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minetest/src/noise.cpp

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/*
Minetest
Copyright (C) 2010-2013 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 Lesser General Public License as published by
the Free Software Foundation; either version 2.1 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 Lesser General Public License for more details.
You should have received a copy of the GNU Lesser 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"
#include "util/numeric.h"
#define NOISE_MAGIC_X 1619
#define NOISE_MAGIC_Y 31337
#define NOISE_MAGIC_Z 52591
#define NOISE_MAGIC_SEED 1013
float 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
};
///////////////////////////////////////////////////////////////////////////////
//noise poly: p(n) = 60493n^3 + 19990303n + 137612589
float 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.f - (float)n / 0x40000000;
}
float 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.f - (float)n / 0x40000000;
}
float dotProduct(float vx, float vy, float wx, float wy) {
return vx * wx + vy * wy;
}
inline float linearInterpolation(float v0, float v1, float t) {
return v0 + (v1 - v0) * t;
}
float biLinearInterpolation(float v00, float v10,
float v01, float v11,
float x, float y) {
float tx = easeCurve(x);
float ty = easeCurve(y);
float u = linearInterpolation(v00, v10, tx);
float v = linearInterpolation(v01, v11, tx);
return linearInterpolation(u, v, ty);
}
float biLinearInterpolationNoEase(float x0y0, float x1y0,
float x0y1, float x1y1,
float x, float y) {
float u = linearInterpolation(x0y0, x1y0, x);
float v = linearInterpolation(x0y1, x1y1, x);
return linearInterpolation(u, v, y);
}
float triLinearInterpolation(
float v000, float v100, float v010, float v110,
float v001, float v101, float v011, float v111,
float x, float y, float z) {
float u = biLinearInterpolationNoEase(v000, v100, v010, v110, x, y);
float v = biLinearInterpolationNoEase(v001, v101, v011, v111, x, y);
return linearInterpolation(u, v, z);
}
#if 0
float triLinearInterpolation(
float v000, float v100, float v010, float v110,
float v001, float v101, float v011, float v111,
float x, float y, float z)
{
/*float tx = easeCurve(x);
float ty = easeCurve(y);
float tz = easeCurve(z);*/
float tx = x;
float ty = y;
float 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
);
}
#endif
#if 0
float noise2d_gradient(float x, float 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
float xl = x - (float)x0;
float yl = y - (float)y0;
// Calculate random cosine lookup table indices for the integer corners.
// They are looked up as unit vector gradients from the lookup table.
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);
// Make a dot product for the gradients and the positions, to get the values
float s = dotProduct(cos_lookup[n00], cos_lookup[(n00+12)%16], xl, yl);
float u = dotProduct(-cos_lookup[n10], cos_lookup[(n10+12)%16], 1.-xl, yl);
float v = dotProduct(cos_lookup[n01], -cos_lookup[(n01+12)%16], xl, 1.-yl);
float w = dotProduct(-cos_lookup[n11], -cos_lookup[(n11+12)%16], 1.-xl, 1.-yl);
// Interpolate between the values
return biLinearInterpolation(s,u,v,w,xl,yl);
}
#endif
float noise2d_gradient(float x, float y, int seed)
{
// Calculate the integer coordinates
int x0 = myfloor(x);
int y0 = myfloor(y);
// Calculate the remaining part of the coordinates
float xl = x - (float)x0;
float yl = y - (float)y0;
// Get values for corners of square
float v00 = noise2d(x0, y0, seed);
float v10 = noise2d(x0+1, y0, seed);
float v01 = noise2d(x0, y0+1, seed);
float v11 = noise2d(x0+1, y0+1, seed);
// Interpolate
return biLinearInterpolation(v00,v10,v01,v11,xl,yl);
}
float noise3d_gradient(float x, float y, float z, int seed)
{
