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/*
 * The MIT License
 *
 * Copyright (c) 2016-2020 JOML
 *
 * Permission is hereby granted, free of charge, to any person obtaining a copy
 * of this software and associated documentation files (the "Software"), to deal
 * in the Software without restriction, including without limitation the rights
 * to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
 * copies of the Software, and to permit persons to whom the Software is
 * furnished to do so, subject to the following conditions:
 *
 * The above copyright notice and this permission notice shall be included in
 * all copies or substantial portions of the Software.
 *
 * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
 * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
 * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
 * AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
 * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
 * OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
 * THE SOFTWARE.
 */
package org.joml;

/**
 * A simplex noise algorithm for 2D, 3D and 4D input.
 * 
 * It was originally authored by Stefan Gustavson.
 * 

 * The original implementation can be found here: http://http://staffwww.itn.liu.se/.
 */
public class SimplexNoise {
    private static class Vector3b {
        byte x, y, z;
        Vector3b(int x, int y, int z) {
            super();
            this.x = (byte) x;
            this.y = (byte) y;
            this.z = (byte) z;
        }
    }
    private static class Vector4b {
        byte x, y, z, w;
        Vector4b(int x, int y, int z, int w) {
            super();
            this.x = (byte) x;
            this.y = (byte) y;
            this.z = (byte) z;
            this.w = (byte) w;
        }
    }

    // Kai Burjack:
    // Use a three-component vector here to save memory. (instead of using 4-component 'Grad' class)
    // And as the original author mentioned on the 'Grad' class, using a class to store the gradient components
    // is indeed faster compared to using a simple int[] array...
    private static final Vector3b[] grad3 = { new Vector3b(1, 1, 0), new Vector3b(-1, 1, 0), new Vector3b(1, -1, 0), new Vector3b(-1, -1, 0),
            new Vector3b(1, 0, 1), new Vector3b(-1, 0, 1), new Vector3b(1, 0, -1), new Vector3b(-1, 0, -1), new Vector3b(0, 1, 1), new Vector3b(0, -1, 1),
            new Vector3b(0, 1, -1), new Vector3b(0, -1, -1) };

    // Kai Burjack:
    // As the original author mentioned on the 'Grad' class, using a class to store the gradient components
    // is indeed faster compared to using a simple int[] array...
    private static final Vector4b[] grad4 = { new Vector4b(0, 1, 1, 1), new Vector4b(0, 1, 1, -1), new Vector4b(0, 1, -1, 1), new Vector4b(0, 1, -1, -1),
            new Vector4b(0, -1, 1, 1), new Vector4b(0, -1, 1, -1), new Vector4b(0, -1, -1, 1), new Vector4b(0, -1, -1, -1), new Vector4b(1, 0, 1, 1),
            new Vector4b(1, 0, 1, -1), new Vector4b(1, 0, -1, 1), new Vector4b(1, 0, -1, -1), new Vector4b(-1, 0, 1, 1), new Vector4b(-1, 0, 1, -1),
            new Vector4b(-1, 0, -1, 1), new Vector4b(-1, 0, -1, -1), new Vector4b(1, 1, 0, 1), new Vector4b(1, 1, 0, -1), new Vector4b(1, -1, 0, 1),
            new Vector4b(1, -1, 0, -1), new Vector4b(-1, 1, 0, 1), new Vector4b(-1, 1, 0, -1), new Vector4b(-1, -1, 0, 1), new Vector4b(-1, -1, 0, -1),
            new Vector4b(1, 1, 1, 0), new Vector4b(1, 1, -1, 0), new Vector4b(1, -1, 1, 0), new Vector4b(1, -1, -1, 0), new Vector4b(-1, 1, 1, 0),
            new Vector4b(-1, 1, -1, 0), new Vector4b(-1, -1, 1, 0), new Vector4b(-1, -1, -1, 0) };

