--- deliantra/server/common/noise.C 2011/04/23 06:35:55 1.7 +++ deliantra/server/common/noise.C 2011/04/26 03:18:06 1.8 @@ -24,9 +24,77 @@ ///////////////////////////////////////////////////////////////////////////// +// perl -e 'for(0..255) { $p = (atan2 1,0) / 64 * $_; printf " %10g, %10g,\n", sin $p, cos $p }' | sort -R +static const float charges2[256][2] = { + -.975702, -.219101, .893224, .449611, .870087, -.492898, .595699, -.803208, + .14673, .989177, .995185, .0980171, .91421, -.405241, -.514103, .857729, + -.985278, -.170962, -.689541, -.724247, -.427555, .903989, .83147, -.55557, + .999699, -.0245412, .634393, .77301, -.514103, -.857729, -.0735646, -.99729, + .514103, -.857729, -.595699, -.803208, -.290285, .95694, .595699, .803208, + .266713, .963776, -.33689, .941544, .492898, -.870087, -.471397, -.881921, + -.99729, -.0735646, .615232, -.788346, -.91421, -.405241, -.575808, .817585, + .0980171, .995185, -.980785, .19509, -.122411, -.99248, .0735646, .99729, + -.634393, .77301, -.91421, .405241, .99248, .122411, .903989, -.427555, + -.24298, .970031, -.857729, .514103, -.359895, .932993, .382683, .92388, + .740951, -.671559, -.893224, .449611, -.95694, -.290285, -.975702, .219101, + -.970031, .24298, .999699, .0245412, -.405241, .91421, .985278, .170962, + .382683, -.92388, .95694, -.290285, .707107, -.707107, -.817585, -.575808, + -.989177, .14673, -.19509, -.980785, -.359895, -.932993, .313682, .949528, + -.0980171, .995185, 1, 6.12323e-17, .963776, -.266713, .998795, -.0490677, + -.998795, -.0490677, -.970031, -.24298, -.55557, .83147, -.14673, .989177, + -.83147, -.55557, -.995185, -.0980171, .870087, .492898, .941544, -.33689, + .575808, -.817585, .33689, .941544, .19509, -.980785, 0, 1, + .219101, -.975702, -.83147, .55557, .757209, -.653173, -.95694, .290285, + -.266713, .963776, -.0490677, .998795, .405241, .91421, -.405241, -.91421, + -.689541, .724247, -.534998, -.844854, -.99248, -.122411, .724247, .689541, + .492898, .870087, .817585, -.575808, .740951, .671559, -.33689, -.941544, + .95694, .290285, .77301, -.634393, .0245412, -.999699, -.77301, -.634393, + -.382683, .92388, -.24298, -.970031, -.893224, -.449611, .449611, .893224, + .975702, -.219101, -.382683, -.92388, .844854, .534998, -.803208, -.595699, + .941544, .33689, .963776, .266713, .932993, .359895, -.0735646, .99729, + .634393, -.77301, .405241, -.91421, .33689, -.941544, .99729, .0735646, + 1.22465e-16, -1, -.941544, -.33689, .0490677, -.998795, -.313682, .949528, + .92388, .382683, -.999699, .0245412, .0245412, .999699, .653173, .757209, + -.803208, .595699, .980785, -.19509, .817585, .575808, .975702, .219101, + -.615232, -.788346, .99248, -.122411, .998795, .0490677, -.707107, .707107, + .803208, -.595699, .671559, .740951, -.757209, -.653173, -.949528, .313682, + -.989177, -.14673, -.817585, .575808, -.14673, -.989177, -1, -1.83697e-16, + .290285, .95694, -.932993, -.359895, .24298, -.970031, .170962, .985278, + -.671559, -.740951, .427555, .903989, .427555, -.903989, -.941544, .33689, + -.492898, -.870087, -.266713, -.963776, .857729, -.514103, -.724247, .689541, + .724247, -.689541, -.653173, .757209, .689541, -.724247, .949528, -.313682, + -.19509, .980785, -.740951, .671559, -.999699, -.0245412, .689541, .724247