PerlinNoise.cs

using Microsoft.Xna.Framework;
using System;
using System.Collections.Generic;
using System.Text;
 
namespace Barotrauma
{
    //By Adrian Biagioli (Flafla2) 
    //under a Creative Commons Attribution 4.0 International License.
 
    public static class PerlinNoise
    {
        public static double OctavePerlin(double x, double y, double z, double frequency, int octaves, double persistence)
        {
            double total = 0;
            double amplitude = 3;
            for (int i = 0; i < octaves; i++)
            {
                total += CalculatePerlin(x * frequency, y * frequency, z * frequency) * amplitude;
 
                amplitude *= persistence;
                frequency *= 2;
            }
 
            return total;
        }
 
        // Hash lookup table as defined by Ken Perlin.  This is a randomly
        // arranged array of all numbers from 0-255 inclusive.
        private static readonly int[] permutation = 
        {
            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
        };
 
        private static readonly int[] p;                                                    // Doubled permutation to avoid overflow
 
        private static readonly float[] cachedNoise;
 
        private const int CacheResolution = 256;
 
        static PerlinNoise()
        {
            p = new int[512];
            for (int x = 0; x < 512; x++)
            {
                p[x] = permutation[x % 256];
            }
 
            float minValue = float.MaxValue;
            float maxValue = float.MinValue;
            cachedNoise = new float[CacheResolution * CacheResolution];
            for (int x = 0; x < CacheResolution; x++)
            {
                for (int y = 0; y < CacheResolution; y++)
                {
                    cachedNoise[x + CacheResolution * y] = (float)OctavePerlin(x / (double)CacheResolution, y / (double)CacheResolution, 0.5, 10, 4, 0.5f);
                }
            }
 
            for (int i = 0; i < CacheResolution * CacheResolution; i++)
            {
                minValue = Math.Min(cachedNoise[i], minValue);
                maxValue = Math.Max(cachedNoise[i], maxValue);
            }
 
            //normalize to 0-1 range
            for (int i = 0; i < CacheResolution * CacheResolution; i++)
            {
                cachedNoise[i] = (cachedNoise[i] - minValue) / (maxValue - minValue);
            }
        }
 
        public static float GetPerlin(float x, float y)
        {
            x = Math.Abs(x) % 1.0f;
            y = Math.Abs(y) % 1.0f;
            
            float xIndex = x < 0.5f ? (x * 2.0f * CacheResolution) : CacheResolution - ((x - 0.5f) * 2.0f * CacheResolution);
            xIndex = Math.Min(xIndex, CacheResolution - 1);
 
            float yIndex = y < 0.5f ? (y * 2.0f * CacheResolution) : CacheResolution - ((y - 0.5f) * 2.0f * CacheResolution);
            yIndex = Math.Min(yIndex, CacheResolution - 1);
 
            int minX = (int)xIndex, maxX = (int)Math.Ceiling(xIndex);
            int minY = (int)yIndex, maxY = (int)Math.Ceiling(yIndex);
            
            return MathHelper.Lerp(
                MathHelper.Lerp(cachedNoise[minX + minY * CacheResolution], cachedNoise[maxX + minY * CacheResolution], xIndex % 1.0f),
                MathHelper.Lerp(cachedNoise[minX + maxY * CacheResolution], cachedNoise[maxX + maxY * CacheResolution], xIndex % 1.0f),
                yIndex % 1.0f);
        }
 
        public static double CalculatePerlin(double x, double y, double z)
        {
            int xi = (int)x & 255;                              // Calculate the "unit cube" that the point asked will be located in
            int yi = (int)y & 255;                              // The left bound is ( |_x_|,|_y_|,|_z_| ) and the right bound is that
            int zi = (int)z & 255;                              // plus 1.  Next we calculate the location (from 0.0 to 1.0) in that cube.
            double xf = x - (int)x;                             // We also fade the location to smooth the result.
            double yf = y - (int)y;
            double zf = z - (int)z;
            double u = Fade(xf);
            double v = Fade(yf);
            double w = Fade(zf);
 