    // Kai Burjack:
    // Use a byte[] instead of a short[] to save memory
    private static final byte[] p = { -105, -96, -119, 91, 90, 15, -125, 13, -55, 95, 96, 53, -62, -23, 7, -31, -116, 36, 103, 30, 69, -114, 8, 99, 37, -16,
            21, 10, 23, -66, 6, -108, -9, 120, -22, 75, 0, 26, -59, 62, 94, -4, -37, -53, 117, 35, 11, 32, 57, -79, 33, 88, -19, -107, 56, 87, -82, 20, 125,
            -120, -85, -88, 68, -81, 74, -91, 71, -122, -117, 48, 27, -90, 77, -110, -98, -25, 83, 111, -27, 122, 60, -45, -123, -26, -36, 105, 92, 41, 55, 46,
            -11, 40, -12, 102, -113, 54, 65, 25, 63, -95, 1, -40, 80, 73, -47, 76, -124, -69, -48, 89, 18, -87, -56, -60, -121, -126, 116, -68, -97, 86, -92,
            100, 109, -58, -83, -70, 3, 64, 52, -39, -30, -6, 124, 123, 5, -54, 38, -109, 118, 126, -1, 82, 85, -44, -49, -50, 59, -29, 47, 16, 58, 17, -74,
            -67, 28, 42, -33, -73, -86, -43, 119, -8, -104, 2, 44, -102, -93, 70, -35, -103, 101, -101, -89, 43, -84, 9, -127, 22, 39, -3, 19, 98, 108, 110,
            79, 113, -32, -24, -78, -71, 112, 104, -38, -10, 97, -28, -5, 34, -14, -63, -18, -46, -112, 12, -65, -77, -94, -15, 81, 51, -111, -21, -7, 14, -17,
            107, 49, -64, -42, 31, -75, -57, 106, -99, -72, 84, -52, -80, 115, 121, 50, 45, 127, 4, -106, -2, -118, -20, -51, 93, -34, 114, 67, 29, 24, 72,
            -13, -115, -128, -61, 78, 66, -41, 61, -100, -76 };
    // To remove the need for index wrapping, float the permutation table length
    private static final byte[] perm = new byte[512];
    private static final byte[] permMod12 = new byte[512];
    static {
        for (int i = 0; i < 512; i++) {
            perm[i] = p[i & 255];
            permMod12[i] = (byte) ((perm[i]&0xFF) % 12);
        }
    }

    // Skewing and unskewing factors for 2, 3, and 4 dimensions
    private static final float F2 = 0.3660254037844386f; // <- (float) (0.5f * (Math.sqrt(3.0f) - 1.0f));
    private static final float G2 = 0.21132486540518713f; // <- (float) ((3.0f - Math.sqrt(3.0f)) / 6.0f);
    private static final float F3 = 1.0f / 3.0f;
    private static final float G3 = 1.0f / 6.0f;
    private static final float F4 = 0.30901699437494745f; // <- (float) ((Math.sqrt(5.0f) - 1.0f) / 4.0f);
    private static final float G4 = 0.1381966011250105f; // <- (float) ((5.0f - Math.sqrt(5.0f)) / 20.0f);

    // This method is a *lot* faster than using (int)Math.floor(x)
    private static int fastfloor(float x) {
        int xi = (int) x;
        return x < xi ? xi - 1 : xi;
    }

    private static float dot(Vector3b g, float x, float y) {
        return g.x * x + g.y * y;
    }

    private static float dot(Vector3b g, float x, float y, float z) {
        return g.x * x + g.y * y + g.z * z;
    }

    private static float dot(Vector4b g, float x, float y, float z, float w) {
        return g.x * x + g.y * y + g.z * z + g.w * w;
    }

    /**
     * Compute 2D simplex noise for the given input vector (x, y).
     * 

     * The result is in the range [-1..+1].
     * 
     * @param x
     *          the x coordinate
     * @param y
     *          the y coordinate
     * @return the noise value (within [-1..+1])
     */
    public static float noise(float x, float y) {
        float n0, n1, n2; // Noise contributions from the three corners
        // Skew the input space to determine which simplex cell we're in
        float s = (x + y) * F2; // Hairy factor for 2D
        int i = fastfloor(x + s);
        int j = fastfloor(y + s);
        float t = (i + j) * G2;
        float X0 = i - t; // Unskew the cell origin back to (x,y) space
        float Y0 = j - t;
        float x0 = x - X0; // The x,y distances from the cell origin
        float y0 = y - 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
        float x1 = x0 - i1 + G2; // Offsets for middle corner in (x,y) unskewed coords
        float y1 = y0 - j1 + G2;
        float x2 = x0 - 1.0f + 2.0f * G2; // Offsets for last corner in (x,y) unskewed coords
        float y2 = y0 - 1.0f + 2.0f * G2;
        // Work out the hashed gradient indices of the three simplex corners
        int ii = i & 255;
        int jj = j & 255;
        int gi0 = permMod12[ii + perm[jj]&0xFF]&0xFF;
        int gi1 = permMod12[ii + i1 + perm[jj + j1]&0xFF]&0xFF;
        int gi2 = permMod12[ii + 1 + perm[jj + 1]&0xFF]&0xFF;
        // Calculate the contribution from the three corners
        float t0 = 0.5f - x0 * x0 - y0 * y0;
        if (t0 < 0.0f)
            n0 = 0.0f;
        else {
            t0 *= t0;
            n0 = t0 * t0 * dot(grad3[gi0], x0, y0); // (x,y) of grad3 used for 2D gradient
        }
        float t1 = 0.5f - x1 * x1 - y1 * y1;
        if (t1 < 0.0f)
            n1 = 0.0f;
        else {
            t1 *= t1;
            n1 = t1 * t1 * dot(grad3[gi1], x1, y1);
        }
        float t2 = 0.5f - x2 * x2 - y2 * y2;
        if (t2 < 0.0f)
            n2 = 0.0f;
        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 70.0f * (n0 + n1 + n2);
    }