// Calculate the integer coordinates
int x0 = myfloor(x);
int y0 = myfloor(y);
int z0 = myfloor(z);
// Calculate the remaining part of the coordinates
float xl = x - (float)x0;
float yl = y - (float)y0;
float zl = z - (float)z0;
// Get values for corners of cube
float v000 = noise3d(x0, y0, z0, seed);
float v100 = noise3d(x0 + 1, y0, z0, seed);
float v010 = noise3d(x0, y0 + 1, z0, seed);
float v110 = noise3d(x0 + 1, y0 + 1, z0, seed);
float v001 = noise3d(x0, y0, z0 + 1, seed);
float v101 = noise3d(x0 + 1, y0, z0 + 1, seed);
float v011 = noise3d(x0, y0 + 1, z0 + 1, seed);
float v111 = noise3d(x0 + 1, y0 + 1, z0 + 1, seed);
// Interpolate
return triLinearInterpolation(v000, v100, v010, v110,
v001, v101, v011, v111,
xl, yl, zl);
}
float noise2d_perlin(float x, float y, int seed,
int octaves, float persistence)
{
float a = 0;
float f = 1.0;
float 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;
}
float noise2d_perlin_abs(float x, float y, int seed,
int octaves, float persistence)
{
float a = 0;
float f = 1.0;
float 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;
}
float noise3d_perlin(float x, float y, float z, int seed,
int octaves, float persistence)
{
float a = 0;
float f = 1.0;
float 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;
}
float noise3d_perlin_abs(float x, float y, float z, int seed,
int octaves, float persistence)
{
float a = 0;
float f = 1.0;
float 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;
}
// -1->0, 0->1, 1->0
float contour(float v)
{
v = fabs(v);
if(v >= 1.0)
return 0.0;
return (1.0-v);
}
///////////////////////// [ New perlin stuff ] ////////////////////////////
Noise::Noise(NoiseParams *np, int seed, int sx, int sy) {
init(np, seed, sx, sy, 1);
}
Noise::Noise(NoiseParams *np, int seed, int sx, int sy, int sz) {
init(np, seed, sx, sy, sz);
}
void Noise::init(NoiseParams *np, int seed, int sx, int sy, int sz) {
this->np = np;
this->seed = seed;
this->sx = sx;
this->sy = sy;
this->sz = sz;
this->noisebuf = NULL;
resizeNoiseBuf(sz > 1);
this->buf = new float[sx * sy * sz];
this->result = new float[sx * sy * sz];
}
Noise::~Noise() {
delete[] buf;
delete[] result;
delete[] noisebuf;
}
void Noise::setSize(int sx, int sy) {
setSize(sx, sy, 1);
}
void Noise::setSize(int sx, int sy, int sz) {
this->sx = sx;
this->sy = sy;
this->sz = sz;
this->noisebuf = NULL;
resizeNoiseBuf(sz > 1);
delete[] buf;
delete[] result;
this->buf = new float[sx * sy * sz];
this->result = new float[sx * sy * sz];
}
void Noise::setSpreadFactor(v3f spread) {
this->np->spread = spread;
resizeNoiseBuf(sz > 1);
}
void Noise::setOctaves(int octaves) {
this->np->octaves = octaves;
resizeNoiseBuf(sz > 1);
}
void Noise::resizeNoiseBuf(bool is3d) {
int nlx, nly, nlz;
float ofactor;
//maximum possible spread value factor
ofactor = (float)(1 << (np->octaves - 1));
//noise lattice point count
//(int)(sz * spread * ofactor) is # of lattice points crossed due to length
// + 2 for the two initial endpoints
// + 1 for potentially crossing a boundary due to offset
nlx = (int)(sx * ofactor / np->spread.X) + 3;
nly = (int)(sy * ofactor / np->spread.Y) + 3;
nlz = is3d ? (int)(sz * ofactor / np->spread.Z) + 3 : 1;
if (noisebuf)
delete[] noisebuf;
noisebuf = new float[nlx * nly * nlz];
}
/*
* NB: This algorithm is not optimal in terms of space complexity. The entire
* integer lattice of noise points could be done as 2 lines instead, and for 3D,
* 2 lines + 2 planes.
* However, this would require the noise calls to be interposed with the
* interpolation loops, which may trash the icache, leading to lower overall
* performance.
* Another optimization that could save half as many noise calls is to carry over
* values from the previous noise lattice as midpoints in the new lattice for the
* next octave.
