393 lines
17 KiB
C#
393 lines
17 KiB
C#
// Copyright(c) 2018, Benjamin Ward
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// All rights reserved.
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// Redistribution and use in source and binary forms, with or without
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// modification, are permitted provided that the following conditions are met:
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// * Redistributions of source code must retain the above copyright notice, this
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// list of conditions and the following disclaimer.
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// * Redistributions in binary form must reproduce the above copyright notice,
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// this list of conditions and the following disclaimer in the documentation
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// and/or other materials provided with the distribution.
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// * Neither the name of the copyright holder nor the names of its
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// contributors may be used to endorse or promote products derived from
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// this software without specific prior written permission.
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// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
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// AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
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// IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
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// DISCLAIMED.IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE
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// FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
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// DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
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// SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
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// CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY,
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// OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
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// OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
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// SimplexNoise for C#
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// Author: Benjamin Ward
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// Github Link: https://github.com/WardBenjamin/SimplexNoise
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// Originally authored by Heikki Törmälä
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using System;
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namespace Simplex
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{
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/// <summary>
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/// Implementation of the Perlin simplex noise, an improved Perlin noise algorithm.
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/// Based loosely on SimplexNoise1234 by Stefan Gustavson <http://staffwww.itn.liu.se/~stegu/aqsis/aqsis-newnoise/>
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/// </summary>
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public class Noise
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{
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public static float[] Calc1D(int width, float scale)
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{
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float[] values = new float[width];
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for (int i = 0; i < width; i++)
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values[i] = Generate(i * scale) * 128 + 128;
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return values;
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}
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public static float[,] Calc2D(int width, int height, float scale)
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{
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float[,] values = new float[width, height];
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for (int i = 0; i < width; i++)
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for (int j = 0; j < height; j++)
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values[i, j] = Generate(i * scale, j * scale) * 128 + 128;
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return values;
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}
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public static float[,,] Calc3D(int width, int height, int length, float scale)
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{
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float[,,] values = new float[width, height, length];
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for (int i = 0; i < width; i++)
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for (int j = 0; j < height; j++)
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for (int k = 0; k < length; k++)
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values[i, j, k] = Generate(i * scale, j * scale, k * scale) * 128 + 128;
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return values;
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}
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public static float CalcPixel1D(int x, float scale)
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{
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return Generate(x * scale) * 128 + 128;
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}
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public static float CalcPixel2D(int x, int y, float scale)
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{
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return Generate(x * scale, y * scale) * 128 + 128;
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}
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public static float CalcPixel3D(int x, int y, int z, float scale)
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{
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return Generate(x * scale, y * scale, z * scale) * 128 + 128;
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}
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static Noise()
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{
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perm = new byte[permOriginal.Length];
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Simplex.Noise.permOriginal.CopyTo(perm, 0);
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}
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public static int Seed
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{
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get { return seed; }
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set
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{
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if (value == 0)
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{
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perm = new byte[permOriginal.Length];
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Simplex.Noise.permOriginal.CopyTo(perm, 0);
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}
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else
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{
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perm = new byte[512];
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Random random = new Random(value);
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random.NextBytes(perm);
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}
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}
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}
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private static int seed = 0;
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/// <summary>
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/// 1D simplex noise
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/// </summary>
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/// <param name="x"></param>
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/// <returns></returns>
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internal static float Generate(float x)
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{
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int i0 = FastFloor(x);
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int i1 = i0 + 1;
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float x0 = x - i0;
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float x1 = x0 - 1.0f;
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float n0, n1;
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float t0 = 1.0f - x0 * x0;
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t0 *= t0;
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n0 = t0 * t0 * grad(perm[i0 & 0xff], x0);
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float t1 = 1.0f - x1 * x1;
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t1 *= t1;
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n1 = t1 * t1 * grad(perm[i1 & 0xff], x1);
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// The maximum value of this noise is 8*(3/4)^4 = 2.53125
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// A factor of 0.395 scales to fit exactly within [-1,1]
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return 0.395f * (n0 + n1);
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}
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/// <summary>
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/// 2D simplex noise
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/// </summary>
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/// <param name="x"></param>
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/// <param name="y"></param>
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/// <returns></returns>
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internal static float Generate(float x, float y)
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{
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const float F2 = 0.366025403f; // F2 = 0.5*(sqrt(3.0)-1.0)
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const float G2 = 0.211324865f; // G2 = (3.0-Math.sqrt(3.0))/6.0
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float n0, n1, n2; // Noise contributions from the three corners
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// Skew the input space to determine which simplex cell we're in
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float s = (x + y) * F2; // Hairy factor for 2D
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float xs = x + s;
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float ys = y + s;
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int i = FastFloor(xs);
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int j = FastFloor(ys);
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float t = (float)(i + j) * G2;
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float X0 = i - t; // Unskew the cell origin back to (x,y) space
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float Y0 = j - t;
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float x0 = x - X0; // The x,y distances from the cell origin
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float y0 = y - Y0;
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// For the 2D case, the simplex shape is an equilateral triangle.
