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99 lines
6.1 KiB
C#
99 lines
6.1 KiB
C#
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namespace MLEM.Noise {
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// The code in this class is based on https://gist.github.com/Flafla2/1a0b9ebef678bbce3215
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public static class Perlin {
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private static readonly int[] P;
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static Perlin() {
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var perm = new[] {
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151, 160, 137, 91, 90, 15, 131, 13, 201, 95, 96, 53, 194, 233, 7, 225, 140, 36, 103, 30, 69,
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142, 8, 99, 37, 240, 21, 10, 23, 190, 6, 148, 247, 120, 234, 75, 0, 26, 197, 62, 94, 252, 219,
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203, 117, 35, 11, 32, 57, 177, 33, 88, 237, 149, 56, 87, 174, 20, 125, 136, 171, 168, 68, 175,
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74, 165, 71, 134, 139, 48, 27, 166, 77, 146, 158, 231, 83, 111, 229, 122, 60, 211, 133, 230,
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220, 105, 92, 41, 55, 46, 245, 40, 244, 102, 143, 54, 65, 25, 63, 161, 1, 216, 80, 73, 209, 76,
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132, 187, 208, 89, 18, 169, 200, 196, 135, 130, 116, 188, 159, 86, 164, 100, 109, 198, 173, 186,
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3, 64, 52, 217, 226, 250, 124, 123, 5, 202, 38, 147, 118, 126, 255, 82, 85, 212, 207, 206, 59,
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227, 47, 16, 58, 17, 182, 189, 28, 42, 223, 183, 170, 213, 119, 248, 152, 2, 44, 154, 163, 70,
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221, 153, 101, 155, 167, 43, 172, 9, 129, 22, 39, 253, 19, 98, 108, 110, 79, 113, 224, 232, 178,
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185, 112, 104, 218, 246, 97, 228, 251, 34, 242, 193, 238, 210, 144, 12, 191, 179, 162, 241, 81,
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51, 145, 235, 249, 14, 239, 107, 49, 192, 214, 31, 181, 199, 106, 157, 184, 84, 204, 176, 115,
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121, 50, 45, 127, 4, 150, 254, 138, 236, 205, 93, 222, 114, 67, 29, 24, 72, 243, 141, 128, 195,
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78, 66, 215, 61, 156, 180
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};
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P = new int[512];
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for (var x = 0; x < P.Length; x++) {
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P[x] = perm[x % 256];
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}
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}
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public static double Generate(double x, double y, double z) {
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var xi = (int) x & 255; // Calculate the "unit cube" that the point asked will be located in
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var yi = (int) y & 255; // The left bound is ( |_x_|,|_y_|,|_z_| ) and the right bound is that
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var zi = (int) z & 255; // plus 1. Next we calculate the location (from 0.0 to 1.0) in that cube.
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var xf = x - (int) x; // We also fade the location to smooth the result.
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var yf = y - (int) y;
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var zf = z - (int) z;
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var u = Fade(xf);
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var v = Fade(yf);
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var w = Fade(zf);
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var a = P[xi] + yi; // This here is Perlin's hash function. We take our x value (remember,
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var aa = P[a] + zi; // between 0 and 255) and get a random value (from our p[] array above) between
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var ab = P[a + 1] + zi; // 0 and 255. We then add y to it and plug that into p[], and add z to that.
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var b = P[xi + 1] + yi; // Then, we get another random value by adding 1 to that and putting it into p[]
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var ba = P[b] + zi; // and add z to it. We do the whole thing over again starting with x+1. Later
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var bb = P[b + 1] + zi; // we plug aa, ab, ba, and bb back into p[] along with their +1's to get another set.
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// in the end we have 8 values between 0 and 255 - one for each vertex on the unit cube.
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// These are all interpolated together using u, v, and w below.
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double x1, x2, y1, y2;
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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
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Grad(P[ba], xf - 1, yf, zf), // our final gradient values. Then, we interpolate between those gradients with the u value to get
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u); // 4 x-values. Next, we interpolate between the 4 x-values with v to get 2 y-values. Finally,
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x2 = Lerp(Grad(P[ab], xf, yf - 1, zf), // we interpolate between the y-values to get a z-value.
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Grad(P[bb], xf - 1, yf - 1, zf),
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u); // When calculating the p[] values, remember that above, p[a+1] expands to p[xi]+yi+1 -- so you are
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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
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// to zi. The other 3 parameters are your possible return values (see grad()), which are actually
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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.
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Grad(P[ba + 1], xf - 1, yf, zf - 1),
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u);
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x2 = Lerp(Grad(P[ab + 1], xf, yf - 1, zf - 1),
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Grad(P[bb + 1], xf - 1, yf - 1, zf - 1),
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u);
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y2 = Lerp(x1, x2, v);
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return (Lerp(y1, y2, w) + 1) / 2; // For convenience we bound it to 0 - 1 (theoretical min/max before is -1 - 1)
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}
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private static double Grad(int hash, double x, double y, double z) {
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var h = hash & 15; // Take the hashed value and take the first 4 bits of it (15 == 0b1111)
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var u = h < 8 /* 0b1000 */ ? x : y; // If the most signifigant bit (MSB) of the hash is 0 then set u = x. Otherwise y.
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double v; // In Ken Perlin's original implementation this was another conditional operator (?:). I
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// expanded it for readability.
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if (h < 4 /* 0b0100 */) // If the first and second signifigant bits are 0 set v = y
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v = y;
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else if (h == 12 /* 0b1100 */ || h == 14 /* 0b1110*/) // If the first and second signifigant bits are 1 set v = x
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v = x;
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else // If the first and second signifigant bits are not equal (0/1, 1/0) set v = z
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v = z;
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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.
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}
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private static double Fade(double t) {
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// Fade function as defined by Ken Perlin. This eases coordinate values
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// so that they will "ease" towards integral values. This ends up smoothing
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// the final output.
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return t * t * t * (t * (t * 6 - 15) + 10); // 6t^5 - 15t^4 + 10t^3
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}
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private static double Lerp(double a, double b, double x) {
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return a + x * (b - a);
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}
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}
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}
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