271 lines
9.6 KiB
C++
271 lines
9.6 KiB
C++
// Copyright © 2008-2021 Pioneer Developers. See AUTHORS.txt for details
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// Licensed under the terms of the GPL v3. See licenses/GPL-3.txt
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#include "perlin.h"
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#include <math.h>
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/* Simplex.cpp
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*
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* Copyright 2007 Eliot Eshelman
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* battlestartux@6by9.net
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*
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*
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* This file is part of Battlestar Tux.
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*
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* Battlestar Tux 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; version 2 of the License.
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*
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* Battlestar Tux 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 Battlestar Tux; if not, write to the Free Software
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* Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
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*
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*/
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/*
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* I noticed this file was GPL2, not 2+, and thus incompatible with the GPL3.
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* I emailed the author asking for permission to use it under GPL3. His
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* response:
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*
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* From: Eliot Eshelman <eliot.eshelman@6by9.net>
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* To: Robert Norris <rob@eatenbyagrue.org>
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* Date: Sat, 16 Jul 2011 09:32:36 -0400
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* Subject: Re: License for Battlestar TUX
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* Message-ID: <CA+5Z5RTS2_wNLz-eBRi93Zi2VW3zEGPsVLWMrT=grEVPpKLFEQ@mail.gmail.com>
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*
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* Hi Rob,
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*
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* I'm glad you've found Simplex useful.
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*
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* You are correct - the headers need updating. The project is GPLv3. You may
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* re-use Simplex.cpp in your GPL3 project.
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*
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* If you feel this covers you, please go ahead and continue to use the file.
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* If it would be more appropriate for me to provide an updated file, I can do
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* so.
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*
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* Best,
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* Eliot
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*/
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inline int fastfloor(const double x) { return int(x > 0 ? x : x - 1); }
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//static double dot( const int* g, const double x, const double y ) { return g[0]*x + g[1]*y; }
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inline double dot(const double *g, const double x, const double y, const double z) { return g[0] * x + g[1] * y + g[2] * z; }
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//static double dot( const int* g, const double x, const double y, const double z, const double w ) { return g[0]*x + g[1]*y + g[2]*z + g[3]*w; }
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// The gradients are the midpoints of the vertices of a cube.
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static const double grad3[12][3] = {
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{ 1, 1, 0 }, { -1, 1, 0 }, { 1, -1, 0 }, { -1, -1, 0 },
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{ 1, 0, 1 }, { -1, 0, 1 }, { 1, 0, -1 }, { -1, 0, -1 },
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{ 0, 1, 1 }, { 0, -1, 1 }, { 0, 1, -1 }, { 0, -1, -1 }
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};
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// Permutation table. The same list is repeated twice.
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static const unsigned char perm[512] = {
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151, 160, 137, 91, 90, 15, 131, 13, 201, 95, 96, 53, 194, 233, 7, 225, 140, 36, 103, 30, 69, 142,
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8, 99, 37, 240, 21, 10, 23, 190, 6, 148, 247, 120, 234, 75, 0, 26, 197, 62, 94, 252, 219, 203, 117,
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35, 11, 32, 57, 177, 33, 88, 237, 149, 56, 87, 174, 20, 125, 136, 171, 168, 68, 175, 74, 165, 71,
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134, 139, 48, 27, 166, 77, 146, 158, 231, 83, 111, 229, 122, 60, 211, 133, 230, 220, 105, 92, 41,
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55, 46, 245, 40, 244, 102, 143, 54, 65, 25, 63, 161, 1, 216, 80, 73, 209, 76, 132, 187, 208, 89,
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18, 169, 200, 196, 135, 130, 116, 188, 159, 86, 164, 100, 109, 198, 173, 186, 3, 64, 52, 217, 226,
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250, 124, 123, 5, 202, 38, 147, 118, 126, 255, 82, 85, 212, 207, 206, 59, 227, 47, 16, 58, 17, 182,
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189, 28, 42, 223, 183, 170, 213, 119, 248, 152, 2, 44, 154, 163, 70, 221, 153, 101, 155, 167, 43,
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172, 9, 129, 22, 39, 253, 19, 98, 108, 110, 79, 113, 224, 232, 178, 185, 112, 104, 218, 246, 97,
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228, 251, 34, 242, 193, 238, 210, 144, 12, 191, 179, 162, 241, 81, 51, 145, 235, 249, 14, 239,
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107, 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, 131, 13, 201, 95, 96, 53, 194, 233, 7, 225, 140, 36, 103, 30, 69, 142,
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8, 99, 37, 240, 21, 10, 23, 190, 6, 148, 247, 120, 234, 75, 0, 26, 197, 62, 94, 252, 219, 203, 117,
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35, 11, 32, 57, 177, 33, 88, 237, 149, 56, 87, 174, 20, 125, 136, 171, 168, 68, 175, 74, 165, 71,
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134, 139, 48, 27, 166, 77, 146, 158, 231, 83, 111, 229, 122, 60, 211, 133, 230, 220, 105, 92, 41,
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55, 46, 245, 40, 244, 102, 143, 54, 65, 25, 63, 161, 1, 216, 80, 73, 209, 76, 132, 187, 208, 89,
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18, 169, 200, 196, 135, 130, 116, 188, 159, 86, 164, 100, 109, 198, 173, 186, 3, 64, 52, 217, 226,
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250, 124, 123, 5, 202, 38, 147, 118, 126, 255, 82, 85, 212, 207, 206, 59, 227, 47, 16, 58, 17, 182,
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189, 28, 42, 223, 183, 170, 213, 119, 248, 152, 2, 44, 154, 163, 70, 221, 153, 101, 155, 167, 43,
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172, 9, 129, 22, 39, 253, 19, 98, 108, 110, 79, 113, 224, 232, 178, 185, 112, 104, 218, 246, 97,
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228, 251, 34, 242, 193, 238, 210, 144, 12, 191, 179, 162, 241, 81, 51, 145, 235, 249, 14, 239,
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107, 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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static const unsigned char mod12[] = {
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0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10,
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11, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9,
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10, 11, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 0, 1, 2, 3, 4, 5, 6, 7, 8,
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9, 10, 11, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 0, 1, 2, 3, 4, 5, 6, 7,
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8, 9, 10, 11, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 0, 1, 2, 3, 4, 5, 6,
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7, 8, 9, 10, 11, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 0, 1, 2, 3, 4, 5,
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6, 7, 8, 9, 10, 11, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 0, 1, 2, 3, 4,
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5, 6, 7, 8, 9, 10, 11, 0, 1, 2, 3
