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/* Copyright (c) 1988 Regents of the University of California */ |
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#ifndef lint |
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static char SCCSid[] = "$SunId$ LBL"; |
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static const char RCSid[] = "$Id$"; |
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#endif |
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|
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/* |
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* noise3.c - noise functions for random textures. |
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* |
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* Credit for the smooth algorithm goes to Ken Perlin. |
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* (ref. SIGGRAPH Vol 19, No 3, pp 287-96) |
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* |
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* 4/15/86 |
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* 5/19/88 Added fractal noise function |
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* Credit for the smooth algorithm goes to Ken Perlin, and code |
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* translation/implementation to Rahul Narain. |
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* (ref. Improving Noise, Computer Graphics; Vol. 35 No. 3., 2002) |
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*/ |
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#include "copyright.h" |
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|
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#define A 0 |
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#define B 1 |
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#define C 2 |
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#define D 3 |
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#include "ray.h" |
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#include "func.h" |
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|
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#define rand3a(x,y,z) frand(67*(x)+59*(y)+71*(z)) |
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#define rand3b(x,y,z) frand(73*(x)+79*(y)+83*(z)) |
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#define rand3c(x,y,z) frand(89*(x)+97*(y)+101*(z)) |
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#define rand3d(x,y,z) frand(103*(x)+107*(y)+109*(z)) |
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static char noise_name[4][8] = {"noise3x", "noise3y", "noise3z", "noise3"}; |
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static char fnoise_name[] = "fnoise3"; |
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|
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#define hermite(p0,p1,r0,r1,t) ( p0*((2.0*t-3.0)*t*t+1.0) + \ |
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p1*(-2.0*t+3.0)*t*t + \ |
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r0*((t-2.0)*t+1.0)*t + \ |
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r1*(t-1.0)*t*t ) |
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#define EPSILON .0005 /* error allowed in fractal */ |
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|
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double *noise3(), noise3coef(), argument(), frand(); |
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|
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static long xlim[3][2]; |
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static double xarg[3]; |
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|
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#define EPSILON .0001 /* error allowed in fractal */ |
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|
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#define frand3(x,y,z) frand(17*(x)+23*(y)+29*(z)) |
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|
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double fnoise3(); |
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static double l_noise3(char *nam); |
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static double noise3(double xnew[3], int i); |
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static double noise3partial(double f3, double x[3], int i); |
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static double perlin_noise (double x, double y, double z); |
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static double frand(long s); |
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static double fnoise3(double x[3]); |
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|
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double |
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l_noise3() /* compute 3-dimensional noise function */ |
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{ |
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return(noise3coef(D)); |
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} |
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|
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|
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double |
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l_noise3a() /* compute x slope of noise function */ |
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{ |
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return(noise3coef(A)); |
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} |
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|
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|
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double |
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l_noise3b() /* compute y slope of noise function */ |
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{ |
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return(noise3coef(B)); |
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} |
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|
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|
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double |
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l_noise3c() /* compute z slope of noise function */ |
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{ |
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return(noise3coef(C)); |
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} |
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|
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|
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double |
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l_fnoise3() /* compute fractal noise function */ |
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{ |
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double x[3]; |
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|
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x[0] = argument(1); |
