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perlin.cpp
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perlin.cpp
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// Copyright © 2008-2012 Pioneer Developers. See AUTHORS.txt for details
// Licensed under the terms of the GPL v3. See licenses/GPL-3.txt
#include <math.h>
/* Simplex.cpp
*
* Copyright 2007 Eliot Eshelman
* battlestartux@6by9.net
*
*
* This file is part of Battlestar Tux.
*
* Battlestar Tux is free software; you can redistribute it and/or modify
* it under the terms of the GNU General Public License as published by
* the Free Software Foundation; version 2 of the License.
*
* Battlestar Tux is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
* GNU General Public License for more details.
*
* You should have received a copy of the GNU General Public License
* along with Battlestar Tux; if not, write to the Free Software
* Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
*
*/
/*
* I noticed this file was GPL2, not 2+, and thus incompatible with the GPL3.
* I emailed the author asking for permission to use it under GPL3. His
* response:
*
* From: Eliot Eshelman <eliot.eshelman@6by9.net>
* To: Robert Norris <rob@eatenbyagrue.org>
* Date: Sat, 16 Jul 2011 09:32:36 -0400
* Subject: Re: License for Battlestar TUX
* Message-ID: <CA+5Z5RTS2_wNLz-eBRi93Zi2VW3zEGPsVLWMrT=grEVPpKLFEQ@mail.gmail.com>
*
* Hi Rob,
*
* I'm glad you've found Simplex useful.
*
* You are correct - the headers need updating. The project is GPLv3. You may
* re-use Simplex.cpp in your GPL3 project.
*
* If you feel this covers you, please go ahead and continue to use the file.
* If it would be more appropriate for me to provide an updated file, I can do
* so.
*
* Best,
* Eliot
*/
static int fastfloor( const double x ) { return int(x > 0 ? x : x - 1); }
//static double dot( const int* g, const double x, const double y ) { return g[0]*x + g[1]*y; }
static double dot( const double* g, const double x, const double y, const double z ) { return g[0]*x + g[1]*y + g[2]*z; }
//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; }
// The gradients are the midpoints of the vertices of a cube.
static const double grad3[12][3] = {
{1,1,0}, {-1,1,0}, {1,-1,0}, {-1,-1,0},
{1,0,1}, {-1,0,1}, {1,0,-1}, {-1,0,-1},
{0,1,1}, {0,-1,1}, {0,1,-1}, {0,-1,-1}
};
// Permutation table. The same list is repeated twice.
static const unsigned char perm[512] = {
151,160,137,91,90,15,131,13,201,95,96,53,194,233,7,225,140,36,103,30,69,142,
8,99,37,240,21,10,23,190,6,148,247,120,234,75,0,26,197,62,94,252,219,203,117,
35,11,32,57,177,33,88,237,149,56,87,174,20,125,136,171,168,68,175,74,165,71,
134,139,48,27,166,77,146,158,231,83,111,229,122,60,211,133,230,220,105,92,41,
55,46,245,40,244,102,143,54,65,25,63,161,1,216,80,73,209,76,132,187,208, 89,
18,169,200,196,135,130,116,188,159,86,164,100,109,198,173,186,3,64,52,217,226,
250,124,123,5,202,38,147,118,126,255,82,85,212,207,206,59,227,47,16,58,17,182,
189,28,42,223,183,170,213,119,248,152,2,44,154,163,70,221,153,101,155,167,43,
172,9,129,22,39,253,19,98,108,110,79,113,224,232,178,185,112,104,218,246,97,
228,251,34,242,193,238,210,144,12,191,179,162,241,81,51,145,235,249,14,239,
107,49,192,214,31,181,199,106,157,184,84,204,176,115,121,50,45,127,4,150,254,
138,236,205,93,222,114,67,29,24,72,243,141,128,195,78,66,215,61,156,180,
151,160,137,91,90,15,131,13,201,95,96,53,194,233,7,225,140,36,103,30,69,142,
8,99,37,240,21,10,23,190,6,148,247,120,234,75,0,26,197,62,94,252,219,203,117,
35,11,32,57,177,33,88,237,149,56,87,174,20,125,136,171,168,68,175,74,165,71,
134,139,48,27,166,77,146,158,231,83,111,229,122,60,211,133,230,220,105,92,41,
55,46,245,40,244,102,143,54,65,25,63,161,1,216,80,73,209,76,132,187,208, 89,
18,169,200,196,135,130,116,188,159,86,164,100,109,198,173,186,3,64,52,217,226,
250,124,123,5,202,38,147,118,126,255,82,85,212,207,206,59,227,47,16,58,17,182,
189,28,42,223,183,170,213,119,248,152,2,44,154,163,70,221,153,101,155,167,43,
172,9,129,22,39,253,19,98,108,110,79,113,224,232,178,185,112,104,218,246,97,
228,251,34,242,193,238,210,144,12,191,179,162,241,81,51,145,235,249,14,239,
107,49,192,214,31,181,199,106,157,184,84,204,176,115,121,50,45,127,4,150,254,
138,236,205,93,222,114,67,29,24,72,243,141,128,195,78,66,215,61,156,180
};
static const unsigned char mod12[] = {
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,
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,
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,
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,
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,
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,
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,
5,6,7,8,9,10,11,0,1,2,3,
};
// 3D raw Simplex noise
double noise( const double x, const double y, const double z ) {
double n0, n1, n2, n3; // Noise contributions from the four corners
// Skew the input space to determine which simplex cell we're in
const double F3 = 1.0/3.0;
double s = (x+y+z)*F3; // Very nice and simple skew factor for 3D
int i = fastfloor(x+s);
int j = fastfloor(y+s);
int k = fastfloor(z+s);
const double G3 = 1.0/6.0; // Very nice and simple unskew factor, too
double t = (i+j+k)*G3;
double X0 = i-t; // Unskew the cell origin back to (x,y,z) space
double Y0 = j-t;
double Z0 = k-t;
double x0 = x-X0; // The x,y,z distances from the cell origin
double y0 = y-Y0;
double z0 = z-Z0;
// For the 3D case, the simplex shape is a slightly irregular tetrahedron.