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};
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const double F3 = 1.0 / 3.0;
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const double G3 = 1.0 / 6.0; // Very nice and simple unskew factor, too
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const double G3mul2 = 0.3333333333333333;
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const double G3mul3 = 0.5;
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// 3D raw Simplex noise
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double noise(const vector3d &p)
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{
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// Skew the input space to determine which simplex cell we're in
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const double s = (p.x + p.y + p.z) * F3; // Very nice and simple skew factor for 3D
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const int i = fastfloor(p.x + s);
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const int j = fastfloor(p.y + s);
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const int k = fastfloor(p.z + s);
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const double t = (i + j + k) * G3;
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const double X0 = i - t; // Unskew the cell origin back to (x,y,z) space
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const double Y0 = j - t;
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const double Z0 = k - t;
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const double x0 = p.x - X0; // The x,y,z distances from the cell origin
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const double y0 = p.y - Y0;
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const double z0 = p.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) {
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i1 = 1;
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j1 = 0;
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k1 = 0;
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i2 = 1;
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j2 = 1;
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k2 = 0;
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} // X Y Z order
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else if (x0 >= z0) {
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i1 = 1;
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j1 = 0;
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k1 = 0;
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i2 = 1;
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j2 = 0;
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k2 = 1;
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} // X Z Y order
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else {
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i1 = 0;
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j1 = 0;
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k1 = 1;
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i2 = 1;
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j2 = 0;
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k2 = 1;
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} // Z X Y order
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} else { // x0<y0
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if (y0 < z0) {
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i1 = 0;
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j1 = 0;
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k1 = 1;
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i2 = 0;
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j2 = 1;
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k2 = 1;
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} // Z Y X order
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else if (x0 < z0) {
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i1 = 0;
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j1 = 1;
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k1 = 0;
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i2 = 0;
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j2 = 1;
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k2 = 1;
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} // Y Z X order
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else {
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i1 = 0;
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j1 = 1;
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k1 = 0;
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i2 = 1;
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j2 = 1;
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k2 = 0;
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} // 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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const double x1 = x0 - i1 + G3; // Offsets for second corner in (x,y,z) coords
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const double y1 = y0 - j1 + G3;
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const double z1 = z0 - k1 + G3;
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const double x2 = x0 - i2 + G3mul2; // Offsets for third corner in (x,y,z) coords
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const double y2 = y0 - j2 + G3mul2;
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const double z2 = z0 - k2 + G3mul2;
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const double x3 = x0 - 1.0 + G3mul3; // Offsets for last corner in (x,y,z) coords
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const double y3 = y0 - 1.0 + G3mul3;
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const double z3 = z0 - 1.0 + G3mul3;
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// Work out the hashed gradient indices of the four simplex corners
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const int ii = i & 255;
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const int jj = j & 255;
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const int kk = k & 255;
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const int gi0 = mod12[perm[ii + perm[jj + perm[kk]]]];
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const int gi1 = mod12[perm[ii + i1 + perm[jj + j1 + perm[kk + k1]]]];
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const int gi2 = mod12[perm[ii + i2 + perm[jj + j2 + perm[kk + k2]]]];
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const int gi3 = mod12[perm[ii + 1 + perm[jj + 1 + perm[kk + 1]]]];
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// Noise contributions from the four corners
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double n0, n1, n2, n3;
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// Calculate the contribution from the four corners
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double t0 = 0.6 - x0 * x0 - y0 * y0 - z0 * z0;
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if (t0 < 0)
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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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double t1 = 0.6 - x1 * x1 - y1 * y1 - z1 * z1;
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if (t1 < 0)
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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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double t2 = 0.6 - x2 * x2 - y2 * y2 - z2 * z2;
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if (t2 < 0)
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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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double t3 = 0.6 - x3 * x3 - y3 * y3 - z3 * z3;
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if (t3 < 0)
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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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#ifdef UNIT_TEST
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#include <stdio.h>
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#include <stdlib.h>
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int main()
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{
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double x, y, z;
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double a = 0.0;
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x = 0.0;
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y = 0.0;
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z = 0.0;
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for (int i = 0; i < 10000000; i++) {
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a += noise(x, y, z);
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x += 0.1;
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y += 0.2;
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z += 0.3;
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}
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return (int)a;
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}
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#endif /* UNIT_TEST */
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