    /**
     * Compute 3D simplex noise for the given input vector (x, y, z).
     * 
     * The result is in the range [-1..+1].
     * 
     * @param x
     *          the x coordinate
     * @param y
     *          the y coordinate
     * @param z
     *          the z coordinate
     * @return the noise value (within [-1..+1])
     */
    public static float noise(float x, float y, float z) {
        float n0, n1, n2, n3; // Noise contributions from the four corners
        // 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(x, y, z, w).
     * 

     * The result is in the range [-1..+1].
     * 
     * @param x
     *          the x coordinate
     * @param y
     *          the y coordinate
     * @param z
     *          the z coordinate
     * @param w
     *          the w coordinate
     * @return the noise value (within [-1..+1])
     */
    public static float noise(float x, float y, float z, float w) {
        float n0, n1, n2, n3, n4; // Noise contributions from the five corners
        // Skew the (x,y,z,w) space to determine which cell of 24 simplices we're in
        float s = (x + y + z + w) * F4; // Factor for 4D skewing
        int i = fastfloor(x + s);
        int j = fastfloor(y + s);
        int k = fastfloor(z + s);
        int l = fastfloor(w + s);
        float t = (i + j + k + l) * G4; // Factor for 4D unskewing
        float X0 = i - t; // Unskew the cell origin back to (x,y,z,w) space
        float Y0 = j - t;
        float Z0 = k - t;
        float W0 = l - t;
        float x0 = x - X0; // The x,y,z,w distances from the cell origin
        float y0 = y - Y0;
        float z0 = z - Z0;
        float w0 = w - W0;
        // For the 4D case, the simplex is a 4D shape I won't even try to describe.
        // To find out which of the 24 possible simplices we're in, we need to
        // determine the magnitude ordering of x0, y0, z0 and w0.
        // Six pair-wise comparisons are performed between each possible pair
        // of the four coordinates, and the results are used to rank the numbers.
        int rankx = 0;
        int ranky = 0;
        int rankz = 0;
        int rankw = 0;
        if (x0 > y0)
            rankx++;
        else
            ranky++;
        if (x0 > z0)
            rankx++;
        else
            rankz++;
        if (x0 > w0)
            rankx++;
        else
            rankw++;
        if (y0 > z0)
            ranky++;
        else
            rankz++;
        if (y0 > w0)
            ranky++;
        else
            rankw++;
        if (z0 > w0)
            rankz++;
        else
            rankw++;
        int i1, j1, k1, l1; // The integer offsets for the second simplex corner
        int i2, j2, k2, l2; // The integer offsets for the third simplex corner
        int i3, j3, k3, l3; // The integer offsets for the fourth simplex corner
        // simplex[c] is a 4-vector with the numbers 0, 1, 2 and 3 in some order.
        // Many values of c will never occur, since e.g. x>y>z>w makes x= 3 ? 1 : 0;
        j1 = ranky >= 3 ? 1 : 0;
        k1 = rankz >= 3 ? 1 : 0;
        l1 = rankw >= 3 ? 1 : 0;
        // Rank 2 denotes the second largest coordinate.
