p, q;
static int counter = 0, first_source = 1;
long int wave_value;
t_wave *wave;
t_laplacian *laplace, *laplace1, *laplace2;
t_wave_source wave_source[25];
t_wave_sphere *wsphere;
if (SAVE_TIME_SERIES)
{
time_series_left = fopen("wave_left.dat", "w");
time_series_right = fopen("wave_right.dat", "w");
}
/* Since NX and NY are big, it seemed wiser to use some memory allocation here */
xy_in = (short int *)malloc(NX*NY*sizeof(short int));
phi = (double *)malloc(NX*NY*sizeof(double));
psi = (double *)malloc(NX*NY*sizeof(double));
tmp = (double *)malloc(NX*NY*sizeof(double));
// total_energy = (double *)malloc(NX*NY*sizeof(double));
color_scale = (double *)malloc(NX*NY*sizeof(double));
tc = (double *)malloc(NX*NY*sizeof(double));
tcc = (double *)malloc(NX*NY*sizeof(double));
tgamma = (double *)malloc(NX*NY*sizeof(double));
wave = (t_wave *)malloc(NX*NY*sizeof(t_wave));
wsphere = (t_wave_sphere *)malloc(NX*NY*sizeof(t_wave_sphere));
laplace = (t_laplacian *)malloc(NX*NY*sizeof(t_laplacian));
laplace1 = (t_laplacian *)malloc(NX*NY*sizeof(t_laplacian));
laplace2 = (t_laplacian *)malloc(NX*NY*sizeof(t_laplacian));
/* initialise positions and radii of circles */
if (COMPARISON)
{
if ((B_DOMAIN == D_CIRCLES)||(B_DOMAIN == D_CIRCLES_IN_RECT))
ncircles = init_circle_config_pattern(circles, CIRCLE_PATTERN);
else if (B_DOMAIN == D_POLYGONS) ncircles = init_polygon_config_pattern(polygons, CIRCLE_PATTERN);
if ((B_DOMAIN_B == D_CIRCLES)||(B_DOMAIN_B == D_CIRCLES_IN_RECT))
ncircles_b = init_circle_config_pattern(circles_b, CIRCLE_PATTERN_B);
else if (B_DOMAIN_B == D_POLYGONS) ncircles_b = init_polygon_config_pattern(polygons_b, CIRCLE_PATTERN_B);
/* TO DO: adapt to different polygon patterns */
}
else
{
if ((B_DOMAIN == D_CIRCLES)||(B_DOMAIN == D_CIRCLES_IN_RECT)) ncircles = init_circle_config(circles);
else if (B_DOMAIN == D_POLYGONS) ncircles = init_polygon_config(polygons);
}
printf("Polygons initialized\n");
/* initialise polyline for von Koch and similar domains */
npolyline = init_polyline(MDEPTH, polyline);
for (i=0; i<npolyline; i++) printf("vertex %i: (%.3f, %.3f)\n", i, polyline[i].x, polyline[i].y);
if (COMPARISON) npolyline_b = init_polyline(MDEPTH, polyline);
npolyrect = init_polyrect(polyrect);
for (i=0; i<npolyrect; i++) printf("polyrect vertex %i: (%.3f, %.3f) - (%.3f, %.3f)\n", i, polyrect[i].x1, polyrect[i].y1, polyrect[i].x2, polyrect[i].y2);
init_polyrect_arc(polyrectrot, polyarc, &npolyrect_rot, &npolyarc);
printf("Rotated rectangles and arcs initialized\n");
printf("%i rotated rectangles, %i arcs\n", npolyrect_rot, npolyarc);
if ((B_DOMAIN == D_SPHERE_CIRCLES)||(B_DOMAIN_B == D_SPHERE_CIRCLES))
{
ncircles = init_circle_sphere(circ_sphere, CIRCLE_PATTERN);
}
courant2 = COURANT*COURANT;
courantb2 = COURANTB*COURANTB;
