475 lines
18 KiB
C++
475 lines
18 KiB
C++
/* Copyright (c) 2007-2012 Eliot Eshelman
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*
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* This program is free software: you can redistribute it and/or modify
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* it under the terms of the GNU General Public License as published by
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* the Free Software Foundation, either version 3 of the License, or
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* (at your option) any later version.
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*
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* This program is distributed in the hope that it will be useful,
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* but WITHOUT ANY WARRANTY; without even the implied warranty of
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* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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* GNU General Public License for more details.
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*
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* You should have received a copy of the GNU General Public License
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* along with this program. If not, see <http://www.gnu.org/licenses/>.
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*
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*/
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#include <math.h>
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#include "simplexnoise.h"
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/* 2D, 3D and 4D Simplex Noise functions return 'random' values in (-1, 1).
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This algorithm was originally designed by Ken Perlin, but my code has been
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adapted from the implementation written by Stefan Gustavson (stegu@itn.liu.se)
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Raw Simplex noise functions return the value generated by Ken's algorithm.
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Scaled Raw Simplex noise functions adjust the range of values returned from the
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traditional (-1, 1) to whichever bounds are passed to the function.
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Multi-Octave Simplex noise functions compine multiple noise values to create a
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more complex result. Each successive layer of noise is adjusted and scaled.
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Scaled Multi-Octave Simplex noise functions scale the values returned from the
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traditional (-1,1) range to whichever range is passed to the function.
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In many cases, you may think you only need a 1D noise function, but in practice
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2D is almost always better. For instance, if you're using the current frame
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number as the parameter for the noise, all objects will end up with the same
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noise value at each frame. By adding a second parameter on the second
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dimension, you can ensure that each gets a unique noise value and they don't
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all look identical.
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*/
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// 2D Multi-octave Simplex noise.
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//
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// For each octave, a higher frequency/lower amplitude function will be added to the original.
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// The higher the persistence [0-1], the more of each succeeding octave will be added.
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float octave_noise_2d( const float octaves, const float persistence, const float scale, const float x, const float y ) {
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float total = 0;
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float frequency = scale;
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float amplitude = 1;
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// We have to keep track of the largest possible amplitude,
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// because each octave adds more, and we need a value in [-1, 1].
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float maxAmplitude = 0;
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for( int i=0; i < octaves; i++ ) {
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total += raw_noise_2d( x * frequency, y * frequency ) * amplitude;
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frequency *= 2;
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maxAmplitude += amplitude;
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amplitude *= persistence;
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}
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return total / maxAmplitude;
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}
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// 3D Multi-octave Simplex noise.
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//
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// For each octave, a higher frequency/lower amplitude function will be added to the original.
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// The higher the persistence [0-1], the more of each succeeding octave will be added.
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float octave_noise_3d( const float octaves, const float persistence, const float scale, const float x, const float y, const float z ) {
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float total = 0;
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float frequency = scale;
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float amplitude = 1;
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// We have to keep track of the largest possible amplitude,
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// because each octave adds more, and we need a value in [-1, 1].
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float maxAmplitude = 0;
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for( int i=0; i < octaves; i++ ) {
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total += raw_noise_3d( x * frequency, y * frequency, z * frequency ) * amplitude;
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frequency *= 2;
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maxAmplitude += amplitude;
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amplitude *= persistence;
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}
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return total / maxAmplitude;
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}
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// 4D Multi-octave Simplex noise.
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//
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// For each octave, a higher frequency/lower amplitude function will be added to the original.
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// The higher the persistence [0-1], the more of each succeeding octave will be added.
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float octave_noise_4d( const float octaves, const float persistence, const float scale, const float x, const float y, const float z, const float w ) {
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float total = 0;
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float frequency = scale;
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float amplitude = 1;
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// We have to keep track of the largest possible amplitude,
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// because each octave adds more, and we need a value in [-1, 1].
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float maxAmplitude = 0;
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for( int i=0; i < octaves; i++ ) {
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total += raw_noise_4d( x * frequency, y * frequency, z * frequency, w * frequency ) * amplitude;
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frequency *= 2;
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maxAmplitude += amplitude;
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amplitude *= persistence;
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}
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return total / maxAmplitude;
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}
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// 2D Scaled Multi-octave Simplex noise.
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//
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// Returned value will be between loBound and hiBound.
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float scaled_octave_noise_2d( const float octaves, const float persistence, const float scale, const float loBound, const float hiBound, const float x, const float y ) {
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return octave_noise_2d(octaves, persistence, scale, x, y) * (hiBound - loBound) / 2 + (hiBound + loBound) / 2;
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}
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// 3D Scaled Multi-octave Simplex noise.
