PyCraft/SimplexNoise.hpp at master · BeneDevRepo/PyCraft · GitHub

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#pragma once

#include <cstdint>
#include <cmath>


// simplex noise translated from https://procedural-content-generation.fandom.com/wiki/Simplex_Noise
class SimplexNoise {
private:
	static constexpr const int grad3[12][3] {
		{ 1, 1, 0 }, { -1,  1, 0}, { 1, -1,  0 }, { -1, -1,  0 },
		{ 1, 0, 1 }, { -1,  0, 1}, { 1,  0, -1 }, { -1,  0, -1 },
		{ 0, 1, 1 }, {  0, -1, 1}, { 0,  1, -1 }, {  0, -1, -1 }
	};

	static constexpr const uint8_t p[256] {
		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
	};

	static inline uint8_t hash(int32_t i) {
		return p[static_cast<uint8_t>(i)];
	}

	static inline float grad(int32_t hash, float x, float y, float z) {
		int h = hash & 15;     // Convert low 4 bits of hash code into 12 simple
		float u = h < 8 ? x : y; // gradient directions, and compute dot product.
		float v = h < 4 ? y : h == 12 || h == 14 ? x : z; // Fix repeats at h = 12 to 15
		return ((h & 1) ? -u : u) + ((h & 2) ? -v : v);
	}

    static int fastfloor(const double x) {
        return x>0 ? (int)x : (int)x-1;
    }

    static double dot(const int* g, const double x, const double y) {
        return g[0]*x + g[1]*y;
    }

public:

	/**
	 * 3D Perlin simplex noise
	 *
	 * @param[in] x float coordinate
	 * @param[in] y float coordinate
	 * @param[in] z float coordinate
	 *
	 * @return Noise value in the range[-1; 1], value of 0 on all integer coordinates.
	 */
	float noise(float x, float y, float z) const {
		float n0, n1, n2, n3; // Noise contributions from the four corners

		// Skewing/Unskewing factors for 3D
		static const float F3 = 1.0f / 3.0f;
		static const float G3 = 1.0f / 6.0f;

		// Skew the input space to determine which simplex cell we're in
		float s = (x + y + z) * F3; // Very nice and simple skew factor for 3D
		int i = fastfloor(x + s);
		int j = fastfloor(y + s);
		int k = fastfloor(z + s);
		float t = (i + j + k) * G3;
		float X0 = i - t; // Unskew the cell origin back to (x,y,z) space
		float Y0 = j - t;
		float Z0 = k - t;
		float x0 = x - X0; // The x,y,z distances from the cell origin
		float y0 = y - Y0;
		float z0 = z - Z0;

		// For the 3D case, the simplex shape is a slightly irregular tetrahedron.
		// Determine which simplex we are in.
		int i1, j1, k1; // Offsets for second corner of simplex in (i,j,k) coords
		int i2, j2, k2; // Offsets for third corner of simplex in (i,j,k) coords
		if (x0 >= y0) {
			if (y0 >= z0) {
				i1 = 1; j1 = 0; k1 = 0; i2 = 1; j2 = 1; k2 = 0; // X Y Z order
			} else if (x0 >= z0) {
				i1 = 1; j1 = 0; k1 = 0; i2 = 1; j2 = 0; k2 = 1; // X Z Y order
			} else {
				i1 = 0; j1 = 0; k1 = 1; i2 = 1; j2 = 0; k2 = 1; // Z X Y order
			}
		} else { // x0<y0
			if (y0 < z0) {
				i1 = 0; j1 = 0; k1 = 1; i2 = 0; j2 = 1; k2 = 1; // Z Y X order
			} else if (x0 < z0) {
				i1 = 0; j1 = 1; k1 = 0; i2 = 0; j2 = 1; k2 = 1; // Y Z X order
			} else {
				i1 = 0; j1 = 1; k1 = 0; i2 = 1; j2 = 1; k2 = 0; // Y X Z order
			}
		}

		// A step of (1,0,0) in (i,j,k) means a step of (1-c,-c,-c) in (x,y,z),
		// a step of (0,1,0) in (i,j,k) means a step of (-c,1-c,-c) in (x,y,z), and
		// a step of (0,0,1) in (i,j,k) means a step of (-c,-c,1-c) in (x,y,z), where
		// c = 1/6.
		float x1 = x0 - i1 + G3; // Offsets for second corner in (x,y,z) coords
		float y1 = y0 - j1 + G3;
		float z1 = z0 - k1 + G3;
		float x2 = x0 - i2 + 2.0f * G3; // Offsets for third corner in (x,y,z) coords
		float y2 = y0 - j2 + 2.0f * G3;
		float z2 = z0 - k2 + 2.0f * G3;
		float x3 = x0 - 1.0f + 3.0f * G3; // Offsets for last corner in (x,y,z) coords
		float y3 = y0 - 1.0f + 3.0f * G3;
		float z3 = z0 - 1.0f + 3.0f * G3;

