1625 lines
64 KiB
Markdown
1625 lines
64 KiB
Markdown
### Parameter values for YouTube simulations ###
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Created by **Nils Berglund** and optimized by **Marco Mancini**
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C code for videos on YouTube Channel https://www.youtube.com/c/NilsBerglund
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Below are parameter values used for different simulations, as well as initial conditions used in
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function animation. Some simulations use variants of the published code. The list is going to be
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updated gradually. Some constants have been moved to global files in later versions.
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Some parameters in early versions may be off, since not all versions were backed up.
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### 30 April 21 - Why the Sinai billiard is chaotic ###
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**Program:** `vid_part_billiard.c` (old version of `part_billiard.c`)
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**Initial condition in function `animation()`:** `init_drop_config(-1.5, 0.0, 0.0, 0.2, configs);`
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```
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#define WINWIDTH 1280 /* window width */
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#define WINHEIGHT 720 /* window height */
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/* Choice of the billiard table */
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#define B_DOMAIN 3 /* choice of domain shape */
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#define D_RECTANGLE 0 /* rectangular domain */
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#define D_ELLIPSE 1 /* elliptical domain */
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#define D_STADIUM 2 /* stadium-shaped domain */
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#define D_SINAI 3 /* Sinai billiard */
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#define D_DIAMOND 4 /* diamond-shaped billiard */
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#define D_TRIANGLE 5 /* triangular billiard */
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#define LAMBDA 0.5 /* parameter controlling shape of billiard */
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#define FOCI 1 /* set to 1 to draw focal points of ellipse */
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#define MOVIE 0 /* set to 1 to generate movie */
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#define RESAMPLE 0 /* set to 1 if particles should be added when dispersion too large */
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#define XMIN -2.0
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#define XMAX 2.0 /* x interval */
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#define YMIN -1.125
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#define YMAX 1.125 /* y interval for 9/16 aspect ratio */
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#define NPART 10000 /* number of particles */
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#define NPARTMAX 50000 /* maximal number of particles after resampling */
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#define LMAX 0.01 /* minimal segment length triggering resampling */
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#define DMIN 0.02 /* minimal distance to boundary for triggering resampling */
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#define CYCLE 1 /* set to 1 for closed curve (start in all directions) */
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#define NSTEPS 5000 /* number of frames of movie */
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#define TIME 2000 /* time between movie frames, for fluidity of real-time simulation */
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#define DPHI 0.00001 /* integration step */
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#define NVID 500 /* number of iterations between images displayed on screen */
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#define NCOLORS 20 /* number of colors */
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#define COLORSHIFT 220 /* hue of initial color */
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#define NSEG 100 /* number of segments of boundary */
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#define LENGTH 0.05 /* length of velocity vectors */
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#define BLACK 1 /* set to 1 for black background */
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/* Decreasing TIME accelerates the animation and the movie */
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/* For constant speed of movie, TIME*DPHI should be kept constant */
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/* However, increasing DPHI too much deterioriates quality of simulation */
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/* NVID tells how often a picture is drawn in the animation, increase it for faster anim */
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/* For a good quality movie, take for instance TIME = 400, DPHI = 0.00005, NVID = 100 */
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#define PAUSE 100 /* number of frames after which to pause */
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#define PSLEEP 1 /* sleep time during pause */
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#define SLEEP1 1 /* initial sleeping time */
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#define SLEEP2 100 /* final sleeping time */
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#define PI 3.141592654
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#define DPI 6.283185307
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#define PID 1.570796327
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```
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### 29 April 21 - The dark side of the pool ###
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**Program:** `wave_billiard.c` (parameters reconstructed for 1 August version)
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**Initial condition in function `animation()`:** `init_wave(LAMBDA, 0.0, phi, psi, xy_in);`
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```
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#define MOVIE 1 /* set to 1 to generate movie */
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/* General geometrical parameters */
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#define WINWIDTH 1280 /* window width */
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#define WINHEIGHT 720 /* window height */
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// #define NX 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 640 /* number of grid points on x axis */
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#define NY 360 /* number of grid points on y axis */
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/* setting NX to WINWIDTH and NY to WINHEIGHT increases resolution */
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/* but will multiply run time by 4 */
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#define XMIN -2.0
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#define XMAX 2.0 /* x interval */
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#define YMIN -1.125
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#define YMAX 1.125 /* y interval for 9/16 aspect ratio */
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#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 1 /* choice of domain shape, see list in global_pdes.c */
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#define CIRCLE_PATTERN 10 /* pattern of circles, 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 LAMBDA 1.5 /* parameter controlling the dimensions of domain */
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#define MU 0.03 /* parameter controlling the dimensions of domain */
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#define NPOLY 3 /* 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 4 /* 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 15 /* number of grid point for grid of disks */
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#define NGRIDY 20 /* number of grid point for grid of disks */
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/* You can add more billiard tables by adapting the functions */
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/* xy_in_billiard and draw_billiard below */
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/* Physical 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 OMEGA 0.9 /* frequency of periodic excitation */
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#define COURANT 0.01 /* Courant number */
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#define COURANTB 0.0075 /* Courant number in medium B */
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#define GAMMA 0.0 /* 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-6 /* damping factor on boundary */
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#define KAPPA 0.0 /* "elasticity" term enforcing oscillations */
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#define KAPPA_SIDES 5.0e-4 /* "elasticity" term on absorbing boundary */
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#define KAPPA_TOPBOT 0.0 /* "elasticity" term on absorbing boundary */
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/* The Courant number is given by c*DT/DX, where DT is the time step and DX the lattice spacing */
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/* The physical damping coefficient is given by GAMMA/(DT)^2 */
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/* Increasing COURANT speeds up the simulation, but decreases accuracy */
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/* For similar wave forms, COURANT^2*GAMMA should be kept constant */