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//
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// Returned value will be between loBound and hiBound.
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float scaled_octave_noise_3d( const float octaves, const float persistence, const float scale, const float loBound, const float hiBound, const float x, const float y, const float z ) {
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return octave_noise_3d(octaves, persistence, scale, x, y, z) * (hiBound - loBound) / 2 + (hiBound + loBound) / 2;
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}
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// 4D Scaled Multi-octave Simplex noise.
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//
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// Returned value will be between loBound and hiBound.
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float scaled_octave_noise_4d( const float octaves, const float persistence, const float scale, const float loBound, const float hiBound, const float x, const float y, const float z, const float w ) {
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return octave_noise_4d(octaves, persistence, scale, x, y, z, w) * (hiBound - loBound) / 2 + (hiBound + loBound) / 2;
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}
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// 2D Scaled Simplex raw noise.
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//
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// Returned value will be between loBound and hiBound.
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float scaled_raw_noise_2d( const float loBound, const float hiBound, const float x, const float y ) {
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return raw_noise_2d(x, y) * (hiBound - loBound) / 2 + (hiBound + loBound) / 2;
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}
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// 3D Scaled Simplex raw noise.
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//
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// Returned value will be between loBound and hiBound.
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float scaled_raw_noise_3d( const float loBound, const float hiBound, const float x, const float y, const float z ) {
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return raw_noise_3d(x, y, z) * (hiBound - loBound) / 2 + (hiBound + loBound) / 2;
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}
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// 4D Scaled Simplex raw noise.
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//
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// Returned value will be between loBound and hiBound.
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float scaled_raw_noise_4d( const float loBound, const float hiBound, const float x, const float y, const float z, const float w ) {
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return raw_noise_4d(x, y, z, w) * (hiBound - loBound) / 2 + (hiBound + loBound) / 2;
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}
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// 2D raw Simplex noise
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float raw_noise_2d( const float x, const float y ) {
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// Noise contributions from the three corners
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float n0, n1, n2;
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// Skew the input space to determine which simplex cell we're in
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float F2 = 0.5 * (sqrtf(3.0) - 1.0);
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// Hairy factor for 2D
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float s = (x + y) * F2;
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int i = fastfloor( x + s );
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int j = fastfloor( y + s );
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float G2 = (3.0 - sqrtf(3.0)) / 6.0;
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float t = (i + j) * G2;
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// Unskew the cell origin back to (x,y) space
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float X0 = i-t;
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float Y0 = j-t;
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// The x,y distances from the cell origin
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float x0 = x-X0;
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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 - 1.0 + 2.0 * G2; // Offsets for last corner in (x,y) unskewed coords
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float y2 = y0 - 1.0 + 2.0 * G2;
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// Work out the hashed gradient indices of the three simplex corners
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int ii = i & 255;
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int jj = j & 255;
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uint8_t gi0 = perm[ii+perm[jj]] % 12;
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uint8_t gi1 = perm[ii+i1+perm[jj+j1]] % 12;
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uint8_t gi2 = perm[ii+1+perm[jj+1]] % 12;
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// Calculate the contribution from the three corners
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float t0 = 0.5 - x0*x0-y0*y0;
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if(t0<0) n0 = 0.0;
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else {
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t0 *= t0;
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n0 = t0 * t0 * dot(grad3[gi0], x0, y0); // (x,y) of grad3 used for 2D gradient
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}
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float t1 = 0.5 - x1*x1-y1*y1;
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if(t1<0) n1 = 0.0;
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else {
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t1 *= t1;
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n1 = t1 * t1 * dot(grad3[gi1], x1, y1);
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}
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float t2 = 0.5 - x2*x2-y2*y2;
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if(t2<0) n2 = 0.0;
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else {
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t2 *= t2;
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n2 = t2 * t2 * dot(grad3[gi2], 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 70.0 * (n0 + n1 + n2);
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}
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// 3D raw Simplex noise
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float raw_noise_3d( const float x, const float y, const float z ) {
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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 F3 = 1.0/3.0;
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float s = (x+y+z)*F3; // Very nice and simple skew factor for 3D
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int i = fastfloor(x+s);
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int j = fastfloor(y+s);
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int k = fastfloor(z+s);
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float G3 = 1.0/6.0; // Very nice and simple unskew factor, too
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float t = (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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if(x0>=y0) {
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if(y0>=z0) { 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 + 2.0*G3; // Offsets for third corner in (x,y,z) coords