        i2 = rankx >= 2 ? 1 : 0;
        j2 = ranky >= 2 ? 1 : 0;
        k2 = rankz >= 2 ? 1 : 0;
        l2 = rankw >= 2 ? 1 : 0;
        // Rank 1 denotes the second smallest coordinate.
        i3 = rankx >= 1 ? 1 : 0;
        j3 = ranky >= 1 ? 1 : 0;
        k3 = rankz >= 1 ? 1 : 0;
        l3 = rankw >= 1 ? 1 : 0;
        // The fifth corner has all coordinate offsets = 1, so no need to compute that.
        float x1 = x0 - i1 + G4; // Offsets for second corner in (x,y,z,w) coords
        float y1 = y0 - j1 + G4;
        float z1 = z0 - k1 + G4;
        float w1 = w0 - l1 + G4;
        float x2 = x0 - i2 + 2.0f * G4; // Offsets for third corner in (x,y,z,w) coords
        float y2 = y0 - j2 + 2.0f * G4;
        float z2 = z0 - k2 + 2.0f * G4;
        float w2 = w0 - l2 + 2.0f * G4;
        float x3 = x0 - i3 + 3.0f * G4; // Offsets for fourth corner in (x,y,z,w) coords
        float y3 = y0 - j3 + 3.0f * G4;
        float z3 = z0 - k3 + 3.0f * G4;
        float w3 = w0 - l3 + 3.0f * G4;
        float x4 = x0 - 1.0f + 4.0f * G4; // Offsets for last corner in (x,y,z,w) coords
        float y4 = y0 - 1.0f + 4.0f * G4;
        float z4 = z0 - 1.0f + 4.0f * G4;
        float w4 = w0 - 1.0f + 4.0f * G4;
        // Work out the hashed gradient indices of the five simplex corners
        int ii = i & 255;
        int jj = j & 255;
        int kk = k & 255;
        int ll = l & 255;
        int gi0 = (perm[ii + perm[jj + perm[kk + perm[ll]&0xFF]&0xFF]&0xFF]&0xFF) % 32;
        int gi1 = (perm[ii + i1 + perm[jj + j1 + perm[kk + k1 + perm[ll + l1]&0xFF]&0xFF]&0xFF]&0xFF) % 32;
        int gi2 = (perm[ii + i2 + perm[jj + j2 + perm[kk + k2 + perm[ll + l2]&0xFF]&0xFF]&0xFF]&0xFF) % 32;
        int gi3 = (perm[ii + i3 + perm[jj + j3 + perm[kk + k3 + perm[ll + l3]&0xFF]&0xFF]&0xFF]&0xFF) % 32;
        int gi4 = (perm[ii + 1 + perm[jj + 1 + perm[kk + 1 + perm[ll + 1]&0xFF]&0xFF]&0xFF]&0xFF) % 32;
        // Calculate the contribution from the five corners
        float t0 = 0.6f - x0 * x0 - y0 * y0 - z0 * z0 - w0 * w0;
        if (t0 < 0.0f)
            n0 = 0.0f;
        else {
            t0 *= t0;
            n0 = t0 * t0 * dot(grad4[gi0], x0, y0, z0, w0);
        }
        float t1 = 0.6f - x1 * x1 - y1 * y1 - z1 * z1 - w1 * w1;
        if (t1 < 0.0f)
            n1 = 0.0f;
        else {
            t1 *= t1;
            n1 = t1 * t1 * dot(grad4[gi1], x1, y1, z1, w1);
        }
        float t2 = 0.6f - x2 * x2 - y2 * y2 - z2 * z2 - w2 * w2;
        if (t2 < 0.0f)
            n2 = 0.0f;
        else {
            t2 *= t2;
            n2 = t2 * t2 * dot(grad4[gi2], x2, y2, z2, w2);
        }
        float t3 = 0.6f - x3 * x3 - y3 * y3 - z3 * z3 - w3 * w3;
        if (t3 < 0.0f)
            n3 = 0.0f;
        else {
            t3 *= t3;
            n3 = t3 * t3 * dot(grad4[gi3], x3, y3, z3, w3);
        }
        float t4 = 0.6f - x4 * x4 - y4 * y4 - z4 * z4 - w4 * w4;
        if (t4 < 0.0f)
            n4 = 0.0f;
        else {
            t4 *= t4;
            n4 = t4 * t4 * dot(grad4[gi4], x4, y4, z4, w4);
        }
        // Sum up and scale the result to cover the range [-1,1]
        return 27.0f * (n0 + n1 + n2 + n3 + n4);
    }

}