/* * This file is part of FFmpeg. * * FFmpeg is free software; you can redistribute it and/or modify * it under the terms of the GNU General Public License as published by * the Free Software Foundation; either version 2 of the License, or * (at your option) any later version. * * FFmpeg is distributed in the hope that it will be useful, * but WITHOUT ANY WARRANTY; without even the implied warranty of * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the * GNU General Public License for more details. * * You should have received a copy of the GNU General Public License along * with FFmpeg; if not, write to the Free Software Foundation, Inc., * 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA. */ /** * @file * Perlin Noise generator, based on code from: * https://adrianb.io/2014/08/09/perlinnoise.html * * Original article from Ken Perlin: * http://mrl.nyu.edu/~perlin/paper445.pdf */ #include #include "libavutil/lfg.h" #include "libavutil/random_seed.h" #include "perlin.h" static inline int inc(int num, int period) { num++; if (period > 0) num %= period; return num; } static inline double grad(int hash, double x, double y, double z) { // Take the hashed value and take the first 4 bits of it (15 == 0b1111) int h = hash & 15; // If the most significant bit (MSB) of the hash is 0 then set u = x. Otherwise y. double u = h < 8 /* 0b1000 */ ? x : y; double v; // In Ken Perlin's original implementation this was another // conditional operator (?:), then expanded for readability. if (h < 4 /* 0b0100 */) // If the first and second significant bits are 0 set v = y v = y; // If the first and second significant bits are 1 set v = x else if (h == 12 /* 0b1100 */ || h == 14 /* 0b1110 */) v = x; else // If the first and second significant bits are not equal (0/1, 1/0) set v = z v = z; // Use the last 2 bits to decide if u and v are positive or negative. Then return their addition. return ((h&1) == 0 ? u : -u)+((h&2) == 0 ? v : -v); } static inline double fade(double t) { // Fade function as defined by Ken Perlin. This eases coordinate values // so that they will "ease" towards integral values. This ends up smoothing // the final output. // use Horner method to compute: 6t^5 - 15t^4 + 10t^3 return t * t * t * (t * (t * 6 - 15) + 10); } static double lerp(double a, double b, double x) { return a + x * (b - a); } // Hash lookup table as defined by Ken Perlin. This is a randomly // arranged array of all numbers from 0-255 inclusive. static uint8_t ken_permutations[] = { 151, 160, 137, 91, 90, 15, 131, 13, 201, 95, 96, 53, 194, 233, 7, 225, 140, 36, 103, 30, 69, 142, 8, 99, 37, 240, 21, 10, 23, 190, 6, 148, 247, 120, 234, 75, 0, 26, 197, 62, 94, 252, 219, 203, 117, 35, 11, 32, 57, 177, 33, 88, 237, 149, 56, 87, 174, 20, 125, 136, 171, 168, 68, 175, 74, 165, 71, 134, 139, 48, 27, 166, 77, 146, 158, 231, 83, 111, 229, 122, 60, 211, 133, 230, 220, 105, 92, 41, 55, 46, 245, 40, 244, 102, 143, 54, 65, 25, 63, 161, 1, 216, 80, 73, 209, 76, 132, 187, 208, 89, 18, 169, 200, 196, 135, 130, 116, 188, 159, 86, 164, 100, 109, 198, 173, 186, 3, 64, 52, 217, 226, 250, 124, 123, 5, 202, 38, 147, 118, 126, 255, 82, 85, 212, 207, 206, 59, 227, 47, 16, 58, 17, 182, 189, 28, 42, 223, 183, 170, 213, 119, 248, 152, 2, 44, 154, 163, 70, 221, 153, 101, 155, 167, 43, 172, 9, 129, 22, 39, 253, 19, 98, 108, 110, 79, 113, 224, 232, 178, 185, 112, 104, 218, 246, 97, 228, 251, 34, 242, 193, 238, 210, 144, 12, 191, 179, 162, 241, 81, 51, 145, 235, 249, 14, 239, 107, 49, 192, 214, 31, 181, 199, 106, 157, 184, 84, 204, 176, 115, 121, 