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float y2 = y0 - j2 + 2.0*G3;
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float z2 = z0 - k2 + 2.0*G3;
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float x3 = x0 - 1.0 + 3.0*G3; // Offsets for last corner in (x,y,z) coords
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float y3 = y0 - 1.0 + 3.0*G3;
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float z3 = z0 - 1.0 + 3.0*G3;
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// Work out the hashed gradient indices of the four simplex corners
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int ii = i & 255;
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int jj = j & 255;
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int kk = k & 255;
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uint8_t gi0 = perm[ii+perm[jj+perm[kk]]] % 12;
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uint8_t gi1 = perm[ii+i1+perm[jj+j1+perm[kk+k1]]] % 12;
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uint8_t gi2 = perm[ii+i2+perm[jj+j2+perm[kk+k2]]] % 12;
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uint8_t gi3 = perm[ii+1+perm[jj+1+perm[kk+1]]] % 12;
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// Calculate the contribution from the four corners
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float t0 = 0.6 - x0*x0 - y0*y0 - z0*z0;
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if(t0<0) n0 = 0.0;
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else {
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t0 *= t0;
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n0 = t0 * t0 * dot(grad3[gi0], x0, y0, z0);
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}
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float t1 = 0.6 - x1*x1 - y1*y1 - z1*z1;
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if(t1<0) n1 = 0.0;
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else {
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t1 *= t1;
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n1 = t1 * t1 * dot(grad3[gi1], x1, y1, z1);
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}
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float t2 = 0.6 - x2*x2 - y2*y2 - z2*z2;
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if(t2<0) n2 = 0.0;
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else {
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t2 *= t2;
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n2 = t2 * t2 * dot(grad3[gi2], x2, y2, z2);
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}
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float t3 = 0.6 - x3*x3 - y3*y3 - z3*z3;
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if(t3<0) n3 = 0.0;
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else {
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t3 *= t3;
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n3 = t3 * t3 * dot(grad3[gi3], 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 32.0*(n0 + n1 + n2 + n3);
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}
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// 4D raw Simplex noise
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float raw_noise_4d( const float x, const float y, const float z, const float w ) {
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// The skewing and unskewing factors are hairy again for the 4D case
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float F4 = (sqrtf(5.0)-1.0)/4.0;
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float G4 = (5.0-sqrtf(5.0))/20.0;
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float n0, n1, n2, n3, n4; // Noise contributions from the five corners
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// Skew the (x,y,z,w) space to determine which cell of 24 simplices we're in
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float s = (x + y + z + w) * F4; // Factor for 4D skewing
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int i = fastfloor(x + s);
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int j = fastfloor(y + s);
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int k = fastfloor(z + s);
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int l = fastfloor(w + s);
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float t = (i + j + k + l) * G4; // Factor for 4D unskewing
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float X0 = i - t; // Unskew the cell origin back to (x,y,z,w) space
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float Y0 = j - t;
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float Z0 = k - t;
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float W0 = l - t;
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float x0 = x - X0; // The x,y,z,w 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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float w0 = w - W0;
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// For the 4D case, the simplex is a 4D shape I won't even try to describe.
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// To find out which of the 24 possible simplices we're in, we need to
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// determine the magnitude ordering of x0, y0, z0 and w0.
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// The method below is a good way of finding the ordering of x,y,z,w and
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// then find the correct traversal order for the simplex we're in.
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// First, six pair-wise comparisons are performed between each possible pair
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// of the four coordinates, and the results are used to add up binary bits
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// for an integer index.
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int c1 = (x0 > y0) ? 32 : 0;
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int c2 = (x0 > z0) ? 16 : 0;
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int c3 = (y0 > z0) ? 8 : 0;
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int c4 = (x0 > w0) ? 4 : 0;
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int c5 = (y0 > w0) ? 2 : 0;
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int c6 = (z0 > w0) ? 1 : 0;
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int c = c1 + c2 + c3 + c4 + c5 + c6;
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int i1, j1, k1, l1; // The integer offsets for the second simplex corner
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int i2, j2, k2, l2; // The integer offsets for the third simplex corner
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int i3, j3, k3, l3; // The integer offsets for the fourth simplex corner
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// simplex[c] is a 4-vector with the numbers 0, 1, 2 and 3 in some order.
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// Many values of c will never occur, since e.g. x>y>z>w makes x<z, y<w and x<w
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// impossible. Only the 24 indices which have non-zero entries make any sense.
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// We use a thresholding to set the coordinates in turn from the largest magnitude.
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// The number 3 in the "simplex" array is at the position of the largest coordinate.
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i1 = simplex[c][0]>=3 ? 1 : 0;
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j1 = simplex[c][1]>=3 ? 1 : 0;
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k1 = simplex[c][2]>=3 ? 1 : 0;
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l1 = simplex[c][3]>=3 ? 1 : 0;
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// The number 2 in the "simplex" array is at the second largest coordinate.