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/* Boundary conditions, see list in global_pdes.c */
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#define B_COND 3
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/* Parameters for length and speed of simulation */
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#define NSTEPS 8000 /* number of frames of movie */
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#define NVID 40 /* 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 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 PAUSE 1000 /* number of frames after which to pause */
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#define PSLEEP 1 /* sleep time during pause */
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#define SLEEP1 1 /* initial sleeping time */
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#define SLEEP2 1 /* final sleeping time */
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/* Plot type, see list in global_pdes.c */
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#define PLOT 0
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/* Color schemes */
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#define BLACK 0 /* background */
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#define COLOR_SCHEME 0 /* 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 2.0 /* sensitivity of color on wave amplitude */
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#define ATTENUATION 0.0 /* exponential attenuation coefficient of contrast with time */
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#define E_SCALE 750.0 /* scaling factor for energy representation */
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#define COLORHUE 260 /* initial hue of water color for scheme C_LUM */
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#define COLORDRIFT 0.0 /* how much the color hue drifts during the whole simulation */
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#define LUMMEAN 0.5 /* amplitude of luminosity variation for scheme C_LUM */
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#define LUMAMP 0.3 /* amplitude of luminosity variation for scheme C_LUM */
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#define HUEMEAN 220.0 /* mean value of hue for color scheme C_HUE */
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#define HUEAMP -220.0 /* amplitude of variation of hue for color scheme C_HUE */
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```
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### 28 April 21 - Squaring the circle ###
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**Program:** `vid_drop_billiard.c` (old version of `drop_billiard.c`)
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**Initial condition in function `animation()`:** `init_drop_config(0.0, 0.0, 0.0, DPI, configs);`
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```
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#define WINWIDTH 1280 /* window width */
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#define WINHEIGHT 720 /* window height */
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/* Choice of the billiard table */
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#define B_DOMAIN 0 /* choice of domain shape */
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#define D_RECTANGLE 0 /* rectangular domain */
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#define D_ELLIPSE 1 /* elliptical domain */
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#define D_STADIUM 2 /* stadium-shaped domain */
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#define D_SINAI 3 /* Sinai billiard */
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#define D_DIAMOND 4 /* diamond-shaped billiard */
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#define D_TRIANGLE 5 /* triangular billiard */
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#define LAMBDA 1.0 /* parameter controlling shape of billiard */
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#define FOCI 1 /* set to 1 to draw focal points of ellipse */
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#define MOVIE 0 /* set to 1 to generate movie */
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#define RESAMPLE 0 /* set to 1 if particles should be added when dispersion too large */
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#define XMIN -2.0
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#define XMAX 2.0 /* x interval */
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#define YMIN -1.125
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#define YMAX 1.125 /* y interval for 9/16 aspect ratio */
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#define NPART 10000 /* number of particles */
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#define NPARTMAX 20000 /* maximal number of particles after resampling */
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#define LMAX 0.01 /* minimal segment length triggering resampling */
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#define DMIN 0.02 /* minimal distance to boundary for triggering resampling */
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#define CYCLE 0 /* set to 1 for closed curve (start in all directions) */
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#define NSTEPS 7500 /* number of frames of movie */
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#define TIME 50 /* time between movie frames, for fluidity of real-time simulation */
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#define DPHI 0.0001 /* integration step */
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#define NVID 20 /* number of iterations between images displayed on screen */
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#define NCOLORS 10 /* number of colors */
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#define COLORSHIFT 200 /* hue of initial color */
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#define NSEG 100 /* number of segments of boundary */
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/* Decreasing TIME accelerates the animation and the movie */
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/* For constant speed of movie, TIME*DPHI should be kept constant */
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/* However, increasing DPHI too much deterioriates quality of simulation */
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/* For a good quality movie, take for instance TIME = 50, DPHI = 0.0002 */
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#define PAUSE 500 /* number of frames after which to pause */
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#define PSLEEP 1 /* sleep time during pause */
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#define SLEEP1 1 /* initial sleeping time */
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#define SLEEP2 100 /* final sleeping time */
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#define PI 3.141592654
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#define DPI 6.283185307
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#define PID 1.570796327
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```
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### 27 April 21 - Sunset at Research Triangle Park ###
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**Program:** `vid_wave_billiard.c` (old version of `wave_billiard.c`)
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**Initial condition in function `animation()`:** `init_wave(0.0, -0.5, phi, psi);`
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```
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#define MOVIE 0 /* set to 1 to generate movie */
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/* General geometrical parameters */
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#define WINWIDTH 1280 /* window width */
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#define WINHEIGHT 720 /* window height */
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#define NX 640 /* number of grid points on x axis */
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#define NY 360 /* number of grid points on y axis */
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/* setting NX to WINWIDTH and NY to WINHEIGHT increases resolution */
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/* but will multiply run time by 4 */
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#define XMIN -2.0
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#define XMAX 2.0 /* x interval */
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#define YMIN -1.125
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#define YMAX 1.125 /* y interval for 9/16 aspect ratio */
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/* Choice of the billiard table */
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#define B_DOMAIN 5 /* choice of domain shape */
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#define D_RECTANGLE 0 /* rectangular domain */
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#define D_ELLIPSE 1 /* elliptical domain */
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#define D_STADIUM 2 /* stadium-shaped domain */
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#define D_SINAI 3 /* Sinai billiard */
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#define D_DIAMOND 4 /* diamond-shaped billiard */
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#define D_TRIANGLE 5 /* triangular billiard */
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#define LAMBDA 1.732050808 /* parameter controlling the dimensions of domain */
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#define FOCI 1 /* set to 1 to draw focal points of ellipse */
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/* You can add more billiard tables by adapting the functions */
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/* xy_in_billiard and draw_billiard below */
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/* Physical parameters of wave equation */
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#define COURANT 0.01 /* Courant number */