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// Determine which simplex we are in.
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int i1, j1; // Offsets for second (middle) corner of simplex in (i,j) coords
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if (x0 > y0) { i1 = 1; j1 = 0; } // lower triangle, XY order: (0,0)->(1,0)->(1,1)
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else { i1 = 0; j1 = 1; } // upper triangle, YX order: (0,0)->(0,1)->(1,1)
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// A step of (1,0) in (i,j) means a step of (1-c,-c) in (x,y), and
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// a step of (0,1) in (i,j) means a step of (-c,1-c) in (x,y), where
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// c = (3-sqrt(3))/6
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float x1 = x0 - i1 + G2; // Offsets for middle corner in (x,y) unskewed coords
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float y1 = y0 - j1 + G2;
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float x2 = x0 - 1.0f + 2.0f * G2; // Offsets for last corner in (x,y) unskewed coords
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float y2 = y0 - 1.0f + 2.0f * G2;
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// Wrap the integer indices at 256, to avoid indexing perm[] out of bounds
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int ii = Mod(i, 256);
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int jj = Mod(j, 256);
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// Calculate the contribution from the three corners
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float t0 = 0.5f - x0 * x0 - y0 * y0;
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if (t0 < 0.0f) n0 = 0.0f;
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else
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{
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t0 *= t0;
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n0 = t0 * t0 * grad(perm[ii + perm[jj]], x0, y0);
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}
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float t1 = 0.5f - x1 * x1 - y1 * y1;
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if (t1 < 0.0f) n1 = 0.0f;
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else
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{
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t1 *= t1;
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n1 = t1 * t1 * grad(perm[ii + i1 + perm[jj + j1]], x1, y1);
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}
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float t2 = 0.5f - x2 * x2 - y2 * y2;
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if (t2 < 0.0f) n2 = 0.0f;
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else
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{
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t2 *= t2;
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n2 = t2 * t2 * grad(perm[ii + 1 + perm[jj + 1]], x2, y2);
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}
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// Add contributions from each corner to get the final noise value.
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// The result is scaled to return values in the interval [-1,1].
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return 40.0f * (n0 + n1 + n2); // TODO: The scale factor is preliminary!
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}
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internal static float Generate(float x, float y, float z)
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{
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// Simple skewing factors for the 3D case
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const float F3 = 0.333333333f;
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const float G3 = 0.166666667f;
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float n0, n1, n2, n3; // Noise contributions from the four corners
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// Skew the input space to determine which simplex cell we're in
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float s = (x + y + z) * F3; // Very nice and simple skew factor for 3D
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float xs = x + s;
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float ys = y + s;
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float zs = z + s;
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int i = FastFloor(xs);
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int j = FastFloor(ys);
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int k = FastFloor(zs);
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float t = (float)(i + j + k) * G3;
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float X0 = i - t; // Unskew the cell origin back to (x,y,z) space
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float Y0 = j - t;
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float Z0 = k - t;
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float x0 = x - X0; // The x,y,z distances from the cell origin
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float y0 = y - Y0;
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float z0 = z - Z0;
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// For the 3D case, the simplex shape is a slightly irregular tetrahedron.
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// Determine which simplex we are in.
