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* 5/19/88 Added fractal noise function |
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*/ |
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#include <math.h> |
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#define A 0 |
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#define B 1 |
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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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#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 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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double *noise3(), noise3coef(), argument(), frand(); |
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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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static char noise_name[4][8] = {"noise3a", "noise3b", "noise3c", "noise3"}; |
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static char fnoise_name[] = "fnoise3"; |
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static char hermite_name[] = "hermite"; |
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double *noise3(), fnoise3(), argument(), frand(); |
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static interpolate(); |
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static long xlim[3][2]; |
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static double xarg[3]; |
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#define EPSILON .0001 /* error allowed in fractal */ |
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#define frand3(x,y,z) frand((long)((12.38*(x)-22.30*(y)-42.63*(z))/EPSILON)) |
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#define frand3(x,y,z) frand(17*(x)+23*(y)+29*(z)) |
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double fnoise3(); |
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double |
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l_noise3() /* compute 3-dimensional noise function */ |
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static double |
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l_noise3(nam) /* compute a noise function */ |
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register char *nam; |
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{ |
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return(noise3coef(D)); |
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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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} |
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double |
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l_noise3a() /* compute x slope of noise function */ |
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l_hermite() /* library call for hermite interpolation */ |
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{ |
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return(noise3coef(A)); |
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double t; |
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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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double |
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l_noise3b() /* compute y slope of noise function */ |
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setnoisefuncs() /* add noise functions to library */ |
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{ |
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return(noise3coef(B)); |
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} |
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register int i; |
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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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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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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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x[0] = argument(1); |
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x[1] = argument(2); |
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x[2] = argument(3); |
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return(fnoise3(x)); |
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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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{ |
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double x[3]; |
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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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return(noise3(x)[coef]); |
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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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{ |
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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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double f[4]; |
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register int i, n; |
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{ |
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double f0[4], f1[4]; |
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double f0[4], f1[4], hp1, hp2; |
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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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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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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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double |
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l_hermite() /* library call for hermite interpolation */ |
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{ |
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double t; |
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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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double |
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fnoise3(p) /* compute fractal noise function */ |
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register double p[3]; |
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double p[3]; |
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{ |
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double floor(); |
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double v[3], beg[3], fval[8], s, fc; |
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int closing, branch; |
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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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for (i = 0; i < 3; i++) |
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beg[i] = floor(p[i]); |
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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] += 1.0; |
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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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s = 1.0; |
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/* compute fractal */ |
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for ( ; ; ) { |
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s *= 0.5; |
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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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closing = 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 (p[i] > v[i]) { |
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if (t[i] > v[i]) { |
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branch |= 1<<i; |
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if (p[i] - v[i] > EPSILON) |
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closing++; |
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} else if (v[i] - p[i] > EPSILON) |
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closing++; |
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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*fc + s*frand3(v[0],v[1],v[2]); |
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if (closing == 0) |
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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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if (branch & 1<<i) |
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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*frand3(v[0],v[1],v[2]); |
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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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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*frand3(v[0],v[1],v[2]); |
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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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v[j] = beg[j] + s; |