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#define GAMMA 0.0 /* damping factor in wave equation */
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#define KAPPA 5.0e-9 /* "elasticity" term enforcing oscillations */
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/* The Courant number is given by c*DT/DX, where DT is the time step and DX the lattice spacing */
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/* The physical damping coefficient is given by GAMMA/(DT)^2 */
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/* Increasing COURANT speeds up the simulation, but decreases accuracy */
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/* For similar wave forms, COURANT^2*GAMMA should be kept constant */
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/* For debugging purposes only */
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#define FLOOR 0 /* set to 1 to limit wave amplitude to VMAX */
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#define VMAX 10.0 /* max value of wave amplitude */
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/* Parameters for length and speed of simulation */
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#define NSTEPS 7500 /* number of frames of movie */
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#define NVID 75 /* 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 PAUSE 10 /* number of frames after which to pause */
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#define PSLEEP 1 /* sleep time during pause */
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#define SLEEP1 1 /* initial sleeping time */
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#define SLEEP2 100000 /* final sleeping time */
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/* Color schemes */
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#define COLOR_SCHEME 1 /* choice of color scheme */
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#define C_LUM 0 /* color scheme modifies luminosity (with slow drift of hue) */
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#define C_HUE 1 /* color scheme modifies hue */
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#define SCALE 1 /* set to 1 to adjust color scheme to variance of field */
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#define SLOPE 1.0 /* sensitivity of color on wave amplitude */
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#define ATTENUATION 0.0 /* exponential attenuation coefficient of contrast with time */
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#define COLORHUE 220 /* initial hue of water color for scheme C_LUM */
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#define COLORDRIFT -40.0 /* how much the color hue drifts during the whole simulation */
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#define LUMMEAN 0.5 /* amplitude of luminosity variation for scheme C_LUM */
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#define LUMAMP 0.2 /* amplitude of luminosity variation for scheme C_LUM */
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#define HUEMEAN 330.0 /* mean value of hue for color scheme C_HUE */
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#define HUEAMP 90.0 /* amplitude of variation of hue for color scheme C_HUE */
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/* Basic math */
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#define PI 3.141592654
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#define DPI 6.283185307
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#define PID 1.570796327
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```
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### 26 April 21 - Is the billiard in a stadium reversible? ###
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**Program:** Variant of `vid_part_billiard.c`
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**Initial condition in function `animation()`:** `init_drop_config(0.5, -1.0, 1.8, 2.0, configs);`
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```
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#define WINWIDTH 1280 /* window width */
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#define WINHEIGHT 720 /* window height */
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/* Choice of the billiard table */
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#define B_DOMAIN 2 /* choice of domain shape */
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#define D_RECTANGLE 0 /* rectangular domain */
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#define D_ELLIPSE 1 /* elliptical domain */
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#define D_STADIUM 2 /* stadium-shaped domain */
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#define D_SINAI 3 /* Sinai billiard */
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#define D_DIAMOND 4 /* diamond-shaped billiard */
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#define LAMBDA 1.0 /* aspect ratio of ellipse */
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#define FOCI 1 /* set to 1 to draw focal points of ellipse */
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#define MOVIE 1 /* set to 1 to generate movie */
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#define RESAMPLE 0 /* set to 1 if particles should be added when dispersion too large */
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#define XMIN -2.0
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#define XMAX 2.0 /* x interval */
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#define YMIN -1.125
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#define YMAX 1.125 /* y interval for 9/16 aspect ratio */
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#define NPART 200 /* number of particles */
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#define NPARTMAX 50000 /* maximal number of particles after resampling */
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#define LMAX 0.01 /* minimal segment length triggering resampling */
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#define DMIN 0.02 /* minimal distance to boundary for triggering resampling */
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#define CYCLE 1 /* set to 1 for closed curve (start in all directions) */
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#define NSTEPS 3000 /* number of frames of movie */
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#define TIME 1000 /* time between movie frames, for fluidity of real-time simulation */
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#define DPHI 0.00001 /* integration step */
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#define NVID 100 /* number of iterations between images displayed on screen */
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#define NCOLORS 20 /* number of colors */
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#define COLORSHIFT 220 /* hue of initial color */
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#define NSEG 100 /* number of segments of boundary */
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#define LENGTH 0.05 /* length of velocity vectors */
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/* Decreasing TIME accelerates the animation and the movie */
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|
/* For constant speed of movie, TIME*DPHI should be kept constant */
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/* However, increasing DPHI too much deterioriates quality of simulation */
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/* NVID tells how often a picture is drawn in the animation, increase it for faster anim */
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/* For a good quality movie, take for instance TIME = 400, DPHI = 0.00005, NVID = 100 */
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#define PAUSE 10 /* number of frames after which to pause */
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#define PSLEEP 1 /* sleep time during pause */
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#define SLEEP1 1 /* initial sleeping time */
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#define SLEEP2 100 /* final sleeping time */
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#define PI 3.141592654
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#define DPI 6.283185307
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#define PID 1.570796327
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```
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### 25 April 21 - Like tears in rain ###
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**Program:** `vid_wave_billiard.c` (old version of `wave_billiard.c`)
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**Initial condition in function `animation()`:** `init_wave(0.4, 0.4, phi, psi);`
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```
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#define MOVIE 1 /* set to 1 to generate movie */
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/* General geometrical parameters */
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#define WINWIDTH 1280 /* window width */
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#define WINHEIGHT 720 /* window height */
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#define NX 640 /* number of grid points on x axis */
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#define NY 360 /* number of grid points on y axis */
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/* setting NX to WINWIDTH and NY to WINHEIGHT increases resolution */
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/* but will multiply run time by 4 */
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#define XMIN -2.0
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#define XMAX 2.0 /* x interval */
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#define YMIN -1.125
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#define YMAX 1.125 /* y interval for 9/16 aspect ratio */
