/*
-Minetest-c55
-Copyright (C) 2010-2011 celeron55, Perttu Ahola <celeron55@gmail.com>
+Minetest
+Copyright (C) 2010-2013 celeron55, Perttu Ahola <celeron55@gmail.com>
+Copyright (C) 2010-2013 kwolekr, Ryan Kwolek <kwolekr@minetest.net>
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
+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 General Public License for more details.
+GNU Lesser General Public License for more details.
-You should have received a copy of the GNU General Public License along
+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 <string.h> // memset
+#include "debug.h"
+#include "util/numeric.h"
-#define NOISE_MAGIC_X 1619
-#define NOISE_MAGIC_Y 31337
+#define NOISE_MAGIC_X 1619
+#define NOISE_MAGIC_Y 31337
+#define NOISE_MAGIC_Z 52591
#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
+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
};
-double dotProduct(double vx, double vy, double wx, double wy){
- return vx*wx+vy*wy;
+
+///////////////////////////////////////////////////////////////////////////////
+
+
+//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;
}
-
-double easeCurve(double t){
- return 6*pow(t,5)-15*pow(t,4)+10*pow(t,3);
+
+
+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);
}
-
-double linearInterpolation(double x0, double x1, double t){
- return x0+(x1-x0)*t;
+
+
+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);
}
-
-double biLinearInterpolation(double x0y0, double x1y0, double x0y1, double x1y1, double x, double y){
- double tx = easeCurve(x);
- double ty = easeCurve(y);
- double u = linearInterpolation(x0y0,x1y0,tx);
- double v = linearInterpolation(x0y1,x1y1,tx);
- return linearInterpolation(u,v,ty);
+
+
+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);
}
-double noise2d(int x, int y, int seed)
+
+#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)
{
- 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;
+ /*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
+
-double noise2d_gradient(double x, double y, int seed)
+#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);
- double xl = x - (double)x0;
- double yl = y - (double)y0;
+ // 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);
- /* In this format, these fail to work on MSVC8 if n00 < 4
- double s = dotProduct(cos_lookup[n00], cos_lookup[(n00-4)%16], xl, yl);
- double u = dotProduct(-cos_lookup[n10], cos_lookup[(n10-4)%16], 1.-xl, yl);
- double v = dotProduct(cos_lookup[n01], -cos_lookup[(n01-4)%16], xl, 1.-yl);
- double w = dotProduct(-cos_lookup[n11], -cos_lookup[(n11-4)%16], 1.-xl, 1.-yl);*/
- 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);
- /*std::cout<<"x="<<x<<" y="<<y<<" x0="<<x0<<" y0="<<y0<<" xl="<<xl<<" yl="<<yl<<" n00="<<n00<<" n10="<<n01<<" s="<<s<<std::endl;
- std::cout<<"cos_lookup[n00]="<<(cos_lookup[n00])<<" cos_lookup[(n00-4)%16]="<<(cos_lookup[(n00-4)%16])<<std::endl;*/
+ // 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);
+}
-double noise2d_perlin(double x, double y, int seed,
- int octaves, double persistence)
+
+float noise2d_perlin(float x, float y, int seed,
+ int octaves, float persistence)
{
- double a = 0;
- double f = 1.0;
- double g = 1.0;
- for(int i=0; i<octaves; i++)
+ 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);
+ 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::perlinMap2DModulated(float x, float y, float *persist_map) {
+ float f = 1.0;
+ int i, j, index, oct;
+
+ x /= np->spread.X;
+ y /= np->spread.Y;
+
+ memset(result, 0, sizeof(float) * sx * sy);
+
+ float *g = new float[sx * sy];
+ for (index = 0; index != sx * sy; index++)
+ g[index] = 1.0;
+
+ 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[index] * buf[index];
+ g[index] *= persist_map[index];
+ index++;
+ }
+ }
+
+ f *= 2.0;
+ }
+
+ delete[] g;
+ 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++;
+ }
+ }
+ }
+}