c = COURANT*(XMAX - XMIN)/(double)NX;
// a = 0.015;
// b = 0.0003;
// a = 0.04;
// b = 0.0018;
a = 0.05;
b = 0.0016;
/* initialize color scale, for option RESCALE_COLOR_IN_CENTER */
if (RESCALE_COLOR_IN_CENTER)
{
for (i=0; i<NX; i++)
for (j=0; j<NY; j++)
{
ij_to_xy(i, j, xy);
r2 = xy[0]*xy[0] + xy[1]*xy[1];
color_scale[i*NY+j] = 1.0 - exp(-4.0*r2/LAMBDA*LAMBDA);
}
}
/* initialize wave with a drop at one point, zero elsewhere */
// init_circular_wave(0.0, -LAMBDA, phi, psi, xy_in);
init_wave_fields(wave);
init_wave_sphere(wsphere);
/* initialize total energy table - no longer needed */
// if ((ZPLOT == P_MEAN_ENERGY)||(ZPLOT_B == P_MEAN_ENERGY)||(ZPLOT == P_LOG_MEAN_ENERGY)||(ZPLOT_B == P_LOG_MEAN_ENERGY))
// for (i=0; i<NX; i++)
// for (j=0; j<NY; j++)
// total_energy[i*NY+j] = 0.0;
ratio = (XMAX - XMIN)/8.4; /* for Tokarsky billiard */
// init_circular_wave_mod(polyline[85].x, polyline[85].y, phi, psi, xy_in);
// init_circular_wave_mod(LAMBDA*cos(APOLY*PID), LAMBDA*sin(APOLY*PID), phi, psi, xy_in);
lambda1 = LAMBDA;
angle = DPI/(double)NPOLY;
// init_circular_wave_mod(lambda1*cos(0.5*angle), lambda1*sin(0.5*angle), phi, psi, xy_in);
// for (j=1; j<NPOLY; j++)
// add_circular_wave_mod(1.0, lambda1*cos(((double)j+0.5)*angle), lambda1*sin(((double)j+0.5)*angle), phi, psi, xy_in);
init_circular_wave_sphere(0.7, 0.5, phi, psi, xy_in, wsphere);
// init_wave_flat_sphere(phi, psi, xy_in, wsphere);
// init_circular_wave_sphere(0.25 + PID, 0.0, phi, psi, xy_in, wsphere);
// add_circular_wave_sphere(-1.0, 0.25 + 3.0*PID, 0.0, phi, psi, xy_in, wsphere);
// printf("Wave initialized\n");
/* initialize table of wave speeds/dissipation */
init_speed_dissipation(xy_in, tc, tcc, tgamma);
/* initialze potential to add to z coordinate */
if (ADD_POTENTIAL)
{
if (POTENTIAL == POT_IOR)
for (i=0; i<NX*NY; i++)
wave[i].potential = &tcc[i];
}
init_zfield(phi, psi, xy_in, ZPLOT, wave, 0);
init_cfield(phi, psi, xy_in, CPLOT, wave, 0);
if (DOUBLE_MOVIE)
{
init_zfield(phi, psi, xy_in, ZPLOT_B, wave, 1);
init_cfield(phi, psi, xy_in, CPLOT_B, wave, 1);
}
blank();
glColor3f(0.0, 0.0, 0.0);
draw_wave_sphere(0, phi, psi, xy_in, wave, wsphere, ZPLOT, CPLOT, COLOR_PALETTE, 0, 1.0, 1);
// draw_billiard();
if (DRAW_COLOR_SCHEME) draw_color_bar_palette(CPLOT, COLORBAR_RANGE, COLOR_PALETTE, CIRC_COLORBAR, 0, 1.0);
glutSwapBuffers();
sleep(SLEEP1);
for (i=0; i<=INITIAL_TIME + NSTEPS; i++)
{
global_time++;
//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_mod(phi,psi, xy_in));
// printf("Scaling factor: %5lg\n", scale);
}
else scale = 1.0;
if (ROTATE_VIEW)
{
viewpoint_schedule(i - INITIAL_TIME);
reset_view = 1;
}
draw_wave_sphere(0, phi, psi, xy_in, wave, wsphere, ZPLOT, CPLOT, COLOR_PALETTE, 0, 1.0, 1);
for (j=0; j<NVID; j++)
{
