perlin.c

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/*
 * 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 <math.h>
 
#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;
}