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int i1, j1, k1; // Offsets for second corner of simplex in (i,j,k) coords
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int i2, j2, k2; // Offsets for third corner of simplex in (i,j,k) coords
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/* This code would benefit from a backport from the GLSL version! */
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if (x0 >= y0)
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{
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if (y0 >= z0)
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{ i1 = 1; j1 = 0; k1 = 0; i2 = 1; j2 = 1; k2 = 0; } // X Y Z order
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else if (x0 >= z0) { i1 = 1; j1 = 0; k1 = 0; i2 = 1; j2 = 0; k2 = 1; } // X Z Y order
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else { i1 = 0; j1 = 0; k1 = 1; i2 = 1; j2 = 0; k2 = 1; } // Z X Y order
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}
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else
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{ // x0<y0
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if (y0 < z0) { i1 = 0; j1 = 0; k1 = 1; i2 = 0; j2 = 1; k2 = 1; } // Z Y X order
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else if (x0 < z0) { i1 = 0; j1 = 1; k1 = 0; i2 = 0; j2 = 1; k2 = 1; } // Y Z X order
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else { i1 = 0; j1 = 1; k1 = 0; i2 = 1; j2 = 1; k2 = 0; } // Y X Z order
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}
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// A step of (1,0,0) in (i,j,k) means a step of (1-c,-c,-c) in (x,y,z),
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// a step of (0,1,0) in (i,j,k) means a step of (-c,1-c,-c) in (x,y,z), and
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// a step of (0,0,1) in (i,j,k) means a step of (-c,-c,1-c) in (x,y,z), where
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// c = 1/6.
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float x1 = x0 - i1 + G3; // Offsets for second corner in (x,y,z) coords
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float y1 = y0 - j1 + G3;
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float z1 = z0 - k1 + G3;
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float x2 = x0 - i2 + 2.0f * G3; // Offsets for third corner in (x,y,z) coords
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float y2 = y0 - j2 + 2.0f * G3;
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float z2 = z0 - k2 + 2.0f * G3;
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float x3 = x0 - 1.0f + 3.0f * G3; // Offsets for last corner in (x,y,z) coords
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float y3 = y0 - 1.0f + 3.0f * G3;
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float z3 = z0 - 1.0f + 3.0f * G3;
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// Wrap the integer indices at 256, to avoid indexing perm[] out of bounds
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int ii = Mod(i, 256);
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int jj = Mod(j, 256);
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int kk = Mod(k, 256);
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// Calculate the contribution from the four corners
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float t0 = 0.6f - x0 * x0 - y0 * y0 - z0 * z0;
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if (t0 < 0.0f) n0 = 0.0f;
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else
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{
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t0 *= t0;
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n0 = t0 * t0 * grad(perm[ii + perm[jj + perm[kk]]], x0, y0, z0);
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}
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float t1 = 0.6f - x1 * x1 - y1 * y1 - z1 * z1;
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if (t1 < 0.0f) n1 = 0.0f;
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else
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{
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t1 *= t1;
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n1 = t1 * t1 * grad(perm[ii + i1 + perm[jj + j1 + perm[kk + k1]]], x1, y1, z1);
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}
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float t2 = 0.6f - x2 * x2 - y2 * y2 - z2 * z2;
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if (t2 < 0.0f) n2 = 0.0f;
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else
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{
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t2 *= t2;
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n2 = t2 * t2 * grad(perm[ii + i2 + perm[jj + j2 + perm[kk + k2]]], x2, y2, z2);
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}
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float t3 = 0.6f - x3 * x3 - y3 * y3 - z3 * z3;
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if (t3 < 0.0f) n3 = 0.0f;
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else
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{
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t3 *= t3;
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n3 = t3 * t3 * grad(perm[ii + 1 + perm[jj + 1 + perm[kk + 1]]], x3, y3, z3);
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}
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// Add contributions from each corner to get the final noise value.
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// The result is scaled to stay just inside [-1,1]
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return 32.0f * (n0 + n1 + n2 + n3); // TODO: The scale factor is preliminary!