evolve_wave(phi, psi, tmp, xy_in, tc, tcc, tgamma, laplace, laplace1, laplace2);
if (SAVE_TIME_SERIES)
{
wave_value = (long int)(phi[sample_left[0]*NY+sample_left[1]]*1.0e16);
fprintf(time_series_left, "%019ld\n", wave_value);
wave_value = (long int)(phi[sample_right[0]*NY+sample_right[1]]*1.0e16);
fprintf(time_series_right, "%019ld\n", wave_value);
if ((j == 0)&&(i%10 == 0)) printf("Frame %i of %i\n", i, NSTEPS);
// fprintf(time_series_right, "%.15f\n", phi[sample_right[0]][sample_right[1]]);
}
// if (i % 10 == 9) oscillate_linear_wave(0.2*scale, 0.15*(double)(i*NVID + j), -1.5, YMIN, -1.5, YMAX, phi, psi);
}
// draw_billiard();
if (DRAW_COLOR_SCHEME) draw_color_bar_palette(CPLOT, COLORBAR_RANGE, COLOR_PALETTE, CIRC_COLORBAR, fade, fade_value);
/* add oscillating waves */
// if ((ADD_OSCILLATING_SOURCE)&&(i%OSCILLATING_SOURCE_PERIOD == OSCILLATING_SOURCE_PERIOD - 1))
if ((ADD_OSCILLATING_SOURCE)&&(i%OSCILLATING_SOURCE_PERIOD == 1))
{
if (ALTERNATE_OSCILLATING_SOURCE) sign = -sign;
add_circular_wave_mod(sign, -0.5, 0.0, phi, psi, xy_in);
}
if (PRINT_SPEED) print_speed_3d(speed, 0, 1.0);
if (!((NO_EXTRA_BUFFER_SWAP)&&(MOVIE))) glutSwapBuffers();
if (MOVIE)
{
if (i >= INITIAL_TIME) save_frame();
// if (i >= INITIAL_TIME) save_frame_counter(i);
// if (i >= INITIAL_TIME) save_frame_counter(NSTEPS + MID_FRAMES + 1 + counter);
else printf("Initial phase time %i of %i\n", i, INITIAL_TIME);
if ((i >= INITIAL_TIME)&&(DOUBLE_MOVIE))
{
draw_wave_sphere(1, phi, psi, xy_in, wave, wsphere, ZPLOT_B, CPLOT_B, COLOR_PALETTE_B, 0, 1.0, 1);
if (DRAW_COLOR_SCHEME) draw_color_bar_palette(CPLOT_B, COLORBAR_RANGE_B, COLOR_PALETTE_B, CIRC_COLORBAR_B, 0, 1.0);
if (PRINT_SPEED) print_speed_3d(speed, 0, 1.0);
glutSwapBuffers();
save_frame_counter(NSTEPS + MID_FRAMES + 1 + counter);
// save_frame_counter(i);
counter++;
}
else if (NO_EXTRA_BUFFER_SWAP) glutSwapBuffers();
/* 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/");
}
}
else printf("Computing frame %i\n", i);
}
if (MOVIE)
{
if (DOUBLE_MOVIE)
{
draw_wave_sphere(0, phi, psi, xy_in, wave, wsphere, ZPLOT, CPLOT, COLOR_PALETTE, 0, 1.0, 1);
if (DRAW_COLOR_SCHEME) draw_color_bar_palette(CPLOT, COLORBAR_RANGE, COLOR_PALETTE, CIRC_COLORBAR, 0, 1.0);
if (PRINT_SPEED) print_speed_3d(speed, 0, 1.0);
glutSwapBuffers();
if (!FADE) for (i=0; i<MID_FRAMES; i++) save_frame();
else for (i=0; i<MID_FRAMES; i++)
{
if ((ROTATE_VIEW)&&(ROTATE_VIEW_WHILE_FADE))
{
viewpoint_schedule(NSTEPS - INITIAL_TIME + i);
reset_view = 1;
}
fade_value = 1.0 - (double)i/(double)MID_FRAMES;
draw_wave_sphere(0, phi, psi, xy_in, wave, wsphere, ZPLOT, CPLOT, COLOR_PALETTE, 1, fade_value, 1);
if (DRAW_COLOR_SCHEME) draw_color_bar_palette(CPLOT, COLORBAR_RANGE, COLOR_PALETTE, CIRC_COLORBAR, 1, fade_value);
