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308 行
13 KiB
308 行
13 KiB
// SimplexNoise for C#
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// Author: Heikki Törmälä
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//This is free and unencumbered software released into the public domain.
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//Anyone is free to copy, modify, publish, use, compile, sell, or
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//distribute this software, either in source code form or as a compiled
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//binary, for any purpose, commercial or non-commercial, and by any
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//means.
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//In jurisdictions that recognize copyright laws, the author or authors
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//of this software dedicate any and all copyright interest in the
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//software to the public domain. We make this dedication for the benefit
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//of the public at large and to the detriment of our heirs and
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//successors. We intend this dedication to be an overt act of
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//relinquishment in perpetuity of all present and future rights to this
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//software under copyright law.
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//THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
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//EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
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//MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.
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//IN NO EVENT SHALL THE AUTHORS BE LIABLE FOR ANY CLAIM, DAMAGES OR
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//OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE,
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//ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
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//OTHER DEALINGS IN THE SOFTWARE.
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//For more information, please refer to <http://unlicense.org/>
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namespace JBooth.VertexPainterPro.SimplexNoise
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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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///
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/// </summary>
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public class Noise
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{
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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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public 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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public 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 = i % 256;
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int jj = 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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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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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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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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public 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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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 { // 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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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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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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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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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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public static byte[] perm = new byte[512] { 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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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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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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}
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