343 lines
16 KiB
C
343 lines
16 KiB
C
/* Global variables and parameters for wave_billiard, heat and schrodinger */
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// #include "hsluv.c"
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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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/* shape of domain */
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#define D_NOTHING 999 /* no boundaries */
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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_EXT_ELLIPSE 199 /* exterior of elliptical domain */
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#define D_EXT_ELLIPSE_CURVED 198 /* exterior of curved elliptical domain */
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#define D_EXT_ELLIPSE_CURVED_BDRY 197 /* exterior of curved elliptical domain, with horizontal boundaries */
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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 D_FLAT 6 /* flat interface */
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#define D_ANNULUS 7 /* annulus */
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#define D_POLYGON 8 /* polygon */
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#define D_YOUNG 9 /* Young diffraction slits */
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#define D_GRATING 10 /* diffraction grating */
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#define D_EHRENFEST 11 /* Ehrenfest urn type geometry */
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/* The following 3 types are superseded by D_CIRCLES and can be removed later */
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#define D_DISK_GRID 12 /* grid of disks */
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#define D_DISK_HEX 13 /* haxagonl grid of disks */
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#define D_DISK_PERCOL 14 /* random grid of percolation type */
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#define D_MENGER 15 /* Menger-Sierpinski carpet */
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#define D_JULIA_INT 16 /* interior of Julia set */
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#define D_MENGER_ROTATED 17 /* rotated Menger-Sierpinski carpet */
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#define D_PARABOLA 18 /* parabolic domain */
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#define D_TWO_PARABOLAS 19 /* two facing parabolic antennas */
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#define D_CIRCLES 20 /* several circles */
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#define D_CIRCLES_IN_RECT 201 /* several circles in a rectangle */
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#define D_FOUR_PARABOLAS 31 /* four parabolas with axes in NSEW directions */
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#define D_POLY_PARABOLAS 32 /* polygon with parabolic sides */
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#define D_PENROSE 33 /* Penrose unilluminable room */
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#define D_HYPERBOLA 34 /* one branch of hyperbola */
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#define D_TOKARSKY 35 /* Tokarsky unilluminable room */
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#define D_TOKA_PRIME 36 /* Tokarsky room made of 86 triangles */
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#define D_ISOSPECTRAL 37 /* isospectral billiards */
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#define D_HOMOPHONIC 38 /* homophonic billiards */
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#define D_POLYGONS 40 /* several polygons */
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#define D_VONKOCH 41 /* von Koch snowflake fractal */
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#define D_STAR 42 /* star shape */
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#define D_FRESNEL 43 /* Fresnel lens */
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#define D_NOISEPANEL 44 /* zigzag noise insulating panel */
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#define D_NOISEPANEL_RECT 441 /* comparison between zigzag noise insulating panel and flat walls */
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#define D_DOUBLE_FRESNEL 45 /* two facing Fresnel lenses */
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#define D_QRD 46 /* quadratic resonance diffuser */
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#define D_QRD_ASYM 461 /* asymmetric quadratic resonance diffuser */
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#define D_CIRCLE_SEGMENT 47 /* lens-shaped circular segment */
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#define D_GROOVE 48 /* groove array supposed to induce polaritons */
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#define D_FABRY_PEROT 49 /* Fabry-Perrot cavity (in fact simply a vertical slab) */
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#define D_LSHAPE 50 /* L-shaped billiard (surface of genus 2) */
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#define D_WAVEGUIDE 51 /* wave guide */
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#define D_WAVEGUIDE_W 52 /* W-shaped wave guide */
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#define D_MAZE 53 /* maze */
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#define D_MAZE_CLOSED 54 /* closed maze */
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#define D_MAZE_CHANNELS 541 /* maze with two channels attached */
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#define D_CHESSBOARD 55 /* chess board configuration */
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#define D_TRIANGLE_TILES 56 /* triangular tiling */
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#define D_HEX_TILES 57 /* honeycomb tiling */
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#define D_FUNNELS 58 /* two funnels */
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#define D_ONE_FUNNEL 581 /* one funnel */
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#define D_LENSES_RING 59 /* several lenses forming a ring */
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#define D_MAZE_CIRCULAR 60 /* circular maze */
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#define D_WING 70 /* complement of wing-shaped domain */
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#define D_TESLA 71 /* Tesla valve */
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#define D_TESLA_FOUR 72 /* four Tesla valves */
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#define NMAXCIRCLES 10000 /* total number of circles/polygons (must be at least NCX*NCY for square grid) */
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#define NMAXPOLY 50000 /* maximal number of vertices of polygonal lines (for von Koch et al) */
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#define C_SQUARE 0 /* square grid of circles */
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#define C_HEX 1 /* hexagonal/triangular grid of circles */
