minetest/src/noise.cpp

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/*
Minetest-c55
Copyright (C) 2010-2011 celeron55, Perttu Ahola <celeron55@gmail.com>
This program 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; either version 2 of the License, or
(at your option) any later version.
This program 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 this program; if not, write to the Free Software Foundation, Inc.,
51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
*/
#include <math.h>
#include "noise.h"
#include <iostream>
#include "debug.h"
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#define NOISE_MAGIC_X 1619
#define NOISE_MAGIC_Y 31337
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#define NOISE_MAGIC_Z 52591
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#define NOISE_MAGIC_SEED 1013
double cos_lookup[16] = {
1.0,0.9238,0.7071,0.3826,0,-0.3826,-0.7071,-0.9238,
1.0,-0.9238,-0.7071,-0.3826,0,0.3826,0.7071,0.9238
};
double dotProduct(double vx, double vy, double wx, double wy){
return vx*wx+vy*wy;
}
double easeCurve(double t){
return 6*pow(t,5)-15*pow(t,4)+10*pow(t,3);
}
double linearInterpolation(double x0, double x1, double t){
return x0+(x1-x0)*t;
}
double biLinearInterpolation(double x0y0, double x1y0, double x0y1, double x1y1, double x, double y){
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double tx = easeCurve(x);
double ty = easeCurve(y);
/*double tx = x;
double ty = y;*/
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double u = linearInterpolation(x0y0,x1y0,tx);
double v = linearInterpolation(x0y1,x1y1,tx);
return linearInterpolation(u,v,ty);
}
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double triLinearInterpolation(
double v000, double v100, double v010, double v110,
double v001, double v101, double v011, double v111,
double x, double y, double z)
{
/*double tx = easeCurve(x);
double ty = easeCurve(y);
double tz = easeCurve(z);*/
double tx = x;
double ty = y;
double tz = z;
return(
v000*(1-tx)*(1-ty)*(1-tz) +
v100*tx*(1-ty)*(1-tz) +
v010*(1-tx)*ty*(1-tz) +
v110*tx*ty*(1-tz) +
v001*(1-tx)*(1-ty)*tz +
v101*tx*(1-ty)*tz +
v011*(1-tx)*ty*tz +
v111*tx*ty*tz
);
}
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double noise2d(int x, int y, int seed)
{
int n = (NOISE_MAGIC_X * x + NOISE_MAGIC_Y * y
+ NOISE_MAGIC_SEED * seed) & 0x7fffffff;
n = (n>>13)^n;
n = (n * (n*n*60493+19990303) + 1376312589) & 0x7fffffff;
return 1.0 - (double)n/1073741824;
}
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double noise3d(int x, int y, int z, int seed)
{
int n = (NOISE_MAGIC_X * x + NOISE_MAGIC_Y * y + NOISE_MAGIC_Z * z
+ NOISE_MAGIC_SEED * seed) & 0x7fffffff;
n = (n>>13)^n;
n = (n * (n*n*60493+19990303) + 1376312589) & 0x7fffffff;
return 1.0 - (double)n/1073741824;
}
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#if 0
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double noise2d_gradient(double x, double y, int seed)
{
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// Calculate the integer coordinates
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int x0 = (x > 0.0 ? (int)x : (int)x - 1);
int y0 = (y > 0.0 ? (int)y : (int)y - 1);
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// Calculate the remaining part of the coordinates
double xl = x - (double)x0;
double yl = y - (double)y0;
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// Calculate random cosine lookup table indices for the integer corners.
// They are looked up as unit vector gradients from the lookup table.
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int n00 = (int)((noise2d(x0, y0, seed)+1)*8);
int n10 = (int)((noise2d(x0+1, y0, seed)+1)*8);
int n01 = (int)((noise2d(x0, y0+1, seed)+1)*8);
int n11 = (int)((noise2d(x0+1, y0+1, seed)+1)*8);
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// Make a dot product for the gradients and the positions, to get the values
double s = dotProduct(cos_lookup[n00], cos_lookup[(n00+12)%16], xl, yl);
double u = dotProduct(-cos_lookup[n10], cos_lookup[(n10+12)%16], 1.-xl, yl);
double v = dotProduct(cos_lookup[n01], -cos_lookup[(n01+12)%16], xl, 1.-yl);
double w = dotProduct(-cos_lookup[n11], -cos_lookup[(n11+12)%16], 1.-xl, 1.-yl);
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// Interpolate between the values
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return biLinearInterpolation(s,u,v,w,xl,yl);
}
#endif
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#if 1
double noise2d_gradient(double x, double y, int seed)
{
// Calculate the integer coordinates
int x0 = (x > 0.0 ? (int)x : (int)x - 1);
int y0 = (y > 0.0 ? (int)y : (int)y - 1);
// Calculate the remaining part of the coordinates
double xl = x - (double)x0;
double yl = y - (double)y0;
// Get values for corners of cube
double v00 = noise2d(x0, y0, seed);
double v10 = noise2d(x0+1, y0, seed);