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}
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private static byte[] perm;
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private static readonly byte[] permOriginal = new byte[]
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{
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151,160,137,91,90,15,
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131,13,201,95,96,53,194,233,7,225,140,36,103,30,69,142,8,99,37,240,21,10,23,
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190, 6,148,247,120,234,75,0,26,197,62,94,252,219,203,117,35,11,32,57,177,33,
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88,237,149,56,87,174,20,125,136,171,168, 68,175,74,165,71,134,139,48,27,166,
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77,146,158,231,83,111,229,122,60,211,133,230,220,105,92,41,55,46,245,40,244,
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102,143,54, 65,25,63,161, 1,216,80,73,209,76,132,187,208, 89,18,169,200,196,
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135,130,116,188,159,86,164,100,109,198,173,186, 3,64,52,217,226,250,124,123,
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5,202,38,147,118,126,255,82,85,212,207,206,59,227,47,16,58,17,182,189,28,42,
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223,183,170,213,119,248,152, 2,44,154,163, 70,221,153,101,155,167, 43,172,9,
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129,22,39,253, 19,98,108,110,79,113,224,232,178,185, 112,104,218,246,97,228,
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251,34,242,193,238,210,144,12,191,179,162,241, 81,51,145,235,249,14,239,107,
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49,192,214, 31,181,199,106,157,184, 84,204,176,115,121,50,45,127, 4,150,254,
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138,236,205,93,222,114,67,29,24,72,243,141,128,195,78,66,215,61,156,180,
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151,160,137,91,90,15,
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131,13,201,95,96,53,194,233,7,225,140,36,103,30,69,142,8,99,37,240,21,10,23,
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190, 6,148,247,120,234,75,0,26,197,62,94,252,219,203,117,35,11,32,57,177,33,
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88,237,149,56,87,174,20,125,136,171,168, 68,175,74,165,71,134,139,48,27,166,
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77,146,158,231,83,111,229,122,60,211,133,230,220,105,92,41,55,46,245,40,244,
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102,143,54, 65,25,63,161, 1,216,80,73,209,76,132,187,208, 89,18,169,200,196,
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135,130,116,188,159,86,164,100,109,198,173,186, 3,64,52,217,226,250,124,123,
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5,202,38,147,118,126,255,82,85,212,207,206,59,227,47,16,58,17,182,189,28,42,
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223,183,170,213,119,248,152, 2,44,154,163, 70,221,153,101,155,167, 43,172,9,
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129,22,39,253, 19,98,108,110,79,113,224,232,178,185, 112,104,218,246,97,228,
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251,34,242,193,238,210,144,12,191,179,162,241, 81,51,145,235,249,14,239,107,
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49,192,214, 31,181,199,106,157,184, 84,204,176,115,121,50,45,127, 4,150,254,
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138,236,205,93,222,114,67,29,24,72,243,141,128,195,78,66,215,61,156,180
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};
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private static int FastFloor(float x)
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{
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return (x > 0) ? ((int)x) : (((int)x) - 1);
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}
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private static int Mod(int x, int m)
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{
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int a = x % m;
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return a < 0 ? a + m : a;
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}
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private static float grad(int hash, float x)
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{
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int h = hash & 15;
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float grad = 1.0f + (h & 7); // Gradient value 1.0, 2.0, ..., 8.0
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if ((h & 8) != 0) grad = -grad; // Set a random sign for the gradient
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return (grad * x); // Multiply the gradient with the distance
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}
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private static float grad(int hash, float x, float y)
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{
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int h = hash & 7; // Convert low 3 bits of hash code
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float u = h < 4 ? x : y; // into 8 simple gradient directions,
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float v = h < 4 ? y : x; // and compute the dot product with (x,y).
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return ((h & 1) != 0 ? -u : u) + ((h & 2) != 0 ? -2.0f * v : 2.0f * v);
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}
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private static float grad(int hash, float x, float y, float z)
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{
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int h = hash & 15; // Convert low 4 bits of hash code into 12 simple
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float u = h < 8 ? x : y; // gradient directions, and compute dot product.
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float v = h < 4 ? y : h == 12 || h == 14 ? x : z; // Fix repeats at h = 12 to 15
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return ((h & 1) != 0 ? -u : u) + ((h & 2) != 0 ? -v : v);
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}
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private static float grad(int hash, float x, float y, float z, float t)
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{
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int h = hash & 31; // Convert low 5 bits of hash code into 32 simple
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float u = h < 24 ? x : y; // gradient directions, and compute dot product.
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float v = h < 16 ? y : z;
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float w = h < 8 ? z : t;
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return ((h & 1) != 0 ? -u : u) + ((h & 2) != 0 ? -v : v) + ((h & 4) != 0 ? -w : w);
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}
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}
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} |