		// Work out the hashed gradient indices of the four simplex corners
		int gi0 = hash(i + hash(j + hash(k)));
		int gi1 = hash(i + i1 + hash(j + j1 + hash(k + k1)));
		int gi2 = hash(i + i2 + hash(j + j2 + hash(k + k2)));
		int gi3 = hash(i + 1 + hash(j + 1 + hash(k + 1)));

		// Calculate the contribution from the four corners
		float t0 = 0.6f - x0*x0 - y0*y0 - z0*z0;
		if (t0 < 0) {
			n0 = 0.0;
		} else {
			t0 *= t0;
			n0 = t0 * t0 * grad(gi0, x0, y0, z0);
		}
		float t1 = 0.6f - x1*x1 - y1*y1 - z1*z1;
		if (t1 < 0) {
			n1 = 0.0;
		} else {
			t1 *= t1;
			n1 = t1 * t1 * grad(gi1, x1, y1, z1);
		}
		float t2 = 0.6f - x2*x2 - y2*y2 - z2*z2;
		if (t2 < 0) {
			n2 = 0.0;
		} else {
			t2 *= t2;
			n2 = t2 * t2 * grad(gi2, x2, y2, z2);
		}
		float t3 = 0.6f - x3*x3 - y3*y3 - z3*z3;
		if (t3 < 0) {
			n3 = 0.0;
		} else {
			t3 *= t3;
			n3 = t3 * t3 * grad(gi3, x3, y3, z3);
		}
		// Add contributions from each corner to get the final noise value.
		// The result is scaled to stay just inside [-1,1]
		return 32.0f*(n0 + n1 + n2 + n3);
	}


	double noise(double xin, double yin) const {
        double n0, n1, n2; // Noise contributions from the three corners

        // Skew the input space to determine which simplex cell we're in
        const double F2 = 0.5*(sqrt(3.0)-1.0);
        double s = (xin+yin)*F2; // Hairy factor for 2D
        int i = fastfloor(xin+s);
        int j = fastfloor(yin+s);
        const double G2 = (3.0-sqrt(3.0))/6.0;
        double t = (i+j)*G2;
        double X0 = i-t; // Unskew the cell origin back to (x,y) space
        double Y0 = j-t;
        double x0 = xin-X0; // The x,y distances from the cell origin
        double y0 = yin-Y0;

        // For the 2D case, the simplex shape is an equilateral triangle.
        // Determine which simplex we are in.
        int i1, j1; // Offsets for second (middle) corner of simplex in (i,j) coords
        if(x0 > y0) {
			i1 = 1; j1 = 0; // lower triangle, XY order: (0,0)->(1,0)->(1,1)
		} else {
			i1 = 0; j1 = 1; // upper triangle, YX order: (0,0)->(0,1)->(1,1)
		}

        // A step of (1,0) in (i,j) means a step of (1-c,-c) in (x,y), and
        // a step of (0,1) in (i,j) means a step of (-c,1-c) in (x,y), where
        // c = (3-sqrt(3))/6
        double x1 = x0 - i1 + G2; // Offsets for middle corner in (x,y) unskewed coords
        double y1 = y0 - j1 + G2;
        double x2 = x0 - 1.0 + 2.0 * G2; // Offsets for last corner in (x,y) unskewed coords
        double y2 = y0 - 1.0 + 2.0 * G2;

        // Work out the hashed gradient indices of the three simplex corners
        int ii = i & 255;
        int jj = j & 255;
        // int gi0 = perm[ii+perm[jj]] % 12;
        // int gi1 = perm[ii+i1+perm[jj+j1]] % 12;
        // int gi2 = perm[ii+1+perm[jj+1]] % 12;
        int gi0 = hash(ii+hash(jj)) % 12;
        int gi1 = hash(ii+i1+hash(jj+j1)) % 12;
        int gi2 = hash(ii+1+hash(jj+1)) % 12;

        // Calculate the contribution from the three corners
        double t0 = 0.5 - x0*x0-y0*y0;
        if(t0 < 0) n0 = 0.0;
        else {
            t0 *= t0;
            n0 = t0 * t0 * dot(grad3[gi0], x0, y0); // (x,y) of grad3 used for 2D gradient
        }

        double t1 = 0.5 - x1*x1-y1*y1;
        if(t1 < 0) n1 = 0.0;
        else {
            t1 *= t1;
            n1 = t1 * t1 * dot(grad3[gi1], x1, y1);
        }

        double t2 = 0.5 - x2*x2-y2*y2;
        if(t2<0) n2 = 0.0;
        else {
            t2 *= t2;
            n2 = t2 * t2 * dot(grad3[gi2], x2, y2);
        }

        // Add contributions from each corner to get the final noise value.
        // The result is scaled to return values in the interval [-1,1].
        return 70.0 * (n0 + n1 + n2);
    }
};