if (PRINT_SPEED) print_speed_3d(speed, 1, fade_value);
if (!NO_EXTRA_BUFFER_SWAP) glutSwapBuffers();
save_frame_counter(NSTEPS + i + 1);
}
if ((ROTATE_VIEW)&&(ROTATE_VIEW_WHILE_FADE))
{
viewpoint_schedule(NSTEPS - INITIAL_TIME);
reset_view = 1;
}
draw_wave_sphere(1, phi, psi, xy_in, wave, wsphere, ZPLOT_B, CPLOT_B, COLOR_PALETTE_B, 0, 1.0, 1);
if (DRAW_COLOR_SCHEME) draw_color_bar_palette(CPLOT_B, COLORBAR_RANGE_B, COLOR_PALETTE_B, CIRC_COLORBAR_B, 0, 1.0);
if (PRINT_SPEED) print_speed_3d(speed, 0, 1.0);
glutSwapBuffers();
if (!FADE) for (i=0; i<END_FRAMES; i++) save_frame_counter(NSTEPS + MID_FRAMES + 1 + counter + i);
else for (i=0; i<END_FRAMES; i++)
{
if ((ROTATE_VIEW)&&(ROTATE_VIEW_WHILE_FADE))
{
viewpoint_schedule(NSTEPS - INITIAL_TIME + i);
reset_view = 1;
}
fade_value = 1.0 - (double)i/(double)END_FRAMES;
draw_wave_sphere(1, phi, psi, xy_in, wave, wsphere, ZPLOT_B, CPLOT_B, COLOR_PALETTE_B, 1, fade_value, 1);
if (DRAW_COLOR_SCHEME) draw_color_bar_palette(CPLOT_B, COLORBAR_RANGE_B, COLOR_PALETTE_B, CIRC_COLORBAR_B, 1, fade_value);
if (PRINT_SPEED) print_speed_3d(speed, 1, fade_value);
glutSwapBuffers();
save_frame_counter(NSTEPS + MID_FRAMES + 1 + counter + i);
}
}
else
{
if (!FADE) for (i=0; i<END_FRAMES; i++) save_frame_counter(NSTEPS + MID_FRAMES + 1 + counter + i);
else for (i=0; i<END_FRAMES; i++)
{
if ((ROTATE_VIEW)&&(ROTATE_VIEW_WHILE_FADE))
{
viewpoint_schedule(NSTEPS - INITIAL_TIME + i);
reset_view = 1;
}
fade_value = 1.0 - (double)i/(double)END_FRAMES;
draw_wave_sphere(0, phi, psi, xy_in, wave, wsphere, ZPLOT, CPLOT, COLOR_PALETTE, 1, fade_value, 1);
if (DRAW_COLOR_SCHEME) draw_color_bar_palette(CPLOT, COLORBAR_RANGE, COLOR_PALETTE, CIRC_COLORBAR, 1, fade_value);
if (PRINT_SPEED) print_speed_3d(speed, 1, fade_value);
glutSwapBuffers();
save_frame_counter(NSTEPS + 1 + counter + i);
}
}
s = system("mv wave*.tif tif_wave/");
}
free(xy_in);
free(phi);
free(psi);
free(tmp);
// free(total_energy);
free(color_scale);
free(tc);
free(tcc);
free(tgamma);
free(wave);
free(laplace);
free(laplace1);
free(laplace2);
if (SAVE_TIME_SERIES)
{
fclose(time_series_left);
fclose(time_series_right);
}
}
void display(void)
{
time_t rawtime;
struct tm * timeinfo;
time(&rawtime);
timeinfo = localtime(&rawtime);
glPushMatrix();
blank();
glutSwapBuffers();
blank();
glutSwapBuffers();
animation();
sleep(SLEEP2);
glPopMatrix();
glutDestroyWindow(glutGetWindow());
printf("Start local time and date: %s", asctime(timeinfo));
time(&rawtime);
timeinfo = localtime(&rawtime);
printf("Current local time and date: %s", asctime(timeinfo));
}
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");
if (PLOT_2D) init_sphere_2D();
else init_3d();
glutDisplayFunc(display);
glutMainLoop();
return 0;
}
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