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/* Choice of the billiard table */
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#define B_DOMAIN 1 /* choice of domain shape */
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#define D_RECTANGLE 0 /* rectangular domain */
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#define D_ELLIPSE 1 /* elliptical domain */
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#define D_STADIUM 2 /* stadium-shaped domain */
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#define D_SINAI 3 /* Sinai billiard */
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#define D_DIAMOND 4 /* diamond-shaped billiard */
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#define LAMBDA 1.0 /* parameter controlling the dimensions of domain */
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#define FOCI 1 /* set to 1 to draw focal points of ellipse */
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/* You can add more billiard tables by adapting the functions */
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/* xy_in_billiard and draw_billiard below */
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/* Physical patameters of wave equation */
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#define COURANT 0.01 /* Courant number */
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#define GAMMA 5.0e-10 /* damping factor in wave equation */
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#define KAPPA 5.0e-8 /* "elasticity" term enforcing oscillations */
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/* The Courant number is given by c*DT/DX, where DT is the time step and DX the lattice spacing */
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/* The physical damping coefficient is given by GAMMA/(DT)^2 */
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/* Increasing COURANT speeds up the simulation, but decreases accuracy */
|
|
/* For similar wave forms, COURANT^2*GAMMA should be kept constant */
|
|
|
|
/* For debugging purposes only */
|
|
#define FLOOR 0 /* set to 1 to limit wave amplitude to VMAX */
|
|
#define VMAX 10.0 /* max value of wave amplitude */
|
|
|
|
/* Parameters for length and speed of simulation */
|
|
|
|
#define NSTEPS 6000 /* number of frames of movie */
|
|
#define NVID 50 /* number of iterations between images displayed on screen */
|
|
#define NSEG 100 /* number of segments of boundary */
|
|
|
|
#define PAUSE 10 /* number of frames after which to pause */
|
|
#define PSLEEP 1 /* sleep time during pause */
|
|
#define SLEEP1 1 /* initial sleeping time */
|
|
#define SLEEP2 100000 /* final sleeping time */
|
|
|
|
/* Color schemes */
|
|
|
|
#define COLOR_SCHEME 1 /* choice of color scheme */
|
|
|
|
#define C_LUM 0 /* color scheme modifies luminosity (with slow drift of hue) */
|
|
#define C_HUE 1 /* color scheme modifies hue */
|
|
|
|
#define SCALE 1 /* 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 COLORHUE 220 /* initial hue of water color for scheme C_LUM */
|
|
#define COLORDRIFT -40.0 /* how much the color hue drifts during the whole simulation */
|
|
#define LUMMEAN 0.5 /* amplitude of luminosity variation for scheme C_LUM */
|
|
#define LUMAMP 0.2 /* amplitude of luminosity variation for scheme C_LUM */
|
|
#define HUEMEAN 150.0 /* mean value of hue for color scheme C_HUE */
|
|
#define HUEAMP -120.0 /* amplitude of variation of hue for color scheme C_HUE */
|
|
|
|
/* Basic math */
|
|
|
|
#define PI 3.141592654
|
|
#define DPI 6.283185307
|
|
#define PID 1.570796327
|
|
|
|
```
|
|
|
|
### 24 April 21 - Contrails in the elliptical billiard ###
|
|
|
|
**Program:** Variant of `vid_part_billiard.c` (contrail part not yet published)
|
|
|
|
**Initial condition in function `animation()`:** `init_boundary_config(-0.35, -0.15, PID, PID, configs);`
|
|
|
|
```
|
|
#define WINWIDTH 1280 /* window width */
|
|
#define WINHEIGHT 720 /* window height */
|
|
|
|
#define LAMBDA 1.5 /* aspect ratio of ellipse */
|
|
#define FOCI 1 /* set to 1 to draw focal points of ellipse */
|
|
|
|
#define MOVIE 0 /* set to 1 to generate movie */
|
|
#define RESAMPLE 0 /* set to 1 if particles should be added when dispersion too large */
|
|
|
|
#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 NPART 501 /* number of particles */
|
|
#define NPARTMAX 50000 /* 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 NSTEPS 4500 /* number of frames of movie */
|
|
#define TIME 2000 /* time between movie frames, for fluidity of real-time simulation */
|
|
#define DPHI 0.00003 /* integration step */
|
|
#define NVID 500 /* number of iterations between images displayed on screen */
|
|
#define NCOLORS 20 /* number of colors */
|
|
#define COLORSHIFT 220 /* hue of initial color */
|
|
#define NSEG 100 /* number of segments of boundary */
|
|
#define LENGTH 0.05 /* length of velocity vectors */
|
|
|
|
/* Decreasing TIME accelerates the animation and the movie */
|
|
/* For constant speed of movie, TIME*DPHI should be kept constant */
|
|
/* However, increasing DPHI too much deterioriates quality of simulation */
|
|
/* NVID tells how often a picture is drawn in the animation, increase it for faster anim */
|
|
/* For a good quality movie, take for instance TIME = 400, DPHI = 0.00005, NVID = 100 */
|
|
|
|
#define PAUSE 10 /* 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 PI 3.141592654
|
|
#define DPI 6.283185307
|
|
#define PID 1.570796327
|
|
|
|
```
|
|
|
|
### 23 April 21 - Low sea in the square with diamonds ###
|
|
|
|
**Program:** `vid_wave_billiard.c` (old version of `wave_billiard.c`)
|
|
|
|
**Initial condition in function `animation()`:** `init_wave(0.0, 0.0, phi, psi);`
|
|
|
|
```
|
|
#define MOVIE 0 /* set to 1 to generate movie */
|
|
|
|
/* General geometrical parameters */
|
|
|
|
#define WINWIDTH 1280 /* window width */
|
|
#define WINHEIGHT 720 /* window height */
|
|
|
|
#define NX 640 /* number of grid points on x axis */
|
|
#define NY 360 /* number of grid points on y axis */
|
|
|
|
/* setting NX to WINWIDTH and NY to WINHEIGHT increases resolution */
|
|
/* but will multiply run time by 4 */
|
|
|
|
#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 */
|
|
|
|
/* Choice of the billiard table */
|
|
|
|
#define B_DOMAIN 0 /* choice of domain shape */
|
|
|
|
#define D_RECTANGLE 0 /* rectangular domain */
|
|
#define D_ELLIPSE 1 /* elliptical domain */
|
|
#define D_STADIUM 2 /* stadium-shaped domain */
|
|
#define D_SINAI 3 /* Sinai billiard */
|
|
#define D_DIAMOND 4 /* diamond-shaped billiard */
|
|
|
|
#define LAMBDA 1.0 /* parameter controlling the dimensions of domain */
|
|
#define FOCI 1 /* set to 1 to draw focal points of ellipse */
|
|
|
|
/* You can add more billiard tables by adapting the functions */
|
|
/* xy_in_billiard and draw_billiard below */
|
|
|
|
/* Physical patameters of wave equation */
|
|
|
|
#define COURANT 0.01 /* Courant number */
|
|
#define GAMMA 5.0e-06 /* damping factor in wave equation */
|
|
/* 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 */
|
|
|
|
/* For debugging purposes only */
|
|
#define FLOOR 0 /* set to 1 to limit wave amplitude to VMAX */
|
|
#define VMAX 10.0 /* max value of wave amplitude */
|
|
|
|
/* Parameters for length and speed of simulation */
|
|
|
|
#define NSTEPS 6000 /* number of frames of movie */
|
|
#define NVID 35 /* number of iterations between images displayed on screen */
|
|
#define NSEG 100 /* number of segments of boundary */
|
|
|
|
#define PAUSE 10 /* number of frames after which to pause */
|
|
#define PSLEEP 1 /* sleep time during pause */
|
|
#define SLEEP1 1 /* initial sleeping time */
|
|
#define SLEEP2 100000 /* final sleeping time */
|
|
|
|
/* Color schemes */
|
|
|
|
#define COLOR_SCHEME 1 /* choice of color scheme */
|
|
|
|
#define C_LUM 0 /* color scheme modifies luminosity (with slow drift of hue) */
|
|
#define C_HUE 1 /* color scheme modifies hue */
|
|
|
|
#define SCALE 1 /* 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 COLORHUE 220 /* initial hue of water color for scheme C_LUM */
|
|
#define COLORDRIFT -40.0 /* how much the color hue drifts during the whole simulation */
|
|
#define LUMMEAN 0.5 /* amplitude of luminosity variation for scheme C_LUM */
|
|
#define LUMAMP 0.2 /* amplitude of luminosity variation for scheme C_LUM */
|
|
#define HUEMEAN 260.0 /* mean value of hue for color scheme C_HUE */
|
|
#define HUEAMP 80.0 /* amplitude of variation of hue for color scheme C_HUE */
|
|
|
|
/* Basic math */
|
|
|
|
#define PI 3.141592654
|
|
#define DPI 6.283185307
|
|
#define PID 1.570796327
|
|
|
|
```
|
|
|
|
### 22 April 21 - Just another drop in the pool ###
|
|
|
|
**Program:** `vid_wave_billiard.c` (old version of `wave_billiard.c`)
|
|
|
|
**Initial condition in function `animation()`:** `init_wave(sqrt(LAMBDA*LAMBDA - 1.0), 0.0, phi, psi); add_drop_to_wave(-1.0,-sqrt(LAMBDA*LAMBDA - 1.0), 0.0, phi, psi);`
|
|
|
|
```
|
|
#define WINWIDTH 1280 /* window width */
|
|
#define WINHEIGHT 720 /* window height */
|
|
|
|
#define NX 640 /* number of grid points on x axis */
|
|
#define NY 360 /* number of grid points on y axis */
|
|
|
|
#define B_DOMAIN 1 /* choice of domain shape */
|
|
|
|
#define D_RECTANGLE 0 /* rectangular domain */
|
|
#define D_ELLIPSE 1 /* elliptical domain */
|
|
#define D_STADIUM 2 /* stadium-shaped domain */
|
|
#define D_SINAI 3 /* Sinai billiard */
|
|
#define D_DIAMOND 4 /* diamond-shaped billiard */
|
|
|
|
#define LAMBDA 1.5 /* parameter controlling the dimensions of domain */
|
|
#define FOCI 1 /* set to 1 to draw focal points of ellipse */
|
|
#define COURANT 0.01 /* Courant number */
|
|
#define GAMMA 5.0e-05 /* damping factor in wave equation */
|
|
// 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
|
|
|
|
#define MOVIE 1 /* set to 1 to generate movie */
|
|
|
|
#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 VMAX 10.0 /* max value of wave amplitude */
|
|
#define FLOOR 0 /* set to 1 to limit wave amplitude to VMAX */
|
|
|
|
#define NSTEPS 4500 /* number of frames of movie */
|
|
#define NVID 35 /* number of iterations between images displayed on screen */
|
|
#define NCOLORS 20 /* number of colors */
|
|
#define COLORHUE 220 /* initial hue of water color */
|
|
