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#ifndef lint |
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static const char RCSid[] = "$Id: noise3.c,v 2.10 2006/03/02 17:16:56 greg Exp $"; |
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#endif |
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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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|
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#include "copyright.h" |
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|
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#include <math.h> |
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|
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#include "calcomp.h" |
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#include "func.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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|
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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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|
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#define hpoly1(t) ((2.0*t-3.0)*t*t+1.0) |
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#define hpoly2(t) (-2.0*t+3.0)*t*t |
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#define hpoly3(t) ((t-2.0)*t+1.0)*t |
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#define hpoly4(t) (t-1.0)*t*t |
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|
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#define hermite(p0,p1,r0,r1,t) ( p0*hpoly1(t) + \ |
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p1*hpoly2(t) + \ |
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r0*hpoly3(t) + \ |
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r1*hpoly4(t) ) |
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|
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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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static char hermite_name[] = "hermite"; |
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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 .001 /* 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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static double l_noise3(char *nam); |
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static double l_hermite(char *nm); |
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static double * noise3(double xnew[3]); |
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static void interpolate(double f[4], int i, int n); |
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static double frand(long s); |
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static double fnoise3(double p[3]); |
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|
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|
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static double |
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l_noise3( /* compute a noise function */ |
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register char *nam |
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) |
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{ |
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register int i; |
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double x[3]; |
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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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/* 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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|
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|
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static double |
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l_hermite(char *nm) /* library call for hermite interpolation */ |
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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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extern void |
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setnoisefuncs(void) /* add noise functions to library */ |
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{ |
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register int i; |
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|
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funset(hermite_name, 5, ':', l_hermite); |
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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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|
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|
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static double * |
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noise3( /* compute the noise function */ |
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register double xnew[3] |
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) |
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{ |
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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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|
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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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} |
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|
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|
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static void |
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interpolate( |
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double f[4], |
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register int i, |
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register int n |
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) |
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{ |
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double f0[4], f1[4], hp1, hp2; |
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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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hp1 = hpoly1(xarg[n]); hp2 = hpoly2(xarg[n]); |
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f[A] = f0[A]*hp1 + f1[A]*hp2; |
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f[B] = f0[B]*hp1 + f1[B]*hp2; |
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f[C] = f0[C]*hp1 + f1[C]*hp2; |
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f[D] = f0[D]*hp1 + f1[D]*hp2 + |
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f0[n]*hpoly3(xarg[n]) + f1[n]*hpoly4(xarg[n]); |
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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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frand( /* get random number from seed */ |
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register long s |
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) |
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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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static double |
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fnoise3( /* compute fractal noise function */ |
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double p[3] |
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) |
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{ |
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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 long s; |
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register 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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} |
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for (j = 0; j < 8; j++) { |
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for (i = 0; i < 3; i++) { |
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v[i] = beg[i]; |
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if (j & 1<<i) |
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v[i] += s; |
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} |
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fval[j] = frand3(v[0],v[1],v[2]); |
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} |
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/* compute fractal */ |
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for ( ; ; ) { |
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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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if (t[i] > v[i]) { |
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branch |= 1<<i; |
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} |
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} |
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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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if (branch & 1<<i) |
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v[i] += s; |
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else |
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v[i] -= s; |
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fc = 0.0; |
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for (j = 0; j < 8; j++) |
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if (~(j^branch) & 1<<i) |
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fc += fval[j]; |
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fc = 0.25*fc + s*EPSILON*frand3(v[0],v[1],v[2]); |
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fval[~(branch^1<<i) & 7] = fc; |
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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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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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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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v[j] -= s; |
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fc = fval[branch & ~(1<<i)]; |
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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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if ((j = i+1) == 3) j = 0; |
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v[j] = beg[j] + s; |
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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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} |
