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wave_billiard.c
153
wave_billiard.c
@@ -42,55 +42,57 @@
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#include <tiffio.h> /* Sam Leffler's libtiff library. */
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#include <omp.h>
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#define MOVIE 1 /* set to 1 to generate movie */
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#define DOUBLE_MOVIE 1 /* set to 1 to produce movies for wave height and energy simultaneously */
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#define MOVIE 0 /* set to 1 to generate movie */
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#define DOUBLE_MOVIE 0 /* set to 1 to produce movies for wave height and energy simultaneously */
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/* General geometrical parameters */
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#define WINWIDTH 1920 /* window width */
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#define WINHEIGHT 1000 /* window height */
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#define NX 1920 /* number of grid points on x axis */
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#define NY 1000 /* number of grid points on y axis */
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/* uncomment for higher resolution version */
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// #define WINWIDTH 1920 /* window width */
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// #define WINHEIGHT 1000 /* window height */
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// #define NX 1920 /* number of grid points on x axis */
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// #define NY 1000 /* number of grid points on y axis */
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//
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// #define XMIN -2.0
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// #define XMAX 2.0 /* x interval */
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// #define YMIN -1.041666667
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// #define YMAX 1.041666667 /* y interval for 9/16 aspect ratio */
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/* comment out for higher resolution version */
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#define WINWIDTH 1280 /* window width */
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#define WINHEIGHT 720 /* window height */
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#define NX 1280 /* number of grid points on x axis */
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#define NY 720 /* number of grid points on y axis */
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#define XMIN -2.0
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#define XMAX 2.0 /* x interval */
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#define YMIN -1.0329
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#define YMAX 1.1129 /* y interval for 9/16 aspect ratio */
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// #define WINWIDTH 1280 /* window width */
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// #define WINHEIGHT 720 /* window height */
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// #define NX 1280 /* number of grid points on x axis */
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// #define NY 720 /* number of grid points on y axis */
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// #define NX 2560 /* number of grid points on x axis */
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// #define NY 1440 /* number of grid points on y axis */
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// #define YMIN -1.125
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// #define YMAX 1.125 /* y interval for 9/16 aspect ratio */
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#define XMAX 2.0 /* x interval */
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#define YMIN -1.125
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#define YMAX 1.125 /* y interval for 9/16 aspect ratio */
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#define JULIA_SCALE 1.0 /* scaling for Julia sets */
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/* Choice of the billiard table */
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#define B_DOMAIN 42 /* choice of domain shape, see list in global_pdes.c */
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#define B_DOMAIN 41 /* choice of domain shape, see list in global_pdes.c */
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#define CIRCLE_PATTERN 2 /* pattern of circles or polygons, see list in global_pdes.c */
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#define CIRCLE_PATTERN 201 /* pattern of circles or polygons, see list in global_pdes.c */
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#define P_PERCOL 0.25 /* probability of having a circle in C_RAND_PERCOL arrangement */
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#define NPOISSON 300 /* number of points for Poisson C_RAND_POISSON arrangement */
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#define RANDOM_POLY_ANGLE 1 /* set to 1 to randomize angle of polygons */
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#define LAMBDA 1.1 /* parameter controlling the dimensions of domain */
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#define MU 0.4 /* parameter controlling the dimensions of domain */
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#define NPOLY 14 /* number of sides of polygon */
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#define APOLY -1.0 /* angle by which to turn polygon, in units of Pi/2 */
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#define MDEPTH 5 /* depth of computation of Menger gasket */
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#define MU 1.0 /* parameter controlling the dimensions of domain */
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#define NPOLY 3 /* number of sides of polygon */
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#define APOLY 0.3333333333333333 /* angle by which to turn polygon, in units of Pi/2 */
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#define MDEPTH 6 /* depth of computation of Menger gasket */
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#define MRATIO 3 /* ratio defining Menger gasket */
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#define MANDELLEVEL 1000 /* iteration level for Mandelbrot set */
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#define MANDELLIMIT 10.0 /* limit value for approximation of Mandelbrot set */
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#define FOCI 1 /* set to 1 to draw focal points of ellipse */
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#define NGRIDX 10 /* number of grid point for grid of disks */
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#define NGRIDY 12 /* number of grid point for grid of disks */