#define COLORDRIFT -40.0 /* how much the color hue drifts during the whole simulation */
|
|
#define NSEG 100 /* number of segments of boundary */
|
|
#define SLOPE 1.0 /* for color scheme: sensitivity of color on wave amplitude */
|
|
#define ATTENUATION 0.0 /* exponential attenuation coefficient of contrat with time */
|
|
#define LUMMEAN 0.5 /* amplitude of luminosity variation */
|
|
#define LUMAMP 0.2 /* amplitude of luminosity variation */
|
|
#define SCALE 1 /* set to 1 to adjust color scheme to variance of field */
|
|
|
|
/* Decreasing TIME accelerates the animation and the movie */
|
|
/* For constant speed of movie, TIME*DPHI should be kept constant */
|
|
/* However, increasing DPHI too much deterioriates quality of simulation */
|
|
/* NVID tells how often a picture is drawn in the animation, increase it for faster anim */
|
|
/* For a good quality movie, take for instance TIME = 400, DPHI = 0.00005, NVID = 100 */
|
|
|
|
#define PAUSE 10 /* number of frames after which to pause */
|
|
#define PSLEEP 1 /* sleep time during pause */
|
|
#define SLEEP1 1 /* initial sleeping time */
|
|
#define SLEEP2 100000 /* final sleeping time */
|
|
|
|
#define PI 3.141592654
|
|
#define DPI 6.283185307
|
|
#define PID 1.570796327
|
|
|
|
```
|
|
|
|
### 21 April 21 - Rain on my crazy diamond ###
|
|
|
|
**Program:** `vid_wave_billiard.c` (old version of `wave_billiard.c`)
|
|
|
|
**Initial condition in function `animation()`:** `init_wave(0.0, 0.0, phi, psi);`
|
|
|
|
```
|
|
#define WINWIDTH 1280 /* window width */
|
|
#define WINHEIGHT 720 /* window height */
|
|
|
|
#define NX 640 /* number of grid points on x axis */
|
|
#define NY 360 /* number of grid points on y axis */
|
|
|
|
#define B_DOMAIN 4 /* choice of domain shape */
|
|
|
|
#define D_RECTANGLE 0 /* rectangular domain */
|
|
#define D_ELLIPSE 1 /* elliptical domain */
|
|
#define D_STADIUM 2 /* stadium-shaped domain */
|
|
#define D_SINAI 3 /* Sinai billiard */
|
|
#define D_DIAMOND 4 /* diamond-shaped billiard */
|
|
|
|
#define LAMBDA 2.0 /* parameter controlling the dimensions of domain */
|
|
#define FOCI 1 /* set to 1 to draw focal points of ellipse */
|
|
#define COURANT 0.01 /* Courant number */
|
|
#define GAMMA 5.0e-05 /* damping factor in wave equation */
|
|
// 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
|
|
|
|
|
|
#define MOVIE 1 /* set to 1 to generate movie */
|
|
|
|
#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 VMAX 10.0 /* max value of wave amplitude */
|
|
#define FLOOR 0 /* set to 1 to limit wave amplitude to VMAX */
|
|
|
|
#define NSTEPS 7500 /* number of frames of movie */
|
|
#define NVID 25 /* number of iterations between images displayed on screen */
|
|
#define NCOLORS 20 /* number of colors */
|
|
#define COLORHUE 220 /* initial hue of water color */
|
|
#define COLORDRIFT -40.0 /* how much the color hue drifts during the whole simulation */
|
|
#define NSEG 100 /* number of segments of boundary */
|
|
#define SLOPE 1.0 /* for color scheme: sensitivity of color on wave amplitude */
|
|
#define ATTENUATION 0.0 /* exponential attenuation coefficient of contrat with time */
|
|
#define LUMMEAN 0.5 /* amplitude of luminosity variation */
|
|
#define LUMAMP 0.2 /* amplitude of luminosity variation */
|
|
#define SCALE 1 /* set to 1 to adjust color scheme to variance of field */
|
|
|
|
/* Decreasing TIME accelerates the animation and the movie */
|
|
/* For constant speed of movie, TIME*DPHI should be kept constant */
|
|
/* However, increasing DPHI too much deterioriates quality of simulation */
|
|
/* NVID tells how often a picture is drawn in the animation, increase it for faster anim */
|
|
/* For a good quality movie, take for instance TIME = 400, DPHI = 0.00005, NVID = 100 */
|
|
|
|
#define PAUSE 10 /* number of frames after which to pause */
|
|
#define PSLEEP 1 /* sleep time during pause */
|
|
#define SLEEP1 1 /* initial sleeping time */
|
|
#define SLEEP2 100000 /* final sleeping time */
|
|
|
|
#define PI 3.141592654
|
|
#define DPI 6.283185307
|
|
#define PID 1.570796327
|
|
|
|
```
|
|
|
|
### 20 April 21 - A saucerful of droplets ###
|
|
|
|
**Program:** Variant of `vid_wave_billiard.c` (old version of `vid_wave_billiard.c`)
|
|
|
|
**Initial condition in function `animation()`:** Raindrops are generated by
|
|
```
|
|
while (!in_bill)
|
|
{
|
|
x = (double)rand() / RAND_MAX;
|
|
y = (double)rand() / RAND_MAX;
|
|
x = LAMBDA*(2.0*x - 1.0);
|
|
y = 2.0*y - 1.0;
|
|
in_bill = xy_in_billiard(x, y);
|
|
}
|
|
init_wave(x, y, phi, psi);
|
|
```
|
|
|
|
|
|
```
|
|
#define WINWIDTH 1280 /* window width */
|
|
#define WINHEIGHT 720 /* window height */
|
|
|
|
#define NX 640 /* number of grid points on x axis */
|
|
#define NY 360 /* number of grid points on y axis */
|
|
|
|
#define B_DOMAIN 1 /* choice of domain shape */
|
|
|
|
#define D_RECTANGLE 0 /* rectangular domain */
|
|
#define D_ELLIPSE 1 /* elliptical domain */
|
|
#define D_STADIUM 2 /* stadium-shaped domain */
|
|
#define D_SINAI 3 /* Sinai billiard */
|
|
|
|
#define LAMBDA 1.3 /* parameter controlling the dimensions of domain */
|
|
#define FOCI 0 /* set to 1 to draw focal points of ellipse */
|
|
#define COURANT 0.003125 /* Courant number */
|
|
#define GAMMA 1e-06 /* damping factor in wave equation */
|
|
// 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
|
|
|
|
|
|
#define MOVIE 1 /* set to 1 to generate movie */
|
|
|
|
#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 VMAX 10.0 /* max value of wave amplitude */
|
|
#define FLOOR 0 /* set to 1 to limit wave amplitude to VMAX */
|
|
|
|
#define NSTEPS 3000 /* number of frames of movie */
|
|
#define NVID 60 /* number of iterations between images displayed on screen */
|
|
#define NCOLORS 20 /* number of colors */
|
|
#define COLORHUE 200 /* initial hue of water color */
|
|
#define COLORDRIFT -20.0 /* how much the color hue drifts during the whole simulation */
|
|
#define NSEG 100 /* number of segments of boundary */
|
|
#define SLOPE 0.75 /* for color scheme: sensitivity of color on wave amplitude */
|
|
#define ATTENUATION 0.0 /* exponential attenuation coefficient of contrat with time */
|
|
#define LUMMEAN 0.5 /* amplitude of luminosity variation */
|
|
#define LUMAMP 0.2 /* amplitude of luminosity variation */
|
|
#define SCALE 1 /* set to 1 to adjust color scheme to variance of field */
|
|
|
|
/* Decreasing TIME accelerates the animation and the movie */
|
|
/* For constant speed of movie, TIME*DPHI should be kept constant */
|
|
/* However, increasing DPHI too much deterioriates quality of simulation */
|
|
/* NVID tells how often a picture is drawn in the animation, increase it for faster anim */
|
|
/* For a good quality movie, take for instance TIME = 400, DPHI = 0.00005, NVID = 100 */
|
|
|
|
#define PAUSE 10 /* number of frames after which to pause */
|
|
#define PSLEEP 1 /* sleep time during pause */
|
|
#define SLEEP1 1 /* initial sleeping time */
|
|
#define SLEEP2 100000 /* final sleeping time */
|
|
|
|
#define PI 3.141592654
|
|
#define DPI 6.283185307
|
|
#define PID 1.570796327
|
|
|
|
```
|
|
|
|
### 19 April 21 - Raindrop in the Sinai billiard ###
|
|
|
|
**Program:** `vid_wave_billiard.c` (old version of `wave_billiard.c`)
|
|
|
|
**Initial condition in function `animation()`:** `init_wave(0.6, 0.9, phi, psi);`
|
|
|
|
```
|
|
#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 NX 640 /* number of grid points on x axis */
|
|
#define NY 360 /* number of grid points on y axis */
|
|
|
|
#define B_DOMAIN 3 /* choice of domain shape */
|
|
|
|
#define D_RECTANGLE 0 /* rectangular domain */
|
|
#define D_ELLIPSE 1 /* elliptical domain */
|
|
#define D_STADIUM 2 /* stadium-shaped domain */
|
|
#define D_SINAI 3 /* Sinai billiard */
|
|
|
|
#define LAMBDA 0.7 /* parameter controlling the dimensions of domain */
|
|
#define FOCI 1 /* set to 1 to draw focal points of ellipse */
|
|
#define K 20.0 /* coupling constant */
|
|
#define GAMMA 0.00005 /* damping factor in wave equation */
|
|
#define DT 0.05 /* time step */
|
|
|
|
#define MOVIE 0 /* set to 1 to generate movie */
|
|
|
|
#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 VMAX 10.0 /* max value of wave amplitude */
|
|
#define FLOOR 0 /* set to 1 to limit wave amplitude to VMAX */
|
|
|
|
#define NSTEPS 7500 /* number of frames of movie */
|
|
#define NVID 60 /* number of iterations between images displayed on screen */
|
|
#define NCOLORS 20 /* number of colors */
|
|
#define COLORHUE 180 /* hue of water color */
|
|
#define COLORDRIFT 180.0 /* how much the color hue drifts during the whole simulation */
|
|
#define NSEG 100 /* number of segments of boundary */
|
|
#define SLOPE 0.75 /* for color scheme: sensitivity of color on wave amplitude */
|
|
#define ATTENUATION 0.0 /* exponential attenuation coefficient of contrat with time */
|
|
#define LUMAMP 0.2 /* amplitude of luminosity variation */
|
|
#define SCALE 1 /* set to 1 to adjust color scheme to variance of field */
|
|
|
|
/* Decreasing TIME accelerates the animation and the movie */
|
|
/* For constant speed of movie, TIME*DPHI should be kept constant */
|
|
/* However, increasing DPHI too much deterioriates quality of simulation */
|
|
/* NVID tells how often a picture is drawn in the animation, increase it for faster anim */
|
|
/* For a good quality movie, take for instance TIME = 400, DPHI = 0.00005, NVID = 100 */
|
|
|
|
#define PAUSE 10 /* number of frames after which to pause */
|
|
#define PSLEEP 1 /* sleep time during pause */
|
|
#define SLEEP1 1 /* initial sleeping time */
|
|
#define SLEEP2 100000 /* final sleeping time */
|
|
|
|
#define PI 3.141592654
|
|
#define DPI 6.283185307
|
|
#define PID 1.570796327
|
|
|
|
```
|
|
|
|
### 18 April 21 - Dropping a stone in a flooded stadium ###
|
|
|
|
**Program:** `xxx.c`
|
|
|
|
**Initial condition in function `animation()`:** `xxx`
|
|
|
|
```
|
|
#define WINWIDTH 1280 /* window width */
|
|
#define WINHEIGHT 720 /* window height */
|
|
|
|
#define NX 640 /* number of grid points on x axis */
|
|
#define NY 360 /* number of grid points on y axis */
|
|
|
|
#define B_DOMAIN 1 /* choice of domain shape */
|
|
|
|
#define D_ELLIPSE 0 /* elliptical domain */
|
|
#define D_STADIUM 1 /* stadium-shaped domain */
|
|
|
|