, + .803208, .595699, -.170962, .985278, .0735646, -.99729, .970031, -.24298, + -.170962, -.985278, .471397, .881921, .91421, .405241, .893224, -.449611, + .0490677, .998795, -.615232, .788346, -.998795, .0490677, -.427555, -.903989, + -.0245412, .999699, -.534998, .844854, -.313682, -.949528, -.55557, -.83147, + -.903989, -.427555, -.724247, -.689541, -.740951, -.671559, .985278, -.170962, + -.857729, -.514103, -.99729, .0735646, .881921, -.471397, .534998, .844854, + .359895, -.932993, .77301, .634393, .99729, -.0735646, .290285, -.95694, + .575808, .817585, .757209, .653173, .903989, .427555, -.995185, .0980171, + -.903989, .427555, -.844854, .534998, -.707107, -.707107, -.92388, .382683, + -.653173, -.757209, -.881921, -.471397, -.219101, .975702, -.595699, .803208, + .0980171, -.995185, -.788346, .615232, -.0980171, -.995185, -.985278, .170962, + .122411, .99248, -.449611, -.893224, .170962, -.985278, .788346, .615232, + -.492898, .870087, .671559, -.740951, .449611, -.893224, -.757209, .653173, + .83147, .55557, -.290285, -.95694, -.932993, .359895, -.870087, -.492898, + .266713, -.963776, -.881921, .471397, -.77301, .634393, -.471397, .881921, + .844854, -.534998, .707107, .707107, .534998, -.844854, .514103, .857729, + .14673, -.989177, .980785, .19509, -.122411, .99248, -.449611, .893224, + .995185, -.0980171, -.634393, -.77301, .857729, .514103, .55557, .83147, + -.92388, -.382683, -.844854, -.534998, -.963776, .266713, .989177, -.14673, + .313682, -.949528, .359895, .932993, .24298, .970031, -.949528, -.313682, + .932993, -.359895, .55557, -.83147, .615232, .788346, -.788346, -.615232, + -.0245412, -.999699, -.219101, -.975702, .788346, -.615232, -.99248, .122411, + -.671559, .740951, -.870087, .492898, .970031, .24298, .881921, .471397, + .122411, -.99248, .471397, -.881921, .19509, .980785, -.963776, -.266713, + .92388, -.382683, .989177, .14673, -.575808, -.817585, .219101, .975702, + -.0490677, -.998795, -.980785, -.19509, .949528, .313682, .653173, -.757209, +}; + // http://www-wales.ch.cam.ac.uk/~wales/CCD/Thomson/table.html, random permutation // used as gradient vectors for noise3d -static const float charges[256][3] = { +static const float charges3[256][3] = { 6.32096444e-01, -6.11406706e-01, 4.76062943e-01, 5.19172442e-01, 8.08229585e-01, -2.77893708e-01, -8.81072422e-01, -4.68301230e-01, 6.63727731e-02, -1.92122323e-01, 9.81341519e-01, -7.60505942e-03, -2.57478265e-01, 9.34157733e-01, -2.47091628e-01, 8.75501090e-01, -1.48087600e-01, -4.59965112e-01, @@ -192,37 +260,6 @@ { seedable_rand_gen rng (seed); -#if 0 - for (int i = 0; i < 256; ++i) - { - vec2d rv (rng () - 0.5f, rng () - 0.5f); - - // normalise - float mag = 1.f / sqrtf (dot (rv, rv)); - - rv[0] *= mag; - rv[1] *= mag; - - rvec[i] = rv; - } -#endif - -#if 1 - float offset = rng () * M_PI; - - for (int i = 0; i < 256; ++i) - { - float phi = i * (M_PI * 2 / 256) + offset; - - rvec[i][0] = sinf (phi); - rvec[i][1] = -cosf (phi); - } - - // fisher-yates to randomly perturb - for (int i = 256; --i; ) - ::swap (rvec [i], rvec [rng (i + 1)]); -#endif - rvmap[0].seed (rng); rvmap[1].seed (rng); } @@ -250,14 +287,14 @@ float p = (4 * t1 - 3) * t4; - int h = rvmap [0](I[0] + i) ^ rvmap [1](I[1] + j); - vec2d G = rvec [h & 0xff]; + int