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x[1] = argument(2); |
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x[2] = argument(3); |
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|
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return(fnoise3(x)); |
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} |
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|
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|
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static double |
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noise3coef(coef) /* return coefficient of noise function */ |
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int coef; |
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l_noise3( /* compute a noise function */ |
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char *nam |
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) |
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{ |
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int i; |
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double x[3]; |
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|
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/* get point */ |
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x[0] = argument(1); |
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x[1] = argument(2); |
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x[2] = argument(3); |
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|
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return(noise3(x)[coef]); |
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/* make appropriate call */ |
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if (nam == fnoise_name) |
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return(fnoise3(x)); |
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i = 4; |
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while (i--) |
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if (nam == noise_name[i]) |
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return(noise3(x,i)); |
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eputs(nam); |
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eputs(": called l_noise3!\n"); |
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quit(1); |
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return 1; /* pro forma return */ |
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} |
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double * |
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noise3(xnew) /* compute the noise function */ |
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register double xnew[3]; |
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void |
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setnoisefuncs(void) /* add noise functions to library */ |
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{ |
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extern double floor(); |
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static double x[3] = {-100000.0, -100000.0, -100000.0}; |
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static double f[4]; |
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int i; |
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|
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if (x[0]==xnew[0] && x[1]==xnew[1] && x[2]==xnew[2]) |
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return(f); |
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x[0] = xnew[0]; x[1] = xnew[1]; x[2] = xnew[2]; |
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xlim[0][0] = floor(x[0]); xlim[0][1] = xlim[0][0] + 1; |
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xlim[1][0] = floor(x[1]); xlim[1][1] = xlim[1][0] + 1; |
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xlim[2][0] = floor(x[2]); xlim[2][1] = xlim[2][0] + 1; |
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xarg[0] = x[0] - xlim[0][0]; |
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xarg[1] = x[1] - xlim[1][0]; |
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xarg[2] = x[2] - xlim[2][0]; |
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interpolate(f, 0, 3); |
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return(f); |
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funset(fnoise_name, 3, ':', l_noise3); |
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i = 4; |
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while (i--) |
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funset(noise_name[i], 3, ':', l_noise3); |
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} |
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static |
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interpolate(f, i, n) |
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double f[4]; |
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register int i, n; |
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static double |
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frand( /* get random number from seed */ |
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long s |
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) |
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{ |
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double f0[4], f1[4]; |
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|
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if (n == 0) { |
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f[A] = rand3a(xlim[0][i&1],xlim[1][i>>1&1],xlim[2][i>>2]); |
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f[B] = rand3b(xlim[0][i&1],xlim[1][i>>1&1],xlim[2][i>>2]); |
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f[C] = rand3c(xlim[0][i&1],xlim[1][i>>1&1],xlim[2][i>>2]); |
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f[D] = rand3d(xlim[0][i&1],xlim[1][i>>1&1],xlim[2][i>>2]); |
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} else { |
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n--; |
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interpolate(f0, i, n); |
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interpolate(f1, i | 1<<n, n); |
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f[A] = (1.0-xarg[n])*f0[A] + xarg[n]*f1[A]; |
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f[B] = (1.0-xarg[n])*f0[B] + xarg[n]*f1[B]; |
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f[C] = (1.0-xarg[n])*f0[C] + xarg[n]*f1[C]; |
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f[D] = hermite(f0[D], f1[D], f0[n], f1[n], xarg[n]); |
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} |
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} |
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|
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|
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double |
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frand(s) /* get random number from seed */ |