#define LAMBDA 1.0 /* parameter controlling the dimensions of domain */
|
|
#define FOCI 1 /* set to 1 to draw focal points of ellipse */
|
|
#define K 20.0 /* coupling constant */
|
|
#define GAMMA 0.00005 /* damping factor in wave equation */
|
|
#define DT 0.05 /* time step */
|
|
|
|
#define MOVIE 0 /* set to 1 to generate movie */
|
|
|
|
#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 VMAX 10.0 /* max value of wave amplitude */
|
|
#define FLOOR 0 /* set to 1 to limit wave amplitude to VMAX */
|
|
|
|
#define NSTEPS 7500 /* number of frames of movie */
|
|
#define NVID 60 /* number of iterations between images displayed on screen */
|
|
#define NCOLORS 20 /* number of colors */
|
|
#define COLORHUE 200 /* hue of water color */
|
|
#define NSEG 100 /* number of segments of boundary */
|
|
#define SLOPE 1.25 /* for color scheme: sensitivity of color on wave amplitude */
|
|
#define ATTENUATION 0.0 /* exponential attenuation coefficient of contrat with time */
|
|
#define LUMAMP 0.25 /* amplitude of luminosity variation */
|
|
|
|
/* Decreasing TIME accelerates the animation and the movie */
|
|
/* For constant speed of movie, TIME*DPHI should be kept constant */
|
|
/* However, increasing DPHI too much deterioriates quality of simulation */
|
|
/* NVID tells how often a picture is drawn in the animation, increase it for faster anim */
|
|
/* For a good quality movie, take for instance TIME = 400, DPHI = 0.00005, NVID = 100 */
|
|
|
|
#define PAUSE 10 /* number of frames after which to pause */
|
|
#define PSLEEP 1 /* sleep time during pause */
|
|
#define SLEEP1 1 /* initial sleeping time */
|
|
#define SLEEP2 100000 /* final sleeping time */
|
|
|
|
#define PI 3.141592654
|
|
#define DPI 6.283185307
|
|
#define PID 1.570796327
|
|
|
|
```
|
|
|
|
### 17 April 21 - Waves in an elliptical swimming pool 3: Starting from a focus ###
|
|
|
|
**Program:** `vid_wave_ellipse.c` (old version of `wave_billiard.c`)
|
|
|
|
**Initial condition in function `animation()`:**
|
|
`init_drop_config(sqrt(LAMBDA*LAMBDA-1.0) - 0.1,0.0, 0.0, DPI, configs);`
|
|
|
|
```
|
|
#define WINWIDTH 1280 /* window width */
|
|
#define WINHEIGHT 720 /* window height */
|
|
|
|
#define LAMBDA 1.5 /* aspect ratio of ellipse */
|
|
#define FOCI 1 /* set to 1 to draw focal points of ellipse */
|
|
|
|
#define MOVIE 1 /* set to 1 to generate movie */
|
|
#define RESAMPLE 1 /* set to 1 if particles should be added when dispersion too large */
|
|
|
|
#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 NPART 2000 /* number of particles */
|
|
#define NPARTMAX 200000 /* 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 NSTEPS 130 /* number of frames of movie */
|
|
#define TIME 25 /* time between movie frames, for fluidity of real-time simulation */
|
|
#define DPHI 0.0004 /* integration step */
|
|
#define NVID 10 /* number of iterations between images displayed on screen */
|
|
#define NCOLORS 10 /* number of colors */
|
|
#define COLORSHIFT 0 /* hue of initial color */
|
|
#define NSEG 100 /* number of segments of boundary */
|
|
|
|
/* Decreasing TIME accelerates the animation and the movie */
|
|
/* For constant speed of movie, TIME*DPHI should be kept constant */
|
|
/* However, increasing DPHI too much deterioriates quality of simulation */
|
|
/* For a good quality movie, take for instance TIME = 50, DPHI = 0.0002 */
|
|
|
|
#define PAUSE 1 /* 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 PI 3.141592654
|
|
#define DPI 6.283185307
|
|
#define PID 1.570796327
|
|
|
|
```
|
|
|
|
### 17 April 21 - Waves in an elliptical swimming pool 2 ###
|
|
|
|
**Program:** `vid_wave_ellipse.c` (old version of `wave_billiard.c`)
|
|
|
|
**Initial condition in function `animation()`:** `init_wave(0.8, 0.6, phi, psi);`
|
|
|
|
```
|
|
#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. */
|
|
|
|
#define WINWIDTH 1280 /* window width */
|
|
#define WINHEIGHT 720 /* window height */
|
|
|
|
#define NX 640 /* number of grid points on x axis */
|
|
#define NY 360 /* number of grid points on y axis */
|
|
|
|
#define B_DOMAIN 1 /* choice of domain shape */
|
|
|
|
#define D_ELLIPSE 0 /* elliptical domain */
|
|
#define D_STADIUM 1 /* stadium-shaped domain */
|
|
|
|
#define LAMBDA 1.0 /* parameter controlling the dimensions of domain */
|
|
#define FOCI 1 /* set to 1 to draw focal points of ellipse */
|
|
#define K 20.0 /* coupling constant */
|
|
#define GAMMA 0.00005 /* damping factor in wave equation */
|
|
#define DT 0.05 /* time step */
|
|
|
|
#define MOVIE 0 /* set to 1 to generate movie */
|
|
|
|
#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 VMAX 10.0 /* max value of wave amplitude */
|
|
#define FLOOR 0 /* set to 1 to limit wave amplitude to VMAX */
|
|
|
|
#define NSTEPS 4500 /* number of frames of movie */
|
|
#define NVID 60 /* number of iterations between images displayed on screen */
|
|
#define NCOLORS 20 /* number of colors */
|
|
#define COLORHUE 200 /* hue of water color */
|
|
#define NSEG 100 /* number of segments of boundary */
|
|
#define SLOPE 1.25 /* for color scheme: sensitivity of color on wave amplitude */
|
|
#define ATTENUATION 0.0 /* exponential attenuation coefficient of contrat with time */
|
|
#define LUMMEAN 0.5 /* amplitude of luminosity variation */
|
|
#define LUMAMP 0.2 /* amplitude of luminosity variation */
|
|
#define SCALE 1 /* set to 1 to adjust color scheme to variance of field */
|
|
|
|
/* Decreasing TIME accelerates the animation and the movie */
|
|
/* For constant speed of movie, TIME*DPHI should be kept constant */
|
|
/* However, increasing DPHI too much deterioriates quality of simulation */
|
|
/* NVID tells how often a picture is drawn in the animation, increase it for faster anim */
|
|
/* For a good quality movie, take for instance TIME = 400, DPHI = 0.00005, NVID = 100 */
|
|
|
|
#define PAUSE 10 /* number of frames after which to pause */
|
|
#define PSLEEP 1 /* sleep time during pause */
|
|
#define SLEEP1 1 /* initial sleeping time */
|
|
#define SLEEP2 100000 /* final sleeping time */
|
|
|
|
#define PI 3.141592654
|
|
#define DPI 6.283185307
|
|
#define PID 1.570796327
|
|
|
|
```
|
|
|
|
### 16 April 21 - Waves in an elliptical swimming pool ###
|
|
|
|
**Program:** `vid_wave_billiard.c` (old version of `wave_billiard.c`)
|
|
|
|
**Initial condition in function `animation()`:** `init_wave(0.8, 0.6, phi, psi);`
|
|
|
|
```
|
|
#define WINWIDTH 1280 /* window width */
|
|
#define WINHEIGHT 720 /* window height */
|
|
|
|
#define NX 640 /* number of grid points on x axis */
|
|
#define NY 360 /* number of grid points on y axis */
|
|
|
|
#define LAMBDA 1.5 /* aspect ratio of ellipse */
|
|
#define FOCI 1 /* set to 1 to draw focal points of ellipse */
|
|
#define K 20.0 /* coupling constant */
|
|
#define GAMMA 0.00005 /* damping */
|
|
#define DT 0.05 /* time step */
|
|
#define PHIMAX 1.0 /* max value of field */
|
|
|
|
#define MOVIE 1 /* set to 1 to generate movie */
|
|
|
|
#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 VMAX 2.0 /* max value for color scheme */
|
|
|
|
#define NSTEPS 4500 /* number of frames of movie */
|
|
#define NVID 50 /* number of iterations between images displayed on screen */
|
|
#define NCOLORS 20 /* number of colors */
|
|
#define COLORSHIFT 220 /* hue of initial color */
|
|
#define NSEG 100 /* number of segments of boundary */
|
|
|
|
/* Decreasing TIME accelerates the animation and the movie */
|
|
/* For constant speed of movie, TIME*DPHI should be kept constant */
|
|
/* However, increasing DPHI too much deterioriates quality of simulation */
|
|
/* NVID tells how often a picture is drawn in the animation, increase it for faster anim */
|
|
/* For a good quality movie, take for instance TIME = 400, DPHI = 0.00005, NVID = 100 */
|
|
|
|
#define PAUSE 10 /* 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 PI 3.141592654
|
|
#define DPI 6.283185307
|
|
#define PID 1.570796327
|
|
|
|
```
|
|
|
|
### 15 April 21 - Starting near a focus in the elliptical billiard ###
|
|
|
|
**Program:** `vid_particle_ellipse.c` (Old version of `particle_billiard.c`)
|
|
|
|
**Initial condition in function `animation()`:** `init_drop_config(sqrt(LAMBDA*LAMBDA-1.0)-0.01,0.0, 0.0, DPI);`
|
|
|
|
```
|
|
#define WINWIDTH 1280 /* window width */
|
|
#define WINHEIGHT 720 /* window height */
|
|
|
|
#define LAMBDA 1.2 /* aspect ratio of ellipse */
|
|
#define FOCI 1 /* set to 1 to draw focal points of ellipse */
|
|
|
|
#define MOVIE 1 /* set to 1 to generate movie */
|
|
#define RESAMPLE 0 /* set to 1 if particles should be added when dispersion too large */
|
|
|
|
#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 NPART 500 /* number of particles */
|
|
#define NPARTMAX 50000 /* 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 NSTEPS 4500 /* number of frames of movie */
|
|
#define TIME 2000 /* time between movie frames, for fluidity of real-time simulation */
|
|
#define DPHI 0.00001 /* integration step */
|
|
#define NVID 500 /* number of iterations between images displayed on screen */
|
|
#define NCOLORS 20 /* number of colors */
|
|
#define COLORSHIFT 220 /* hue of initial color */
|
|
#define NSEG 100 /* number of segments of boundary */
|
|
#define LENGTH 0.05 /* length of velocity vectors */
|
|
|
|
/* Decreasing TIME accelerates the animation and the movie */
|
|
/* For constant speed of movie, TIME*DPHI should be kept constant */
|
|
/* However, increasing DPHI too much deterioriates quality of simulation */
|
|
/* NVID tells how often a picture is drawn in the animation, increase it for faster anim */
|
|
/* For a good quality movie, take for instance TIME = 400, DPHI = 0.00005, NVID = 100 */
|
|
|
|
#define PAUSE 10 /* 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 PI 3.141592654
|
|
#define DPI 6.283185307
|
|
#define PID 1.570796327
|
|
|
|
```
|
|
|
|
### 14 April 21 - Billiard in an ellipse ###
|
|
|
|
**Program:** `vid_particle_ellipse.c` (Old version of `particle_billiard.c`)
|
|
|
|
**Initial condition in function `animation()`:** ?
|
|
|
|
```
|
|
#define WINWIDTH 1280 /* window width */
|
|
#define WINHEIGHT 720 /* window height */
|
|
|
|
#define LAMBDA 1.2 /* aspect ratio of ellipse */
|
|
#define FOCI 1 /* set to 1 to draw focal points of ellipse */
|
|
|
|
#define MOVIE 1 /* set to 1 to generate movie */