h = rvmap[0](I[0] + i) ^ rvmap[1](I[1] + j); + vec2d G = charges2[h & 0xff]; v += dot (A, G) * p; } } - return clamp (v, -.9999999f, .9999999f); + return clamp (v, -.9999999, .9999999); } ///////////////////////////////////////////////////////////////////////////// @@ -296,13 +333,13 @@ float p = (4 * t1 - 3) * t4; int h = rvmap[0](I[0] + i) ^ rvmap[1](I[1] + j) ^ rvmap[2](I[2] + k); - const float *G = charges[h & 0xff]; + const float *G = charges3[h & 0xff]; v += dot (A, vec3d (G[0], G[1], G[2])) * p; } } - return clamp (v * 2, -.9999999f, .9999999f); + return clamp (v * 2, -.9999999, .9999999); } vec3d::T_numtype @@ -339,14 +376,14 @@ float p = (4 * t1 - 3) * t4 * (3 * o2 - 2 * o2 * o); int h = rvmap[0](I[0] + i) ^ rvmap[1](I[1] + j) ^ rvmap[2](I[2] + k); - const float *G = charges[h & 0xff]; + const float *G = charges3[h & 0xff]; v += dot (A, vec3d (G[0], G[1], G[2])) * p; } } } - return clamp (v, -.9999999f, .9999999f); + return clamp (v, -.9999999, .9999999); } template class noise_gen; @@ -354,12 +391,16 @@ ///////////////////////////////////////////////////////////////////////////// +// find some uncorrelated spot - we assume that noise 2 units away +// is completely uncorrelated - this is not true for other coordinates, +// but generally works well. template static vec_t ith_octave (vec_t P, int i) { vec_t r = P; r[0] += i; + r[1] += i * 2; return r; } @@ -368,13 +409,14 @@ : h (hurst_expo), lac (lacunarity), noise_gen (0) { value_t exsum = 0; + value_t phi = noise (vec_t (value_t (0))) * 0.5 + 1; for (int i = 0; i < MAX_OCTAVES; ++i) { - ex [i] = powf (lac, -h * i); + ex [i] = pow (lac, -h * i); exsum += ex [i]; - fbm_mul [i] = 0.5f / (exsum * 0.75f); // .75f is a heuristic - rot [i].set (0.4488f * i); + fbm_mul [i] = 0.5 / (exsum * 0.75); // .75 is a heuristic + rot [i].set (phi * i + 1); } } @@ -382,7 +424,7 @@ typename frac_gen::value_t frac_gen::fBm (vec_t P, int octaves) { - value_t v = 0.f; + value_t v = 0; for (int i = 0; i < octaves; ++i) { @@ -391,14 +433,14 @@ P *= lac; } - return clamp (v * fbm_mul [octaves - 1] + 0.5f, 0.f, .9999999f); + return clamp (v * fbm_mul [octaves - 1] + 0.5, 0, .9999999); } template typename frac_gen::value_t frac_gen::turbulence (vec_t P, int octaves) { - value_t v = 0.f; + value_t v = 0; for (int i = 0; i < octaves; ++i) { @@ -407,14 +449,14 @@ P *= lac; } - return clamp (v * fbm_mul [octaves - 1] * 2.f, 0.f, .9999999f); + return clamp (v * fbm_mul [octaves - 1] * (0.5 / noise_gen::abs_avg ()), 0, .9999999); } template typename frac_gen::value_t frac_gen::multifractal (vec_t P, int octaves, value_t offset) { - value_t v = 1.f; + value_t v = 1; for (int i = 0; i < octaves; ++i) { @@ -423,7 +465,7 @@ P *= lac; } - return clamp (v * 0.5f, 0.f, .9999999f); + return clamp (v * 0.5, 0, .9999999); } template @@ -431,16 +473,15 @@ frac_gen::heterofractal (vec_t P, int octaves, value_t offset) { value_t v = noise (P) + offset; - int i; - for (i = 1; i < octaves; ++i) + for (int i = 1; i < octaves; ++i) { rot [i](P); P *= lac; v += v * (noise (P) * ex [i] + offset); } - return v / powf (2., octaves); + return v / (1 << octaves); } template @@ -449,21 +490,20 @@ { value_t v = (noise (P) + offset) * ex [0]; value_t weight = v; - int i; - for (i = 1; i < octaves; ++i) + for (int i = 1; i < octaves; ++i) { rot [i](P); P *= lac; - min_it (weight, 1.f); + min_it (weight, 1); value_t sig = (noise (P) + offset) * ex [i]; v += weight * sig; weight *= gain * sig; } - return clamp (v * 0.5f + 0.5f, 0.f, .9999999f); + return clamp (v * 0.5 + 0.5, 0, .9999999); } template @@ -479,7 +519,7 @@ rot [i](P); P *= lac; - value_t w = clamp (sig * gain, 0.f, 1.f); + value_t w = clamp (sig * gain, 0, 1); sig = offset - abs (noise (P)); sig *= sig; @@ -488,7 +528,25 @@ v += sig * ex [i]; } - return clamp (v * 0.25f, 0.f, .9999999f); + return clamp (v * 0.25, 0, .9999999); +} + +template +typename frac_gen::value_t +frac_gen::billowfractal (vec_t P, int octaves, value_t offset, value_t gain) +{ + value_t v = 0; + + offset += 2 * noise_gen::abs_avg () - 1; + + for (int i = 0; i < octaves; ++i) + { + rot [i](P); + v += (abs (noise (ith_octave (P, i))) * gain - offset) * ex [i]; + P *= lac; + } + + return clamp (v, -.9999999, .9999999); } // http://www.gamasutra.com/view/feature/3098/a_realtime_procedural_universe_.php?page=2 @@ -496,7 +554,7 @@ typename frac_gen::value_t frac_gen::terrain (vec_t P, int octaves) { - value_t v = 0.f; + value_t v = 0; for (int i = 0; i < octaves; ++i) { @@ -507,7 +565,7 @@ v *= fbm_mul [octaves - 1]; - return v <= 0.f ? - powf (-v, 0.7f) : powf (v, 1. + noise (P) * v); + return v <= 0 ? - pow (-v, 0.7) : pow (v, 1 + noise (P) * v); } template @@ -518,17 +576,17 @@ value_t b = ridgedmultifractal (P, octaves, 1, 8); value_t fade = fBm (P + vec_t(10.3), octaves); - const value_t width = 0.05f; + const value_t width = 0.05; - if (fade > 0.5f + width) + if (fade > 0.5 + width) return a; - else if (fade < 0.5f - width) + else if (fade < 0.5 - width) return b; - fade = (fade - 0.5f + width) / (width * 2); + fade = (fade - 0.5 + width) / (width * 2); // sigmoidal curve - fade = fade * fade * 2 * (1.5f - fade); + fade = fade * fade * 2 * (1.5 - fade); return a * fade + b * (1 - fade); } @@ -554,21 +612,21 @@ if (!(y&63))fprintf (stderr, "y %d\n", y);//D for (int x = 0; x < N; ++x) { - //putc (127 * n.noise (x * 0.1, y * 0.1, 0, 0,0,1) + 128, stdout); + //putc (127 * gen.noise (vec2d (x * 0.01, y * 0.01)) + 128, stdout); //putc (256 * gen.terrain2 (x * 0.004, y * 0.004, 8), stdout); - //putc (256 * gen.fBm (x * 0.01, y * 0.01, 3), stdout); - putc (256 * gen.turbulence (vec2d (x * 0.004 - 1, y * 0.004 - 1), 8), stdout); - //putc (256 * gen.heterofractal (x * 0.008, y * 0.008, 8, 0.9), stdout); + //putc (256 * gen.fBm (vec2d(x * 0.01, y * 0.01), 16), stdout); + putc (256 * gen.turbulence (vec2d (x * 0.004 - 1, y * 0.004 - 1), 10), stdout); + //putc (256 * gen.heterofractal (vec2d (x * 0.008, y * 0.008), 8, 0.9), stdout); // mountais or somesuch(?) - //putc (256 * gen.hybridfractal (x * 0.01, y * 0.01, 8, -.4, -4), stdout); + //putc (256 * gen.hybridfractal (vec2d (x * 0.01, y * 0.01), 8, -.4, -4), stdout); // temperature - //putc (256 * gen.fBm (x * 0.002, y * 0.002, 2), stdout); + //putc (256 * gen.fBm (vec2d (x * 0.002, y * 0.002), 2), stdout); // rain //cells - //putc (256 * gen.ridgedmultifractal (vec2d (x * 0.01, y * 0.01), 3, 0.5 + gen.noise(vec2d(x*0.01,y*0.01)), 2), stdout); + //putc (127.49 * gen.billowfractal (vec2d (x * 0.01, y * 0.01), 9) + 128, stdout); } } #else