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#define NGRIDX 36 /* number of grid point for grid of disks */
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#define NGRIDY 6 /* number of grid point for grid of disks */
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#define X_SHOOTER -0.2
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#define Y_SHOOTER -0.6
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@@ -108,16 +110,16 @@
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/* Physical parameters of wave equation */
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#define TWOSPEEDS 0 /* set to 1 to replace hardcore boundary by medium with different speed */
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#define TWOSPEEDS 0 /* set to 1 to replace hardcore boundary by medium with different speed */
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#define OSCILLATE_LEFT 0 /* set to 1 to add oscilating boundary condition on the left */
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#define OSCILLATE_TOPBOT 0 /* set to 1 to enforce a planar wave on top and bottom boundary */
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#define OMEGA 0.002 /* frequency of periodic excitation */
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#define AMPLITUDE 1.0 /* amplitude of periodic excitation */
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#define COURANT 0.04 /* Courant number */
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#define COURANTB 0.01 /* Courant number in medium B */
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#define COURANT 0.03 /* Courant number */
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#define COURANTB 0.01 /* Courant number in medium B */
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#define GAMMA 0.0 /* damping factor in wave equation */
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#define GAMMAB 1.0e-6 /* damping factor in wave equation */
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#define GAMMAB 5.0e-4 /* damping factor in wave equation */
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#define GAMMA_SIDES 1.0e-4 /* damping factor on boundary */
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#define GAMMA_TOPBOT 1.0e-7 /* damping factor on boundary */
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#define KAPPA 0.0 /* "elasticity" term enforcing oscillations */
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@@ -128,20 +130,24 @@
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/* Increasing COURANT speeds up the simulation, but decreases accuracy */
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/* For similar wave forms, COURANT^2*GAMMA should be kept constant */
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#define ADD_OSCILLATING_SOURCE 1 /* set to 1 to add an oscillating wave source */
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#define OSCILLATING_SOURCE_PERIOD 100 /* period of oscillating source */
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/* Boundary conditions, see list in global_pdes.c */
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#define B_COND 3
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#define B_COND 2
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/* Parameters for length and speed of simulation */
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#define NSTEPS 2100 /* number of frames of movie */
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#define NSTEPS 2200 /* number of frames of movie */
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// #define NSTEPS 100 /* number of frames of movie */
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#define NVID 25 /* number of iterations between images displayed on screen */
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#define NSEG 100 /* number of segments of boundary */
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#define NSEG 1000 /* number of segments of boundary */
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#define INITIAL_TIME 0 /* time after which to start saving frames */
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#define BOUNDARY_WIDTH 3 /* width of billiard boundary */
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#define BOUNDARY_WIDTH 1 /* width of billiard boundary */
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#define PAUSE 1000 /* number of frames after which to pause */
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#define PSLEEP 1 /* sleep time during pause */
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#define PAUSE 200 /* number of frames after which to pause */
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#define PSLEEP 2 /* sleep time during pause */
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#define SLEEP1 1 /* initial sleeping time */
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#define SLEEP2 1 /* final sleeping time */
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#define MID_FRAMES 20 /* number of still frames between parts of two-part movie */
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@@ -150,28 +156,30 @@
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/* Parameters of initial condition */
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#define INITIAL_AMP 0.75 /* amplitude of initial condition */
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#define INITIAL_VARIANCE 0.0003 /* variance of initial condition */
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#define INITIAL_VARIANCE 0.00025 /* variance of initial condition */
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#define INITIAL_WAVELENGTH 0.015 /* wavelength of initial condition */
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/* Plot type, see list in global_pdes.c */
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#define PLOT 1
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#define PLOT 0
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#define PLOT_B 0 /* plot type for second movie */
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#define PLOT_B 5 /* plot type for second movie */
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/* Color schemes */
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#define COLOR_PALETTE 12 /* Color palette, see list in global_pdes.c */
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#define COLOR_PALETTE 18 /* Color palette, see list in global_pdes.c */
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#define BLACK 1 /* background */
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#define COLOR_SCHEME 3 /* choice of color scheme, see list in global_pdes.c */
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#define SCALE 0 /* set to 1 to adjust color scheme to variance of field */
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#define SLOPE 0.5 /* sensitivity of color on wave amplitude */
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#define SLOPE 0.2 /* sensitivity of color on wave amplitude */