|
|
#define RESAMPLE 0 /* set to 1 if particles should be added when dispersion too large */
|
|
|
|
#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 NPART 500 /* number of particles */
|
|
#define NPARTMAX 50000 /* 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 NSTEPS 4500 /* number of frames of movie */
|
|
#define TIME 2000 /* time between movie frames, for fluidity of real-time simulation */
|
|
#define DPHI 0.00001 /* integration step */
|
|
#define NVID 500 /* number of iterations between images displayed on screen */
|
|
#define NCOLORS 20 /* number of colors */
|
|
#define COLORSHIFT 220 /* hue of initial color */
|
|
#define NSEG 100 /* number of segments of boundary */
|
|
#define LENGTH 0.05 /* length of velocity vectors */
|
|
|
|
/* Decreasing TIME accelerates the animation and the movie */
|
|
/* For constant speed of movie, TIME*DPHI should be kept constant */
|
|
/* However, increasing DPHI too much deterioriates quality of simulation */
|
|
/* NVID tells how often a picture is drawn in the animation, increase it for faster anim */
|
|
/* For a good quality movie, take for instance TIME = 400, DPHI = 0.00005, NVID = 100 */
|
|
|
|
#define PAUSE 10 /* 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 PI 3.141592654
|
|
#define DPI 6.283185307
|
|
#define PID 1.570796327
|
|
|
|
```
|
|
|
|
### 14 April 21 - Billiard in an ellipse ###
|
|
|
|
**Program:** `vid_particle_ellipse.c` (Old version of `particle_billiard.c`)
|
|
|
|
**Initial condition in function `animation()`:** ?
|
|
|
|
```
|
|
#define WINWIDTH 1280 /* window width */
|
|
#define WINHEIGHT 720 /* window height */
|
|
|
|
#define LAMBDA 1.2 /* aspect ratio of ellipse */
|
|
#define FOCI 1 /* set to 1 to draw focal points of ellipse */
|
|
|
|
#define MOVIE 1 /* set to 1 to generate movie */
|
|
#define RESAMPLE 0 /* set to 1 if particles should be added when dispersion too large */
|
|
|
|
#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 NPART 500 /* number of particles */
|
|
#define NPARTMAX 50000 /* 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 NSTEPS 4500 /* number of frames of movie */
|
|
#define TIME 2000 /* time between movie frames, for fluidity of real-time simulation */
|
|
#define DPHI 0.00001 /* integration step */
|
|
#define NVID 500 /* number of iterations between images displayed on screen */
|
|
#define NCOLORS 20 /* number of colors */
|
|
#define COLORSHIFT 220 /* hue of initial color */
|
|
#define NSEG 100 /* number of segments of boundary */
|
|
#define LENGTH 0.05 /* length of velocity vectors */
|
|
|
|
/* Decreasing TIME accelerates the animation and the movie */
|
|
/* For constant speed of movie, TIME*DPHI should be kept constant */
|
|
/* However, increasing DPHI too much deterioriates quality of simulation */
|
|
/* NVID tells how often a picture is drawn in the animation, increase it for faster anim */
|
|
/* For a good quality movie, take for instance TIME = 400, DPHI = 0.00005, NVID = 100 */
|
|
|
|
#define PAUSE 10 /* 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 PI 3.141592654
|
|
#define DPI 6.283185307
|
|
#define PID 1.570796327
|
|
|
|
```
|
|
|
|
### 14 April 21 - Billiard in a circle (very long and HD-ish) ###
|
|
|
|
**Program:** `xxx.c`
|
|
|
|
**Initial condition in function `animation()`:** `xxx`
|
|
|
|
```
|
|
|
|
```
|
|
|
|
### 11 April 21 - Drop in an elliptic pond ###
|
|
|
|
**Program:** `vid_drop_ellipse.c` (Old version of `drop_billiard.c`)
|
|
|
|
**Initial condition in function `animation()`:** `init_boundary_config(0.0, 0.0, 0.0, PI, configs);`
|
|
|
|
```
|
|
#define WINWIDTH 1280 /* window width */
|
|
#define WINHEIGHT 720 /* window height */
|
|
|
|
#define LAMBDA 1.5 /* aspect ratio of ellipse */
|
|
#define FOCI 1 /* set to 1 to draw focal points of ellipse */
|
|
|
|
#define MOVIE 0 /* set to 1 to generate movie */
|
|
#define RESAMPLE 1 /* set to 1 if particles should be added when dispersion too large */
|
|
|
|
#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 NPART 2000 /* number of particles */
|
|
#define NPARTMAX 50000 /* 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 NSTEPS 2000 /* number of frames of movie */
|
|
#define TIME 25 /* time between movie frames, for fluidity of real-time simulation */
|
|
#define DPHI 0.0004 /* integration step */
|
|
#define NVID 10 /* number of iterations between images displayed on screen */
|
|
#define NCOLORS 10 /* number of colors */
|
|
#define COLORSHIFT 0 /* hue of initial color */
|
|
#define NSEG 100 /* number of segments of boundary */
|
|
|
|
/* Decreasing TIME accelerates the animation and the movie */
|
|
/* For constant speed of movie, TIME*DPHI should be kept constant */
|
|
/* However, increasing DPHI too much deterioriates quality of simulation */
|
|
/* For a good quality movie, take for instance TIME = 50, DPHI = 0.0002 */
|
|
|
|
#define PAUSE 10 /* 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 PI 3.141592654
|
|
#define DPI 6.283185307
|
|
#define PID 1.570796327
|
|
|
|
```
|
|
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### 11 April 21 - Drop in an elliptic pond ###
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**Program:** `vid_drop_ellipse.c` (Old version of `drop_billiard.c`)
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**Initial condition in function `animation()`:** `init_drop_config(0.8, 0.6, 0.0, DPI, configs);`
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```
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#define WINWIDTH 1280 /* window width */
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#define WINHEIGHT 720 /* window height */
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#define LAMBDA 1.5 /* aspect ratio of ellipse */
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#define XMIN -2.0
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#define XMAX 2.0 /* x interval */
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#define YMIN -1.125
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#define YMAX 1.125 /* y interval for 9/16 aspect ratio */
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#define NPART 2000 /* number of particles */
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#define NPARTMAX 50000 /* maximal number of particles after resampling */
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#define LMAX 0.01 /* minimal segment length triggering resampling */
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#define DMIN 0.02 /* minimal distance to boundary for triggering resampling */
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#define CYCLE 1 /* set to 1 for closed curve (start in all directions) */
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#define NSTEPS 2000 /* number of frames of movie */
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#define TIME 25 /* time between movie frames, for fluidity of real-time simulation */
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#define DPHI 0.0004 /* integration step */
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#define NCOLORS 10 /* number of colors */
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#define COLORSHIFT 0 /* hue of initial color */
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#define NSEG 100 /* number of segments of boundary */
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/* Decreasing TIME accelerates the animation and the movie */
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/* For constant speed of movie, TIME*DPHI should be kept constant */
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/* However, increasing DPHI too much deterioriates quality of simulation */
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#define SLEEP1 1 /* initial sleeping time */
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#define SLEEP2 100 /* final sleeping time */
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#define PI 3.141592654
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#define DPI 6.283185307
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#define PID 1.570796327
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```
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### 11 April 21 - Drop in an elliptic pond, starting from a focus ###
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**Program:** `vid_drop_ellipse.c` (Old version of `drop_billiard.c`)
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**Initial condition in function `animation()`:** `init_drop_config(sqrt(LAMBDA*LAMBDA-1.0),0.0, 0.0, DPI, configs);`
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```
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#define WINWIDTH 1280 /* window width */
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#define WINHEIGHT 720 /* window height */
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#define LAMBDA 1.5 /* aspect ratio of ellipse */
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#define XMIN -2.0
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#define XMAX 2.0 /* x interval */
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#define YMIN -1.125
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#define YMAX 1.125 /* y interval for 9/16 aspect ratio */
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#define NPART 2000 /* number of particles */
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#define NPARTMAX 50000 /* maximal number of particles after resampling */
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#define LMAX 0.01 /* minimal segment length triggering resampling */
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#define DMIN 0.02 /* minimal distance to boundary for triggering resampling */
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#define CYCLE 1 /* set to 1 for closed curve (start in all directions) */
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#define NSTEPS 2000 /* number of frames of movie */
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#define TIME 25 /* time between movie frames, for fluidity of real-time simulation */
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#define DPHI 0.0004 /* integration step */