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#define C_RAND_DISPLACED 2 /* randomly displaced square grid */
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#define C_RAND_PERCOL 3 /* random percolation arrangement */
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#define C_RAND_POISSON 4 /* random Poisson point process */
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#define C_CLOAK 5 /* invisibility cloak */
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#define C_CLOAK_A 6 /* first optimized invisibility cloak */
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#define C_LASER 7 /* laser fight in a room of mirrors */
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#define C_POISSON_DISC 8 /* Poisson disc sampling */
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#define C_GOLDEN_MEAN 10 /* pattern based on vertical shifts by golden mean */
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#define C_GOLDEN_SPIRAL 11 /* spiral pattern based on golden mean */
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#define C_SQUARE_HEX 12 /* alternating between square and hexagonal/triangular */
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#define C_HEX_NONUNIF 13 /* triangular grid with non-constant column distance */
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#define C_RINGS 20 /* obstacles arranged in concentric rings */
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#define C_RINGS_T 201 /* obstacles arranged in concentric rings, triangular lattice */
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#define C_RINGS_SPIRAL 202 /* obstacles arranged on a "subflower" spiral, similar to C_GOLDEN_SPIRAL */
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#define C_ONE 97 /* one single circle, as for Sinai */
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#define C_TWO 98 /* two concentric circles of different type */
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#define C_NOTHING 99 /* no circle at all, for comparisons */
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/* Billiard tables for heat equation */
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#define D_ANNULUS_HEATED 21 /* annulus with different temperatures */
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#define D_MENGER_HEATED 22 /* Menger gasket with different temperatures */
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#define D_MENGER_H_OPEN 23 /* Menger gasket with different temperatures and larger domain */
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#define D_MANDELBROT 24 /* Mandelbrot set */
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#define D_JULIA 25 /* Julia set */
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#define D_MANDELBROT_CIRCLE 26 /* Mandelbrot set with circular conductor */
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#define D_VONKOCH_HEATED 27 /* von Koch snowflake in larger circle */
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/* Variable index of refraction */
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#define IOR_MANDELBROT 1 /* index of refraction depends on escape time in Mandelbrot set (log) */
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#define IOR_MANDELBROT_LIN 100 /* index of refraction depends on escape time in Mandelbrot set (linear) */
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#define IOR_MANDELBROT_MOD 101 /* index of refraction depends on escape time in Mandelbrot set (linear) */
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#define IOR_EARTH 2 /* index of refraction models speed of seismic waves */
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#define IOR_EXPLO_LENSING 3 /* explosive lensing */
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#define IOR_PERIODIC_WELLS 4 /* periodic superposition of "wells" */
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#define IOR_RANDOM_WELLS 5 /* random superposition of "wells" */
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#define IOR_PERIODIC_WELLS_ROTATING 6 /* periodic superposition rotating in time */
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#define IOR_PERIODIC_WELLS_ROTATING_LARGE 7 /* periodic superposition rotating in time, larger area */
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/* Boundary conditions */
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#define BC_DIRICHLET 0 /* Dirichlet boundary conditions */
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#define BC_PERIODIC 1 /* periodic boundary conditions */
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#define BC_ABSORBING 2 /* absorbing boundary conditions (beta version) */
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#define BC_VPER_HABS 3 /* vertically periodic and horizontally absorbing boundary conditions */
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#define BC_ABS_REFLECT 4 /* absorbing boundary conditions, except reflecting at y=0, for comparisons */
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#define BC_LSHAPE 10 /* L-shaped boundary conditions (surface of genus 2) */
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// #define BC_OSCILL_ABSORB 5 /* oscillating boundary condition on the left, absorbing on other walls */
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/* Oscillating boundary conditions */
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#define OSC_PERIODIC 0 /* periodic oscillation */
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#define OSC_SLOWING 1 /* oscillation of slowing frequency (anti-chirp) */
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#define OSC_WAVE_PACKET 2 /* Gaussian wave packet */
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#define OSC_CHIRP 3 /* chirp (linearly accelerating frequency) */
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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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/* Plot types */
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/* For wave equation */
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#define P_AMPLITUDE 0 /* plot amplitude of wave */
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#define P_ENERGY 1 /* plot energy of wave */
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#define P_MIXED 2 /* plot amplitude in upper half, energy in lower half */
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#define P_MEAN_ENERGY 3 /* energy averaged over time */
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#define P_LOG_ENERGY 4 /* log of energy averaged over time */
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#define P_LOG_MEAN_ENERGY 5 /* log of energy averaged over time */
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#define P_ENERGY_FLUX 6 /* energy flux */
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#define P_TOTAL_ENERGY_FLUX 7 /* energy flux averaged over time */
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/* For Schrodinger equation */
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#define P_MODULE 10 /* plot module of wave function squared */