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#define ATTENUATION 0.0 /* exponential attenuation coefficient of contrast with time */
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#define E_SCALE 150.0 /* scaling factor for energy representation */
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#define LOG_SCALE 2.5 /* scaling factor for energy log representation */
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#define LOG_SCALE 1.5 /* scaling factor for energy log representation */
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#define LOG_SHIFT 0.0 /* shift of colors on log scale */
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#define RESCALE_COLOR_IN_CENTER 0 /* set to 1 to decrease color intentiy in the center (for wave escaping ring) */
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#define COLORHUE 260 /* initial hue of water color for scheme C_LUM */
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#define COLORDRIFT 0.0 /* how much the color hue drifts during the whole simulation */
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@@ -181,8 +189,8 @@
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#define HUEAMP -180.0 /* amplitude of variation of hue for color scheme C_HUE */
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#define DRAW_COLOR_SCHEME 1 /* set to 1 to plot the color scheme */
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#define COLORBAR_RANGE 6.0 /* scale of color scheme bar */
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#define COLORBAR_RANGE_B 10.0 /* scale of color scheme bar for 2nd part */
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#define COLORBAR_RANGE 6.0 /* scale of color scheme bar */
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#define COLORBAR_RANGE_B 12.0 /* scale of color scheme bar for 2nd part */
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#define ROTATE_COLOR_SCHEME 0 /* set to 1 to draw color scheme horizontally */
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#define SAVE_TIME_SERIES 0 /* set to 1 to save wave time series at a point */
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@@ -592,8 +600,6 @@ void evolve_wave(double *phi[NX], double *psi[NX], double *phi_tmp[NX], double *
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{
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evolve_wave_half(phi, psi, phi_tmp, psi_tmp, xy_in);
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evolve_wave_half(phi_tmp, psi_tmp, phi, psi, xy_in);
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// evolve_wave_half_old(phi, psi, phi_tmp, psi_tmp, xy_in);
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// evolve_wave_half_old(phi_tmp, psi_tmp, phi, psi, xy_in);
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}
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@@ -601,15 +607,16 @@ void draw_color_bar(int plot, double range)
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{
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if (ROTATE_COLOR_SCHEME) draw_color_scheme(-1.0, -0.8, XMAX - 0.1, -1.0, plot, -range, range);
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else draw_color_scheme(1.7, YMIN + 0.1, 1.9, YMAX - 0.1, plot, -range, range);
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// else draw_color_scheme(1.7, YMIN + 0.25, 1.9, YMAX - 0.25, plot, -range, range);
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}
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void animation()
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{
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double time, scale, ratio, startleft[2], startright[2], sign;
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double *phi[NX], *psi[NX], *phi_tmp[NX], *psi_tmp[NX], *total_energy[NX];
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double time, scale, ratio, startleft[2], startright[2], sign, r2, xy[2];
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double *phi[NX], *psi[NX], *phi_tmp[NX], *psi_tmp[NX], *total_energy[NX], *color_scale[NX];
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short int *xy_in[NX];
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int i, j, s, sample_left[2], sample_right[2];
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int i, j, s, sample_left[2], sample_right[2], period = 0;
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static int counter = 0;
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long int wave_value;
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@@ -628,6 +635,7 @@ void animation()
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psi_tmp[i] = (double *)malloc(NY*sizeof(double));
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total_energy[i] = (double *)malloc(NY*sizeof(double));
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xy_in[i] = (short int *)malloc(NY*sizeof(short int));
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color_scale[i] = (double *)malloc(NY*sizeof(double));
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}
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/* initialise positions and radii of circles */
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@@ -641,6 +649,18 @@ void animation()
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courant2 = COURANT*COURANT;
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courantb2 = COURANTB*COURANTB;
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/* initialize color scale, for option RESCALE_COLOR_IN_CENTER */
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if (RESCALE_COLOR_IN_CENTER)
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{
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for (i=0; i<NX; i++)
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for (j=0; j<NY; j++)
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{
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ij_to_xy(i, j, xy);
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r2 = xy[0]*xy[0] + xy[1]*xy[1];
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color_scale[i][j] = 1.0 - exp(-4.0*r2/LAMBDA*LAMBDA);
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}
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}
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/* initialize wave with a drop at one point, zero elsewhere */
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// init_circular_wave(0.0, -LAMBDA, phi, psi, xy_in);
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@@ -670,7 +690,8 @@ void animation()
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// printf("Initializing wave\n");
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// init_circular_wave(-1.0, 0.0, phi, psi, xy_in);
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// printf("Wave initialized\n");
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init_circular_wave(0.0, 0.0, phi, psi, xy_in);