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#define NCOLORS 10 /* number of colors */
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#define COLORSHIFT 0 /* hue of initial color */
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#define NSEG 100 /* number of segments of boundary */
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/* Decreasing TIME accelerates the animation and the movie */
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/* For constant speed of movie, TIME*DPHI should be kept constant */
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/* However, increasing DPHI too much deterioriates quality of simulation */
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#define SLEEP1 1 /* initial sleeping time */
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#define SLEEP2 100 /* final sleeping time */
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#define PI 3.141592654
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#define DPI 6.283185307
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#define PID 1.570796327
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```
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### 11 April 21 - Drop in an elliptic pond ###
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**Program:** `vid_drop_ellipse.c` (Old version of `drop_billiard.c`)
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**Initial condition in function `animation()`:** `init_drop_config(0.0, 0.0, 0.0, DPI, configs);`
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```
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#define WINWIDTH 1280 /* window width */
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#define WINHEIGHT 720 /* window height */
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#define LAMBDA 1.5 /* aspect ratio of ellipse */
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#define XMIN -2.0
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#define XMAX 2.0 /* x interval */
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#define YMIN -1.125
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#define YMAX 1.125 /* y interval for 9/16 aspect ratio */
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#define NPART 2000 /* number of particles */
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#define NPARTMAX 50000 /* maximal number of particles after resampling */
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#define LMAX 0.01 /* minimal segment length triggering resampling */
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#define DMIN 0.02 /* minimal distance to boundary for triggering resampling */
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#define CYCLE 1 /* set to 1 for closed curve (start in all directions) */
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#define NSTEPS 2000 /* number of frames of movie */
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#define TIME 25 /* time between movie frames, for fluidity of real-time simulation */
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#define DPHI 0.0004 /* integration step */
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#define NCOLORS 10 /* number of colors */
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#define COLORSHIFT 0 /* hue of initial color */
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#define NSEG 100 /* number of segments of boundary */
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/* Decreasing TIME accelerates the animation and the movie */
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/* For constant speed of movie, TIME*DPHI should be kept constant */
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/* However, increasing DPHI too much deterioriates quality of simulation */
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#define SLEEP1 1 /* initial sleeping time */
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#define SLEEP2 100 /* final sleeping time */
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#define PI 3.141592654
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#define DPI 6.283185307
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#define PID 1.570796327
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```
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### 9 April 21 - Drop in a circular water bowl (higher resolution) ###
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**Program:** `vid_drop_circle.c` (ancestor of `drop_billiard.c`)
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```
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#define NPART 5000 /* number of particles */
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#define LAMBDA 0.0 /* aspect ratio of ellipse */
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#define MU 2.0 /* Larmor radius for billiard in magnetic field */
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#define XMIN -2.0
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#define XMAX 2.0 /* x interval */
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#define YMIN -1.125
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#define YMAX 1.125 /* y interval */
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#define NSTEPS 3200
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#define TIME 400
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#define DPHI 0.00003
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#define LPART 0.001
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#define NCOLORS 15
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#define COLORSHIFT 220
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#define SLEEP1 1 /* initial sleeping time */
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#define SLEEP2 100000 /* final sleeping time */
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```
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### 9 April 21 - Droplet in a stadium-shaped billiard (higher res version) ###
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**Program:** `vid_drop_stadium.c` (ancestor of `drop_billiard.c`)
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**Initial condition in function `animation()`:** `init_drop_config(0.0,0.0);`
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```
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#define NPART 20000 /* number of particles */
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#define LAMBDA 0.75 /* dimensions of stadium */
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#define XMIN -2.0
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#define XMAX 2.0 /* x interval */
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#define YMIN -1.125
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#define YMAX 1.125 /* y interval */
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#define NSTEPS 1600
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#define TIME 400
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#define DPHI 0.00003
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#define LPART 0.001
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#define NCOLORS 10
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#define SLEEP1 1 /* initial sleeping time */
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#define SLEEP2 100000 /* final sleeping time */
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```
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### 7 April 21 - Droplet in a stadium-shaped billiard ###
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**Program:** `xxx.c`
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**Initial condition in function `animation()`:** `xxx`
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```
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```
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### 6 April 21 - Drop in a circular water bowl ###
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**Program:** `xxx.c`
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**Initial condition in function `animation()`:** `xxx`
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```
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```
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### 6 April 21 - Drop in a circular water bowl ###
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**Program:** `xxx.c`
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**Initial condition in function `animation()`:** `xxx`
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```
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```
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### 4 April 21 - Billiard in a circle (long version) ###
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**Program:** `vid_circle_new.c` (Longer version of old 2012 code)
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```
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#define NPART 500 /* number of particles */
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#define LAMBDA 0.0 /* aspect ratio of ellipse */
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#define MU 2.0 /* Larmor radius for billiard in magnetic field */
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#define XMIN -2.0
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#define XMAX 2.0 /* x interval */
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#define YMIN -1.125
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#define YMAX 1.125 /* y interval */
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#define NSTEPS 3200
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#define TIME 400
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#define DPHI 0.0001
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#define LPART 0.05
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#define SLEEP1 1 /* initial sleeping time */
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#define SLEEP2 100000 /* final sleeping time */
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```
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