double v01 = noise2d(x0, y0+1, seed);
double v11 = noise2d(x0+1, y0+1, seed);
// Interpolate
return biLinearInterpolation(v00,v10,v01,v11,xl,yl);
}
#endif
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double noise3d_gradient(double x, double y, double z, int seed)
{
// Calculate the integer coordinates
int x0 = (x > 0.0 ? (int)x : (int)x - 1);
int y0 = (y > 0.0 ? (int)y : (int)y - 1);
int z0 = (z > 0.0 ? (int)z : (int)z - 1);
// Calculate the remaining part of the coordinates
double xl = x - (double)x0;
double yl = y - (double)y0;
double zl = z - (double)z0;
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// Get values for corners of cube
double v000 = noise3d(x0, y0, z0, seed);
double v100 = noise3d(x0+1, y0, z0, seed);
double v010 = noise3d(x0, y0+1, z0, seed);
double v110 = noise3d(x0+1, y0+1, z0, seed);
double v001 = noise3d(x0, y0, z0+1, seed);
double v101 = noise3d(x0+1, y0, z0+1, seed);
double v011 = noise3d(x0, y0+1, z0+1, seed);
double v111 = noise3d(x0+1, y0+1, z0+1, seed);
// Interpolate
return triLinearInterpolation(v000,v100,v010,v110,v001,v101,v011,v111,xl,yl,zl);
}
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double noise2d_perlin(double x, double y, int seed,
int octaves, double persistence)
{
double a = 0;
double f = 1.0;
double g = 1.0;
for(int i=0; i<octaves; i++)
{
a += g * noise2d_gradient(x*f, y*f, seed+i);
f *= 2.0;
g *= persistence;
}
return a;
}
double noise2d_perlin_abs(double x, double y, int seed,
int octaves, double persistence)
{
double a = 0;
double f = 1.0;
double g = 1.0;
for(int i=0; i<octaves; i++)
{
a += g * fabs(noise2d_gradient(x*f, y*f, seed+i));
f *= 2.0;
g *= persistence;
}
return a;
}
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double noise3d_perlin(double x, double y, double z, int seed,
int octaves, double persistence)
{
double a = 0;
double f = 1.0;
double g = 1.0;
for(int i=0; i<octaves; i++)
{
a += g * noise3d_gradient(x*f, y*f, z*f, seed+i);
f *= 2.0;
g *= persistence;
}
return a;
}
double noise3d_perlin_abs(double x, double y, double z, int seed,
int octaves, double persistence)
{
double a = 0;
double f = 1.0;
double g = 1.0;
for(int i=0; i<octaves; i++)
{
a += g * fabs(noise3d_gradient(x*f, y*f, z*f, seed+i));
f *= 2.0;
g *= persistence;
}
return a;
}
/*
NoiseBuffer
*/
NoiseBuffer::NoiseBuffer():
m_data(NULL)
{
}
NoiseBuffer::~NoiseBuffer()
{
clear();
}
void NoiseBuffer::clear()
{
if(m_data)
delete[] m_data;
m_data = NULL;
m_size_x = 0;
m_size_y = 0;
m_size_z = 0;
}
void NoiseBuffer::create(int seed, int octaves, double persistence,
double pos_scale,
double first_x, double first_y, double first_z,
double last_x, double last_y, double last_z,
double samplelength_x, double samplelength_y, double samplelength_z)
{
clear();
m_start_x = first_x - samplelength_x;
m_start_y = first_y - samplelength_y;
m_start_z = first_z - samplelength_z;
m_samplelength_x = samplelength_x;
m_samplelength_y = samplelength_y;
m_samplelength_z = samplelength_z;
m_size_x = (last_x - m_start_x)/samplelength_x + 2;
m_size_y = (last_y - m_start_y)/samplelength_y + 2;
m_size_z = (last_z - m_start_z)/samplelength_z + 2;
/*dstream<<"m_size_x="<<m_size_x<<", m_size_y="<<m_size_y
<<", m_size_z="<<m_size_z<<std::endl;*/
m_data = new double[m_size_x*m_size_y*m_size_z];
for(int x=0; x<m_size_x; x++)
for(int y=0; y<m_size_y; y++)
for(int z=0; z<m_size_z; z++)
{
double xd = (m_start_x + (double)x*m_samplelength_x)/pos_scale;
double yd = (m_start_y + (double)y*m_samplelength_y)/pos_scale;
double zd = (m_start_z + (double)z*m_samplelength_z)/pos_scale;
intSet(x,y,z, noise3d_perlin(xd,yd,zd,seed,octaves,persistence));
}
}
void NoiseBuffer::intSet(int x, int y, int z, double d)
{
int i = m_size_x*m_size_y*z + m_size_x*y + x;
assert(i >= 0);
assert(i < m_size_x*m_size_y*m_size_z);
m_data[i] = d;
}
double NoiseBuffer::intGet(int x, int y, int z)
{
int i = m_size_x*m_size_y*z + m_size_x*y + x;
assert(i >= 0);
assert(i < m_size_x*m_size_y*m_size_z);
return m_data[i];
}
double NoiseBuffer::get(double x, double y, double z)
{
x -= m_start_x;
y -= m_start_y;
z -= m_start_z;
x /= m_samplelength_x;
y /= m_samplelength_y;
z /= m_samplelength_z;
// Calculate the integer coordinates
int x0 = (x > 0.0 ? (int)x : (int)x - 1);
int y0 = (y > 0.0 ? (int)y : (int)y - 1);
int z0 = (z > 0.0 ? (int)z : (int)z - 1);
// Calculate the remaining part of the coordinates
double xl = x - (double)x0;
double yl = y - (double)y0;
double zl = z - (double)z0;
// Get values for corners of cube
double v000 = intGet(x0, y0, z0);
double v100 = intGet(x0+1, y0, z0);
double v010 = intGet(x0, y0+1, z0);
double v110 = intGet(x0+1, y0+1, z0);
double v001 = intGet(x0, y0, z0+1);
double v101 = intGet(x0+1, y0, z0+1);
double v011 = intGet(x0, y0+1, z0+1);
double v111 = intGet(x0+1, y0+1, z0+1);
// Interpolate
return triLinearInterpolation(v000,v100,v010,v110,v001,v101,v011,v111,xl,yl,zl);
}