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init_circular_wave(0.6*cos((double)(period)*DPI/3.0), 0.6*sin((double)(period)*DPI/3.0), phi, psi, xy_in);
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period++;
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// for (i=0; i<3; i++)
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// {
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// add_circular_wave(-1.0, 0.6*cos(PID + (double)(i)*DPI/3.0), 0.6*sin(PID + (double)(i)*DPI/3.0), phi, psi, xy_in);
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@@ -697,7 +718,8 @@ void animation()
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blank();
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glColor3f(0.0, 0.0, 0.0);
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// draw_wave(phi, psi, xy_in, 1.0, 0, PLOT);
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draw_wave_e(phi, psi, total_energy, xy_in, 1.0, 0, PLOT);
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draw_wave_e(phi, psi, total_energy, color_scale, xy_in, 1.0, 0, PLOT);
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// draw_wave_highres(2, phi, psi, total_energy, xy_in, 1.0, 0, PLOT);
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draw_billiard();
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@@ -722,7 +744,8 @@ void animation()
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else scale = 1.0;
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// draw_wave(phi, psi, xy_in, scale, i, PLOT);
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draw_wave_e(phi, psi, total_energy, xy_in, scale, i, PLOT);
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draw_wave_e(phi, psi, total_energy, color_scale, xy_in, scale, i, PLOT);
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// draw_wave_highres(2, phi, psi, total_energy, xy_in, scale, i, PLOT);
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for (j=0; j<NVID; j++)
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{
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evolve_wave(phi, psi, phi_tmp, psi_tmp, xy_in);
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@@ -743,10 +766,12 @@ void animation()
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if (DRAW_COLOR_SCHEME) draw_color_bar(PLOT, COLORBAR_RANGE);
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/* add oscillating waves */
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// if (i%345 == 344)
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// {
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// add_circular_wave(1.0, -LAMBDA, 0.0, phi, psi, xy_in);
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// }
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if ((ADD_OSCILLATING_SOURCE)&&(i%OSCILLATING_SOURCE_PERIOD == OSCILLATING_SOURCE_PERIOD - 1))
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{
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// add_circular_wave(1.0, -1.5*LAMBDA, 0.0, phi, psi, xy_in);
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add_circular_wave(-1.0, 0.6*cos((double)(period)*DPI/3.0), 0.6*sin((double)(period)*DPI/3.0), phi, psi, xy_in);
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period++;
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}
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glutSwapBuffers();
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@@ -758,9 +783,10 @@ void animation()
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if ((i >= INITIAL_TIME)&&(DOUBLE_MOVIE))
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{
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// draw_wave(phi, psi, xy_in, scale, i, PLOT_B);
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draw_wave_e(phi, psi, total_energy, xy_in, scale, i, PLOT_B);
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if (DRAW_COLOR_SCHEME) draw_color_bar(PLOT_B, COLORBAR_RANGE_B);
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draw_wave_e(phi, psi, total_energy, color_scale, xy_in, scale, i, PLOT_B);
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// draw_wave_highres(2, phi, psi, total_energy, xy_in, scale, i, PLOT_B);
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draw_billiard();
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if (DRAW_COLOR_SCHEME) draw_color_bar(PLOT_B, COLORBAR_RANGE_B);
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glutSwapBuffers();
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save_frame_counter(NSTEPS + 21 + counter);
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counter++;
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@@ -783,7 +809,8 @@ void animation()
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if (DOUBLE_MOVIE)
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{
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// draw_wave(phi, psi, xy_in, scale, i, PLOT);
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draw_wave_e(phi, psi, total_energy, xy_in, scale, NSTEPS, PLOT);
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draw_wave_e(phi, psi, total_energy, color_scale, xy_in, scale, NSTEPS, PLOT);
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// draw_wave_highres(2, phi, psi, total_energy, xy_in, scale, NSTEPS, PLOT);
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draw_billiard();
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if (DRAW_COLOR_SCHEME) draw_color_bar(PLOT, COLORBAR_RANGE);
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glutSwapBuffers();
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@@ -792,7 +819,8 @@ void animation()
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if (DOUBLE_MOVIE)
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{
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// draw_wave(phi, psi, xy_in, scale, i, PLOT_B);
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draw_wave_e(phi, psi, total_energy, xy_in, scale, NSTEPS, PLOT_B);
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draw_wave_e(phi, psi, total_energy, color_scale, xy_in, scale, NSTEPS, PLOT_B);
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// draw_wave_highres(2, phi, psi, total_energy, xy_in, scale, NSTEPS, PLOT_B);
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draw_billiard();
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if (DRAW_COLOR_SCHEME) draw_color_bar(PLOT_B, COLORBAR_RANGE_B);
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glutSwapBuffers();
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@@ -809,6 +837,7 @@ void animation()
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free(psi_tmp[i]);
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free(total_energy[i]);
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free(xy_in[i]);
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free(color_scale[i]);
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}
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if (SAVE_TIME_SERIES)
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