*/
#define idx(x, y) ((y) * nlx + (x))
void Noise::gradientMap2D(float x, float y, float step_x, float step_y, int seed) {
float v00, v01, v10, v11, u, v, orig_u;
int index, i, j, x0, y0, noisex, noisey;
int nlx, nly;
x0 = floor(x);
y0 = floor(y);
u = x - (float)x0;
v = y - (float)y0;
orig_u = u;
//calculate noise point lattice
nlx = (int)(u + sx * step_x) + 2;
nly = (int)(v + sy * step_y) + 2;
index = 0;
for (j = 0; j != nly; j++)
for (i = 0; i != nlx; i++)
noisebuf[index++] = noise2d(x0 + i, y0 + j, seed);
//calculate interpolations
index = 0;
noisey = 0;
for (j = 0; j != sy; j++) {
v00 = noisebuf[idx(0, noisey)];
v10 = noisebuf[idx(1, noisey)];
v01 = noisebuf[idx(0, noisey + 1)];
v11 = noisebuf[idx(1, noisey + 1)];
u = orig_u;
noisex = 0;
for (i = 0; i != sx; i++) {
buf[index++] = biLinearInterpolation(v00, v10, v01, v11, u, v);
u += step_x;
if (u >= 1.0) {
u -= 1.0;
noisex++;
v00 = v10;
v01 = v11;
v10 = noisebuf[idx(noisex + 1, noisey)];
v11 = noisebuf[idx(noisex + 1, noisey + 1)];
}
}
v += step_y;
if (v >= 1.0) {
v -= 1.0;
noisey++;
}
}
}
#undef idx
#define idx(x, y, z) ((z) * nly * nlx + (y) * nlx + (x))
void Noise::gradientMap3D(float x, float y, float z,
float step_x, float step_y, float step_z,
int seed) {
float v000, v010, v100, v110;
float v001, v011, v101, v111;
float u, v, w, orig_u, orig_v;
int index, i, j, k, x0, y0, z0, noisex, noisey, noisez;
int nlx, nly, nlz;
x0 = floor(x);
y0 = floor(y);
z0 = floor(z);
u = x - (float)x0;
v = y - (float)y0;
w = z - (float)z0;
orig_u = u;
orig_v = v;
//calculate noise point lattice
nlx = (int)(u + sx * step_x) + 2;
nly = (int)(v + sy * step_y) + 2;
nlz = (int)(w + sz * step_z) + 2;
index = 0;
for (k = 0; k != nlz; k++)
for (j = 0; j != nly; j++)
for (i = 0; i != nlx; i++)
noisebuf[index++] = noise3d(x0 + i, y0 + j, z0 + k, seed);
//calculate interpolations
index = 0;
noisey = 0;
noisez = 0;
for (k = 0; k != sz; k++) {
v = orig_v;
noisey = 0;
for (j = 0; j != sy; j++) {
v000 = noisebuf[idx(0, noisey, noisez)];
v100 = noisebuf[idx(1, noisey, noisez)];
v010 = noisebuf[idx(0, noisey + 1, noisez)];
v110 = noisebuf[idx(1, noisey + 1, noisez)];
v001 = noisebuf[idx(0, noisey, noisez + 1)];
v101 = noisebuf[idx(1, noisey, noisez + 1)];
v011 = noisebuf[idx(0, noisey + 1, noisez + 1)];
v111 = noisebuf[idx(1, noisey + 1, noisez + 1)];
u = orig_u;
noisex = 0;
for (i = 0; i != sx; i++) {
buf[index++] = triLinearInterpolation(
v000, v100, v010, v110,
v001, v101, v011, v111,
u, v, w);
u += step_x;
if (u >= 1.0) {
u -= 1.0;
noisex++;
v000 = v100;
v010 = v110;
v100 = noisebuf[idx(noisex + 1, noisey, noisez)];
v110 = noisebuf[idx(noisex + 1, noisey + 1, noisez)];
v001 = v101;
v011 = v111;
v101 = noisebuf[idx(noisex + 1, noisey, noisez + 1)];
v111 = noisebuf[idx(noisex + 1, noisey + 1, noisez + 1)];
}
}
v += step_y;
if (v >= 1.0) {
v -= 1.0;
noisey++;
}
}
w += step_z;
if (w >= 1.0) {
w -= 1.0;
noisez++;
}
}
}
#undef idx
float *Noise::perlinMap2D(float x, float y) {
float f = 1.0, g = 1.0;
int i, j, index, oct;
x /= np->spread.X;
y /= np->spread.Y;
memset(result, 0, sizeof(float) * sx * sy);
for (oct = 0; oct < np->octaves; oct++) {
gradientMap2D(x * f, y * f,
f / np->spread.X, f / np->spread.Y,
seed + np->seed + oct);
index = 0;
for (j = 0; j != sy; j++) {
for (i = 0; i != sx; i++) {
result[index] += g * buf[index];
index++;
}
}
f *= 2.0;
g *= np->persist;
}
return result;
}
float *Noise::perlinMap3D(float x, float y, float z) {
float f = 1.0, g = 1.0;
int i, j, k, index, oct;
x /= np->spread.X;
y /= np->spread.Y;
z /= np->spread.Z;
memset(result, 0, sizeof(float) * sx * sy * sz);
for (oct = 0; oct < np->octaves; oct++) {
gradientMap3D(x * f, y * f, z * f,
f / np->spread.X, f / np->spread.Y, f / np->spread.Z,
seed + np->seed + oct);
index = 0;
for (k = 0; k != sz; k++) {
for (j = 0; j != sy; j++) {
for (i = 0; i != sx; i++) {
result[index] += g * buf[index];
index++;
}
}
}
f *= 2.0;
g *= np->persist;
}
return result;
}
void Noise::transformNoiseMap() {
int i = 0;
for (int z = 0; z != sz; z++) {
for (int y = 0; y != sy; y++) {
for (int x = 0; x != sx; x++) {
result[i] = result[i] * np->scale + np->offset;
i++;
}
}
}
}
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