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#define P_PHASE 11 /* plot phase of wave function */
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#define P_REAL 12 /* plot real part */
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#define P_IMAGINARY 13 /* plot imaginary part */
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/* Color schemes */
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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 C_PHASE 2 /* color scheme shows phase */
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#define C_ONEDIM 3 /* use preset 1d color scheme (for Turbo, Viridis, Magma, Inferno, Plasma) */
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#define C_ONEDIM_LINEAR 4 /* use preset 1d color scheme with linear scale */
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/* Color palettes */
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#define COL_JET 0 /* JET color palette */
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#define COL_HSLUV 1 /* HSLUV color palette (perceptually uniform) */
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#define COL_GRAY 2 /* grayscale */
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#define COL_TURBO 10 /* TURBO color palette (by Anton Mikhailov) */
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#define COL_VIRIDIS 11 /* Viridis color palette */
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#define COL_MAGMA 12 /* Magma color palette */
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#define COL_INFERNO 13 /* Inferno color palette */
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#define COL_PLASMA 14 /* Plasma color palette */
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#define COL_CIVIDIS 15 /* Cividis color palette */
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#define COL_PARULA 16 /* Parula color palette */
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#define COL_TWILIGHT 17 /* Twilight color palette */
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#define COL_TWILIGHT_SHIFTED 18 /* Shifted twilight color palette */
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#define COL_TURBO_CYCLIC 101 /* TURBO color palette (by Anton Mikhailov) corrected to be cyclic, beta */
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#define NPWIDTH 0.02 /* width of noise panel separation */
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/* plot types used by rde */
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#define Z_AMPLITUDE 0 /* amplitude of first field */
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#define Z_RGB 20 /* RGB plot */
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#define Z_POLAR 21 /* polar angle associated with RBG plot */
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#define Z_NORM_GRADIENT 22 /* gradient of polar angle */
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#define Z_ANGLE_GRADIENT 221 /* direction of polar angle */
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#define Z_NORM_GRADIENTX 23 /* norm of gradient of u */
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#define Z_ANGLE_GRADIENTX 231 /* direction of gradient of u */
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#define Z_NORM_GRADIENT_INTENSITY 24 /* gradient and intensity of polar angle */
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#define Z_VORTICITY 25 /* curl of polar angle */
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#define Z_VORTICITY_ABS 251 /* absolute value of curl of polar angle */
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/* for Schrodinger equation */
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#define Z_MODULE 30 /* module squared of first two fields */
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#define Z_ARGUMENT 31 /* argument of first two fields, with luminosity depending on module */
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#define Z_REALPART 32 /* first field, with luminosity depending on module */
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/* for RPSLZ equation */
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#define Z_MAXTYPE_RPSLZ 40 /* color of type with maximal density */
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#define Z_THETA_RPSLZ 41 /* polar angle */
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#define Z_NORM_GRADIENT_RPSLZ 42 /* gradient of polar angle */
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/* for Euler incompressible Euler equation */
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#define Z_EULER_VORTICITY 50 /* vorticity of velocity */
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#define Z_EULER_LOG_VORTICITY 51 /* log of vorticity of velocity */
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#define Z_EULER_VORTICITY_ASYM 52 /* vorticity of velocity */
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#define Z_EULER_LPRESSURE 53 /* Laplacian of pressure */
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#define Z_EULER_PRESSURE 54 /* pressure */
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/* for Euler compressible Euler equation */
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#define Z_EULER_DENSITY 60 /* density */
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#define Z_EULER_SPEED 61 /* norm of velocity */
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#define Z_EULERC_VORTICITY 62 /* vorticity of velocity */
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#define Z_EULER_DIRECTION 63 /* direction of velocity */
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#define Z_EULER_DIRECTION_SPEED 64 /* hut for direction of velocity, luminosity for speed */
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/* special boundary conditions for Euler equation */
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#define BCE_TOPBOTTOM 1 /* special flow at top and bottom */
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#define BCE_TOPBOTTOMLEFT 2 /* special flow at top, bottom and left side */
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#define BCE_CHANNELS 3 /* special flow in channels at left and right */
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#define BCE_MIDDLE_STRIP 4 /* special flow in horizontal strip in the middle */
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#define BCE_LEFT 5 /* special flow at left side */
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#define BCE_FOUR_CHANNELS 6 /* special flow in four channels at left and right */
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/* flow types for boundary conditions in Euler equation */
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#define BCF_LAMINAR 0 /* laminar flow */
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#define BCF_PRESSURE 1 /* laminar flow with pressure gradient */
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typedef struct
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{