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i2 = simplex[c][0]>=2 ? 1 : 0;
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j2 = simplex[c][1]>=2 ? 1 : 0;
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k2 = simplex[c][2]>=2 ? 1 : 0;
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l2 = simplex[c][3]>=2 ? 1 : 0;
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// The number 1 in the "simplex" array is at the second smallest coordinate.
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i3 = simplex[c][0]>=1 ? 1 : 0;
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j3 = simplex[c][1]>=1 ? 1 : 0;
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k3 = simplex[c][2]>=1 ? 1 : 0;
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l3 = simplex[c][3]>=1 ? 1 : 0;
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// The fifth corner has all coordinate offsets = 1, so no need to look that up.
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float x1 = x0 - i1 + G4; // Offsets for second corner in (x,y,z,w) coords
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float y1 = y0 - j1 + G4;
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float z1 = z0 - k1 + G4;
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float w1 = w0 - l1 + G4;
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float x2 = x0 - i2 + 2.0*G4; // Offsets for third corner in (x,y,z,w) coords
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float y2 = y0 - j2 + 2.0*G4;
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float z2 = z0 - k2 + 2.0*G4;
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float w2 = w0 - l2 + 2.0*G4;
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float x3 = x0 - i3 + 3.0*G4; // Offsets for fourth corner in (x,y,z,w) coords
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float y3 = y0 - j3 + 3.0*G4;
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float z3 = z0 - k3 + 3.0*G4;
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float w3 = w0 - l3 + 3.0*G4;
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float x4 = x0 - 1.0 + 4.0*G4; // Offsets for last corner in (x,y,z,w) coords
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float y4 = y0 - 1.0 + 4.0*G4;
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float z4 = z0 - 1.0 + 4.0*G4;
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float w4 = w0 - 1.0 + 4.0*G4;
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// Work out the hashed gradient indices of the five simplex corners
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int ii = i & 255;
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int jj = j & 255;
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int kk = k & 255;
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int ll = l & 255;
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uint8_t gi0 = perm[ii+perm[jj+perm[kk+perm[ll]]]] % 32;
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uint8_t gi1 = perm[ii+i1+perm[jj+j1+perm[kk+k1+perm[ll+l1]]]] % 32;
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uint8_t gi2 = perm[ii+i2+perm[jj+j2+perm[kk+k2+perm[ll+l2]]]] % 32;
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uint8_t gi3 = perm[ii+i3+perm[jj+j3+perm[kk+k3+perm[ll+l3]]]] % 32;
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uint8_t gi4 = perm[ii+1+perm[jj+1+perm[kk+1+perm[ll+1]]]] % 32;
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// Calculate the contribution from the five corners
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float t0 = 0.6 - x0*x0 - y0*y0 - z0*z0 - w0*w0;
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if(t0<0) n0 = 0.0;
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else {
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t0 *= t0;
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n0 = t0 * t0 * dot(grad4[gi0], x0, y0, z0, w0);
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}
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float t1 = 0.6 - x1*x1 - y1*y1 - z1*z1 - w1*w1;
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if(t1<0) n1 = 0.0;
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else {
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t1 *= t1;
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n1 = t1 * t1 * dot(grad4[gi1], x1, y1, z1, w1);
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}
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float t2 = 0.6 - x2*x2 - y2*y2 - z2*z2 - w2*w2;
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if(t2<0) n2 = 0.0;
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else {
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t2 *= t2;
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n2 = t2 * t2 * dot(grad4[gi2], x2, y2, z2, w2);
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}
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float t3 = 0.6 - x3*x3 - y3*y3 - z3*z3 - w3*w3;
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if(t3<0) n3 = 0.0;
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else {
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t3 *= t3;
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n3 = t3 * t3 * dot(grad4[gi3], x3, y3, z3, w3);
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}
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float t4 = 0.6 - x4*x4 - y4*y4 - z4*z4 - w4*w4;
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if(t4<0) n4 = 0.0;
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else {
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t4 *= t4;
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n4 = t4 * t4 * dot(grad4[gi4], x4, y4, z4, w4);
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}
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// Sum up and scale the result to cover the range [-1,1]
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return 27.0 * (n0 + n1 + n2 + n3 + n4);
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}
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int fastfloor( const float x ) { return x > 0 ? (int) x : (int) x - 1; }
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float dot( const int8_t* g, const float x, const float y ) { return g[0]*x + g[1]*y; }
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float dot( const int8_t* g, const float x, const float y, const float z ) { return g[0]*x + g[1]*y + g[2]*z; }
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float dot( const int8_t* g, const float x, const float y, const float z, const float w ) { return g[0]*x + g[1]*y + g[2]*z + g[3]*w; }
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