// Determine which simplex we are in.
int i1, j1, k1; // Offsets for second corner of simplex in (i,j,k) coords
int i2, j2, k2; // Offsets for third corner of simplex in (i,j,k) coords
if(x0>=y0) {
if(y0>=z0)
{ i1=1; j1=0; k1=0; i2=1; j2=1; k2=0; } // X Y Z order
else if(x0>=z0) { i1=1; j1=0; k1=0; i2=1; j2=0; k2=1; } // X Z Y order
else { i1=0; j1=0; k1=1; i2=1; j2=0; k2=1; } // Z X Y order
}
else { // x0<y0
if(y0<z0) { i1=0; j1=0; k1=1; i2=0; j2=1; k2=1; } // Z Y X order
else if(x0<z0) { i1=0; j1=1; k1=0; i2=0; j2=1; k2=1; } // Y Z X order
else { i1=0; j1=1; k1=0; i2=1; j2=1; k2=0; } // Y X Z order
}
// A step of (1,0,0) in (i,j,k) means a step of (1-c,-c,-c) in (x,y,z),
// a step of (0,1,0) in (i,j,k) means a step of (-c,1-c,-c) in (x,y,z), and
// a step of (0,0,1) in (i,j,k) means a step of (-c,-c,1-c) in (x,y,z), where
// c = 1/6.
double x1 = x0 - i1 + G3; // Offsets for second corner in (x,y,z) coords
double y1 = y0 - j1 + G3;
double z1 = z0 - k1 + G3;
double x2 = x0 - i2 + 2.0*G3; // Offsets for third corner in (x,y,z) coords
double y2 = y0 - j2 + 2.0*G3;
double z2 = z0 - k2 + 2.0*G3;
double x3 = x0 - 1.0 + 3.0*G3; // Offsets for last corner in (x,y,z) coords
double y3 = y0 - 1.0 + 3.0*G3;
double z3 = z0 - 1.0 + 3.0*G3;
// Work out the hashed gradient indices of the four simplex corners
int ii = i & 255;
int jj = j & 255;
int kk = k & 255;
int gi0 = mod12[perm[ii+perm[jj+perm[kk]]]];
int gi1 = mod12[perm[ii+i1+perm[jj+j1+perm[kk+k1]]]];
int gi2 = mod12[perm[ii+i2+perm[jj+j2+perm[kk+k2]]]];
int gi3 = mod12[perm[ii+1+perm[jj+1+perm[kk+1]]]];
// Calculate the contribution from the four corners
double t0 = 0.6 - x0*x0 - y0*y0 - z0*z0;
if(t0<0) n0 = 0.0;
else {
t0 *= t0;
n0 = t0 * t0 * dot(grad3[gi0], x0, y0, z0);
}
double t1 = 0.6 - x1*x1 - y1*y1 - z1*z1;
if(t1<0) n1 = 0.0;
else {
t1 *= t1;
n1 = t1 * t1 * dot(grad3[gi1], x1, y1, z1);
}
double t2 = 0.6 - x2*x2 - y2*y2 - z2*z2;
if(t2<0) n2 = 0.0;
else {
t2 *= t2;
n2 = t2 * t2 * dot(grad3[gi2], x2, y2, z2);
}
double t3 = 0.6 - x3*x3 - y3*y3 - z3*z3;
if(t3<0) n3 = 0.0;
else {
t3 *= t3;
n3 = t3 * t3 * dot(grad3[gi3], x3, y3, z3);
}
// Add contributions from each corner to get the final noise value.
// The result is scaled to stay just inside [-1,1]
return 32.0*(n0 + n1 + n2 + n3);
}
#ifdef UNIT_TEST
#include <stdlib.h>
#include <stdio.h>
int main()
{
double x,y,z;
double a = 0.0;
x = 0.0; y = 0.0; z = 0.0;
for (int i=0; i<10000000; i++) {
a += noise(x,y,z);
x += 0.1;
y += 0.2;
z += 0.3;
}
return (int)a;
}
#endif /* UNIT_TEST */