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register long s; |
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{ |
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s = s<<13 ^ s; |
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return(1.0-((s*(s*s*15731+789221)+1376312589)&0x7fffffff)/1073741824.0); |
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} |
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|
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|
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double |
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l_hermite() /* library call for hermite interpolation */ |
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static double |
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fnoise3( /* compute fractal noise function */ |
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double x[3] |
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) |
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{ |
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double t; |
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|
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t = argument(5); |
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return( hermite(argument(1), argument(2), |
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argument(3), argument(4), t) ); |
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} |
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|
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|
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double |
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fnoise3(p) /* compute fractal noise function */ |
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double p[3]; |
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{ |
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double floor(); |
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long t[3], v[3], beg[3], s; |
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long t[3], v[3], beg[3]; |
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double fval[8], fc; |
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int branch; |
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register int i, j; |
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long s; |
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int i, j; |
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/* get starting cube */ |
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s = (long)(1.0/EPSILON); |
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for (i = 0; i < 3; i++) { |
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t[i] = s*p[i]; |
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beg[i] = s*floor(p[i]); |
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t[i] = s*x[i]; |
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beg[i] = s*floor(x[i]); |
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} |
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for (j = 0; j < 8; j++) { |
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for (i = 0; i < 3; i++) { |
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} |
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/* compute fractal */ |
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for ( ; ; ) { |
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s >>= 1; |
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fc = 0.0; |
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for (j = 0; j < 8; j++) |
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fc += fval[j]; |
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fc *= 0.125; |
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if ((s >>= 1) == 0) |
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return(fc); /* close enough */ |
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branch = 0; |
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for (i = 0; i < 3; i++) { /* do center */ |
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v[i] = beg[i] + s; |
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branch |= 1<<i; |
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} |
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} |
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fc = 0.0; |
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for (j = 0; j < 8; j++) |
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fc += fval[j]; |
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fc *= 0.125; |
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if (s < 1) |
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return(fc); /* close enough */ |
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fc += s*EPSILON*frand3(v[0],v[1],v[2]); |
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fval[~branch & 7] = fc; |
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for (i = 0; i < 3; i++) { /* do faces */ |
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v[i] = beg[i] + s; |
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} |
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for (i = 0; i < 3; i++) { /* do edges */ |
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j = (i+1)%3; |
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if ((j = i+1) == 3) j = 0; |
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if (branch & 1<<j) |
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v[j] += s; |
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else |
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v[j] -= s; |
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j = (i+2)%3; |
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> |
if (++j == 3) j = 0; |
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if (branch & 1<<j) |
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v[j] += s; |
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else |
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fc += fval[branch | 1<<i]; |
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fc = 0.5*fc + s*EPSILON*frand3(v[0],v[1],v[2]); |
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fval[branch^1<<i] = fc; |
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j = (i+1)%3; |
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> |
if ((j = i+1) == 3) j = 0; |
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v[j] = beg[j] + s; |
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j = (i+2)%3; |
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> |
if (++j == 3) j = 0; |
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v[j] = beg[j] + s; |
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} |
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for (i = 0; i < 3; i++) /* new cube */ |
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if (branch & 1<<i) |
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beg[i] += s; |
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} |