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double xc, yc, radius; /* center and radius of circle */
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short int active, top; /* circle is active, circle is in top half */
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} t_circle;
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typedef struct
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{
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double xc, yc, radius, angle; /* center, radius and angle of polygon */
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int nsides; /* number of sides of polygon */
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short int active, top; /* polygon is active, polygon is in top half */
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} t_polygon;
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typedef struct
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{
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double x, y; /* (x,y) coordinates of vertex */
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double posi, posj; /* (i,j) coordinates of vertex */
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} t_vertex;
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typedef struct
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{
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double x1, y1, x2, y2; /* (x,y) coordinates of vertices */
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double posi1, posj1, posi2, posj2; /* (i,j) coordinates of vertices */
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} t_rectangle;
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typedef struct
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{
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double x1, y1, x2, y2; /* (x,y) coordinates of long symmetry axis */
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double width; /* width of rectangle */
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double posi1, posj1, posi2, posj2; /* (i,j) coordinates of vertices */
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double posi3, posj3, posi4, posj4; /* (i,j) coordinates of vertices */
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} t_rect_rotated;
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typedef struct
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{
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double xc, yc; /* (x,y) coordinates of center */
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double r, width; /* radius and width of arc */
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double angle1, dangle; /* start angle and angular width */
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double posi1, posj1; /* (i,j) coordinates of center */
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// double posi3, posj3, posi4, posj4; /* (i,j) coordinates of vertices */
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} t_arc;
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typedef struct
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{
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int nneighb; /* number of neighbours to compute Laplacian */
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double *nghb[4]; /* pointers to neighbours */
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} t_laplacian;
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typedef struct
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{
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double xc, yc; /* (x,y) coordinates of center */
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int ix, iy; /* lattice coordinates of center */
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double period, amp; /* period and amplitude */
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double phase; /* phase shift */
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double var_envelope; /* variance of Gaussian envelope */
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int time_shift; /* time shift */
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} t_wave_packet;
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typedef struct
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{
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double xc, yc; /* (x,y) coordinates of center */
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double phase; /* phase of source */
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double amp; /* amplitude */
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int sign;
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} t_wave_source;
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int ncircles = NMAXCIRCLES; /* actual number of circles, can be decreased e.g. for random patterns */
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int npolyline = NMAXPOLY; /* actual length of polyline */
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int npolyrect = NMAXPOLY; /* actual number of polyrect */
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int npolyrect_rot = NMAXPOLY; /* actual number of rotated polyrect */
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int npolyarc = NMAXPOLY; /* actual number of arcs */
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t_circle circles[NMAXCIRCLES]; /* circular scatterers */
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t_polygon polygons[NMAXCIRCLES]; /* polygonal scatterers */
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t_vertex polyline[NMAXPOLY]; /* vertices of polygonal line */
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t_rectangle polyrect[NMAXPOLY]; /* vertices of rectangles */
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t_rect_rotated polyrectrot[NMAXPOLY]; /* data of rotated rectangles */
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t_arc polyarc[NMAXPOLY]; /* data of arcs */
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/* the same for comparisons between different domains */
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int ncircles_b = NMAXCIRCLES; /* actual number of circles, can be decreased e.g. for random patterns */
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int npolyline_b = NMAXPOLY; /* actual length of polyline */
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t_circle circles_b[NMAXCIRCLES]; /* circular scatterers */
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t_polygon polygons_b[NMAXCIRCLES]; /* polygonal scatterers */
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t_vertex polyline_b[NMAXPOLY]; /* vertices of polygonal line */
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// double julia_x = -0.5, julia_y = 0.5; /* parameters for Julia sets */
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// double julia_x = 0.33267, julia_y = 0.06395; /* parameters for Julia sets */
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double julia_x = 0.37468, julia_y = 0.21115; /* parameters for Julia sets */
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