50, 45, 127, 4, 150, 254, 138, 236, 205, 93, 222, 114, 67, 29, 24, 72, 243, 141, 128, 195, 78, 66, 215, 61, 156, 180 }; int ff_perlin_init(FFPerlin *perlin, double period, int octaves, double persistence, enum FFPerlinRandomMode random_mode, unsigned int random_seed) { int i; perlin->period = period; perlin->octaves = octaves; perlin->persistence = persistence; perlin->random_mode = random_mode; perlin->random_seed = random_seed; if (perlin->random_mode == FF_PERLIN_RANDOM_MODE_KEN) { for (i = 0; i < 512; i++) { perlin->permutations[i] = ken_permutations[i % 256]; } } else { AVLFG lfg; uint8_t random_permutations[256]; if (perlin->random_mode == FF_PERLIN_RANDOM_MODE_RANDOM) perlin->random_seed = av_get_random_seed(); av_lfg_init(&lfg, perlin->random_seed); for (i = 0; i < 256; i++) { random_permutations[i] = i; } for (i = 0; i < 256; i++) { unsigned int random_idx = av_lfg_get(&lfg) % (256-i); uint8_t random_val = random_permutations[random_idx]; random_permutations[random_idx] = random_permutations[255-i]; perlin->permutations[i] = perlin->permutations[i+256] = random_val; } } return 0; } static double perlin_get(FFPerlin *perlin, double x, double y, double z) { int xi, yi, zi; double xf, yf, zf; double u, v, w; const uint8_t *p = perlin->permutations; double period = perlin->period; int aaa, aba, aab, abb, baa, bba, bab, bbb; double x1, x2, y1, y2; if (perlin->period > 0) { // If we have any period on, change the coordinates to their "local" repetitions x = fmod(x, perlin->period); y = fmod(y, perlin->period); z = fmod(z, perlin->period); } // Calculate the "unit cube" that the point asked will be located in // The left bound is ( |_x_|,|_y_|,|_z_| ) and the right bound is that // plus 1. Next we calculate the location (from 0.0 to 1.0) in that cube. xi = (int)x & 255; yi = (int)y & 255; zi = (int)z & 255; xf = x - (int)x; yf = y - (int)y; zf = z - (int)z; // We also fade the location to smooth the result. u = fade(xf); v = fade(yf); w = fade(zf); aaa = p[p[p[ xi ] + yi ] + zi ]; aba = p[p[p[ xi ] + inc(yi, period)] + zi ]; aab = p[p[p[ xi ] + yi ] + inc(zi, period)]; abb = p[p[p[ xi ] + inc(yi, period)] + inc(zi, period)]; baa = p[p[p[inc(xi, period)] + yi ] + zi ]; bba = p[p[p[inc(xi, period)] + inc(yi, period)] + zi ]; bab = p[p[p[inc(xi, period)] + yi ] + inc(zi, period)]; bbb = p[p[p[inc(xi, period)] + inc(yi, period)] + inc(zi, period)]; // The gradient function calculates the dot product between a pseudorandom // gradient vector and the vector from the input coordinate to the 8 // surrounding points in its unit cube. // This is all then lerped together as a sort of weighted average based on the faded (u,v,w) // values we made earlier. x1 = lerp(grad(aaa, xf , yf , zf), grad(baa, xf-1, yf , zf), u); x2 = lerp(grad(aba, xf , yf-1, zf), grad(bba, xf-1, yf-1, zf), u); y1 = lerp(x1, x2, v); x1 = lerp(grad(aab, xf , yf , zf-1), grad(bab, xf-1, yf , zf-1), u); x2 = lerp(grad(abb, xf , yf-1, zf-1), grad(bbb, xf-1, yf-1, zf-1), u); y2 = lerp(x1, x2, v); // For convenience we bound it to 0 - 1 (theoretical min/max before is -1 - 1) return (lerp(y1, y2, w) + 1) / 2; } double ff_perlin_get(FFPerlin *perlin, double x, double y, double z) { double total = 0; double frequency = 1; double amplitude = 1; double max_value = 0; // Used for normalizing result to 0.0 - 1.0 for (int i = 0; i < perlin->octaves; i++) { total += perlin_get(perlin, x * frequency, y * frequency, z * frequency) * amplitude; max_value += amplitude; amplitude *= perlin->persistence; frequency *= 2; } return total / max_value; }