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} |
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|
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|
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static double |
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noise3( /* compute the revised Perlin noise function */ |
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double xnew[3], int i |
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) |
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{ |
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static int gotV; |
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static double x[3]; |
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static double f[4]; |
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|
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if (!gotV || xnew[0] != x[0] || (xnew[1] != x[1]) | (xnew[2] != x[2])) { |
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f[3] = perlin_noise(x[0]=xnew[0], x[1]=xnew[1], x[2]=xnew[2]); |
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gotV = 0x8; |
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} |
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if (!(gotV>>i & 1)) { |
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f[i] = noise3partial(f[3], x, i); |
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gotV |= 1<<i; |
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} |
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return(f[i]); |
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} |
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+ |
|
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static double |
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+ |
noise3partial( /* compute partial derivative for ith coordinate */ |
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double f3, double x[3], int i |
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) |
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{ |
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double fc; |
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|
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switch (i) { |
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case 0: |
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fc = perlin_noise(x[0]-EPSILON, x[1], x[2]); |
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break; |
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case 1: |
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fc = perlin_noise(x[0], x[1]-EPSILON, x[2]); |
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break; |
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case 2: |
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fc = perlin_noise(x[0], x[1], x[2]-EPSILON); |
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break; |
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default: |
| 198 |
+ |
return(.0); |
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+ |
} |
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return((f3 - fc)/EPSILON); |
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} |
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|
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#define fade(t) ((t)*(t)*(t)*((t)*((t)*6. - 15.) + 10.)) |
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|
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static double lerp(double t, double a, double b) {return a + t*(b - a);} |
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|
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static double |
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grad(int hash, double x, double y, double z) |
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{ |
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int h = hash & 15; // CONVERT LO 4 BITS OF HASH CODE |
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double u = h<8 ? x : y, // INTO 12 GRADIENT DIRECTIONS. |
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v = h<4 ? y : h==12|h==14 ? x : z; |
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return (!(h&1) ? u : -u) + (!(h&2) ? v : -v); |
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+ |
} |
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+ |
|
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+ |
static const int permutation[256] = {151,160,137,91,90,15, |
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131,13,201,95,96,53,194,233,7,225,140,36,103,30,69,142,8,99,37,240,21,10,23, |
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+ |
190, 6,148,247,120,234,75,0,26,197,62,94,252,219,203,117,35,11,32,57,177,33, |
| 219 |
+ |
88,237,149,56,87,174,20,125,136,171,168, 68,175,74,165,71,134,139,48,27,166, |
| 220 |
+ |
77,146,158,231,83,111,229,122,60,211,133,230,220,105,92,41,55,46,245,40,244, |
| 221 |
+ |
102,143,54, 65,25,63,161, 1,216,80,73,209,76,132,187,208, 89,18,169,200,196, |
| 222 |
+ |
135,130,116,188,159,86,164,100,109,198,173,186, 3,64,52,217,226,250,124,123, |
| 223 |
+ |
5,202,38,147,118,126,255,82,85,212,207,206,59,227,47,16,58,17,182,189,28,42, |
| 224 |
+ |
223,183,170,213,119,248,152, 2,44,154,163, 70,221,153,101,155,167, 43,172,9, |
| 225 |
+ |
129,22,39,253, 19,98,108,110,79,113,224,232,178,185, 112,104,218,246,97,228, |
| 226 |
+ |
251,34,242,193,238,210,144,12,191,179,162,241, 81,51,145,235,249,14,239,107, |
| 227 |
+ |
49,192,214, 31,181,199,106,157,184, 84,204,176,115,121,50,45,127, 4,150,254, |
| 228 |
+ |
138,236,205,93,222,114,67,29,24,72,243,141,128,195,78,66,215,61,156,180 |
| 229 |
+ |
}; |
| 230 |
+ |
|
| 231 |
+ |
#define p(i) permutation[(i)&0xff] |
| 232 |
+ |
|
| 233 |
+ |
static double |
| 234 |
+ |
perlin_noise(double x, double y, double z) |
| 235 |
+ |
{ |
| 236 |
+ |
int X, Y, Z; |
| 237 |
+ |
double u, v, w; |
| 238 |
+ |
int A, AA, AB, B, BA, BB; |
| 239 |
+ |
|
| 240 |
+ |
X = (int)x-(x<0); // FIND UNIT CUBE THAT |
| 241 |
+ |
Y = (int)y-(y<0); // CONTAINS POINT. |
| 242 |
+ |
Z = (int)z-(z<0); |
| 243 |
+ |
x -= (double)X; // FIND RELATIVE X,Y,Z |
| 244 |
+ |
y -= (double)Y; // OF POINT IN CUBE. |
| 245 |
+ |
z -= (double)Z; |
| 246 |
+ |
X &= 0xff; Y &= 0xff; Z &= 0xff; |
| 247 |
+ |
|
| 248 |
+ |
u = fade(x); // COMPUTE FADE CURVES |
| 249 |
+ |
v = fade(y); // FOR EACH OF X,Y,Z. |
| 250 |
+ |
w = fade(z); |
| 251 |
+ |
|
| 252 |
+ |
A = p(X )+Y; AA = p(A)+Z; AB = p(A+1)+Z; // HASH COORDINATES OF |
| 253 |
+ |
B = p(X+1)+Y; BA = p(B)+Z; BB = p(B+1)+Z; // THE 8 CUBE CORNERS, |
| 254 |
+ |
|
| 255 |
+ |
return lerp(w, lerp(v, lerp(u, grad(p(AA ), x , y , z ), // AND ADD |
| 256 |
+ |
grad(p(BA ), x-1, y , z )), // BLENDED |
| 257 |
+ |
lerp(u, grad(p(AB ), x , y-1, z ), // RESULTS |
| 258 |
+ |
grad(p(BB ), x-1, y-1, z ))),// FROM 8 |
| 259 |
+ |
lerp(v, lerp(u, grad(p(AA+1), x , y , z-1), // CORNERS |
| 260 |
+ |
grad(p(BA+1), x-1, y , z-1)), // OF CUBE |
| 261 |
+ |
lerp(u, grad(p(AB+1), x , y-1, z-1), |
| 262 |
+ |
grad(p(BB+1), x-1, y-1, z-1)))); |
| 263 |
|
} |