            int a = p[xi] + yi;                             // This here is Perlin's hash function.  We take our x value (remember,
            int aa = p[a] + zi;                             // between 0 and 255) and get a random value (from our p[] array above) between
            int ab = p[a + 1] + zi;                             // 0 and 255.  We then add y to it and plug that into p[], and add z to that.
            int b = p[xi + 1] + yi;                             // Then, we get another random value by adding 1 to that and putting it into p[]
            int ba = p[b] + zi;                             // and add z to it.  We do the whole thing over again starting with x+1.  Later
            int bb = p[b + 1] + zi;                             // we plug aa, ab, ba, and bb back into p[] along with their +1's to get another set.
                                                                // in the end we have 8 values between 0 and 255 - one for each vertex on the unit cube.
                                                                // These are all interpolated together using u, v, and w below.
 
            double x1, x2, y1, y2;
            x1 = Lerp(Grad(p[aa], xf, yf, zf),          // This is where the "magic" happens.  We calculate a new set of p[] values and use that to get
                        Grad(p[ba], xf - 1, yf, zf),            // our final gradient values.  Then, we interpolate between those gradients with the u value to get
                        u);                                     // 4 x-values.  Next, we interpolate between the 4 x-values with v to get 2 y-values.  Finally,
            x2 = Lerp(Grad(p[ab], xf, yf - 1, zf),          // we interpolate between the y-values to get a z-value.
                        Grad(p[bb], xf - 1, yf - 1, zf),
                        u);                                     // When calculating the p[] values, remember that above, p[a+1] expands to p[xi]+yi+1 -- so you are
            y1 = Lerp(x1, x2, v);                               // essentially adding 1 to yi.  Likewise, p[ab+1] expands to p[p[xi]+yi+1]+zi+1] -- so you are adding
                                                                // to zi.  The other 3 parameters are your possible return values (see grad()), which are actually
            x1 = Lerp(Grad(p[aa + 1], xf, yf, zf - 1),      // the vectors from the edges of the unit cube to the point in the unit cube itself.
                        Grad(p[ba + 1], xf - 1, yf, zf - 1),
                        u);
            x2 = Lerp(Grad(p[ab + 1], xf, yf - 1, zf - 1),
                          Grad(p[bb + 1], xf - 1, yf - 1, zf - 1),
                          u);
            y2 = Lerp(x1, x2, v);
 
            return (Lerp(y1, y2, w) + 1) / 2;                       // For convenience we bound it to 0 - 1 (theoretical min/max before is -1 - 1)
        }
 
        public static double Grad(int hash, double x, double y, double z)
        {
            int h = hash & 15;                                  // Take the hashed value and take the first 4 bits of it (15 == 0b1111)
            double u = h < 8 /* 0b1000 */ ? x : y;              // If the most signifigant bit (MSB) of the hash is 0 then set u = x.  Otherwise y.
 
            double v;                                           // In Ken Perlin's original implementation this was another conditional operator (?:).  I
                                                                // expanded it for readability.
 
            if (h < 4 /* 0b0100 */)                             // If the first and second signifigant bits are 0 set v = y
                v = y;
            else if (h == 12 /* 0b1100 */ || h == 14 /* 0b1110*/)// If the first and second signifigant bits are 1 set v = x
                v = x;
            else                                                // If the first and second signifigant bits are not equal (0/1, 1/0) set v = z
                v = z;
 
            return ((h & 1) == 0 ? u : -u) + ((h & 2) == 0 ? v : -v); // Use the last 2 bits to decide if u and v are positive or negative.  Then return their addition.
        }
 
        public static 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.
            return t * t * t * (t * (t * 6 - 15) + 10);         // 6t^5 - 15t^4 + 10t^3
        }
 
        public static double Lerp(double a, double b, double x)
        {
            return a + x * (b - a);
        }
    }
}