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/*
* Minetest
* Copyright (C) 2010-2014 celeron55, Perttu Ahola <celeron55@gmail.com>
* Copyright (C) 2010-2014 kwolekr, Ryan Kwolek <kwolekr@minetest.net>
* All rights reserved.
*
* Redistribution and use in source and binary forms, with or without modification, are
* permitted provided that the following conditions are met:
* 1. Redistributions of source code must retain the above copyright notice, this list of
* conditions and the following disclaimer.
* 2. Redistributions in binary form must reproduce the above copyright notice, this list
* of conditions and the following disclaimer in the documentation and/or other materials
* provided with the distribution.
*
* THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND ANY EXPRESS OR IMPLIED
* WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND
* FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR
* CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
* CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
* SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON
* ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
* NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF
* ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
*/
#include <math.h>
#include "noise.h"
#include <iostream>
#include <string.h> // memset
#include "debug.h"
#include "util/numeric.h"
#include "util/string.h"
#include "exceptions.h"
#define NOISE_MAGIC_X 1619
#define NOISE_MAGIC_Y 31337
#define NOISE_MAGIC_Z 52591
#define NOISE_MAGIC_SEED 1013
typedef float (*Interp2dFxn)(
float v00, float v10, float v01, float v11,
float x, float y);
typedef float (*Interp3dFxn)(
float v000, float v100, float v010, float v110,
float v001, float v101, float v011, float v111,
float x, float y, float z);
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
};
FlagDesc flagdesc_noiseparams[] = {
{"defaults", NOISE_FLAG_DEFAULTS},
{"eased", NOISE_FLAG_EASED},
{"absvalue", NOISE_FLAG_ABSVALUE},
{"pointbuffer", NOISE_FLAG_POINTBUFFER},
{"simplex", NOISE_FLAG_SIMPLEX},
{NULL, 0}
};
///////////////////////////////////////////////////////////////////////////////
PcgRandom::PcgRandom(u64 state, u64 seq)
{
seed(state, seq);
}
void PcgRandom::seed(u64 state, u64 seq)
{
m_state = 0U;
m_inc = (seq << 1u) | 1u;
next();
m_state += state;
next();
}
u32 PcgRandom::next()
{
u64 oldstate = m_state;
m_state = oldstate * 6364136223846793005ULL + m_inc;
u32 xorshifted = ((oldstate >> 18u) ^ oldstate) >> 27u;
u32 rot = oldstate >> 59u;
return (xorshifted >> rot) | (xorshifted << ((-rot) & 31));
}
u32 PcgRandom::range(u32 bound)
{
// If the bound is 0, we cover the whole RNG's range
if (bound == 0)
return next();
/*
This is an optimization of the expression:
0x100000000ull % bound
since 64-bit modulo operations typically much slower than 32.
*/
u32 threshold = -bound % bound;
u32 r;
/*
If the bound is not a multiple of the RNG's range, it may cause bias,
e.g. a RNG has a range from 0 to 3 and we take want a number 0 to 2.
Using rand() % 3, the number 0 would be twice as likely to appear.
With a very large RNG range, the effect becomes less prevalent but
still present.
This can be solved by modifying the range of the RNG to become a
multiple of bound by dropping values above the a threshold.
In our example, threshold == 4 % 3 == 1, so reject values < 1
(that is, 0), thus making the range == 3 with no bias.
This loop may look dangerous, but will always terminate due to the
RNG's property of uniformity.
*/
while ((r = next()) < threshold)
;
return r % bound;
}
s32 PcgRandom::range(s32 min, s32 max)
{
if (max < min)
throw PrngException("Invalid range (max < min)");
u32 bound = max - min + 1;
return range(bound) + min;
}
void PcgRandom::bytes(void *out, size_t len)
{
u8 *outb = (u8 *)out;
int bytes_left = 0;
u32 r;
while (len--) {
if (bytes_left == 0) {
bytes_left = sizeof(u32);
r = next();
}
*outb = r & 0xFF;
outb++;
bytes_left--;
r >>= CHAR_BIT;
}
}
s32 PcgRandom::randNormalDist(s32 min, s32 max, int num_trials)
{
s32 accum = 0;
for (int i = 0; i != num_trials; i++)
accum += range(min, max);
return myround((float)accum / num_trials);
}
///////////////////////////////////////////////////////////////////////////////
float noise2d(int x, int y, s32 seed)
{
unsigned 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)(int)n / 0x40000000;
}
float noise3d(int x, int y, int z, s32 seed)
{
unsigned 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)(int)n / 0x40000000;
}
inline 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;
}
inline 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);
}
inline float biLinearInterpolationNoEase(
float v00, float v10,
float v01, float v11,
float x, float y)
{
float u = linearInterpolation(v00, v10, x);
float v = linearInterpolation(v01, v11, 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 tx = easeCurve(x);
float ty = easeCurve(y);
float tz = easeCurve(z);
float u = biLinearInterpolationNoEase(v000, v100, v010, v110, tx, ty);
float v = biLinearInterpolationNoEase(v001, v101, v011, v111, tx, ty);
return linearInterpolation(u, v, tz);
}
float triLinearInterpolationNoEase(
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);
}
float noise2d_gradient(float x, float y, s32 seed, bool eased)
{
// 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
if (eased)
return biLinearInterpolation(v00, v10, v01, v11, xl, yl);
else
return biLinearInterpolationNoEase(v00, v10, v01, v11, xl, yl);
}
float noise3d_gradient(float x, float y, float z, s32 seed, bool eased)
{
// 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
if (eased) {
return triLinearInterpolation(
v000, v100, v010, v110,
v001, v101, v011, v111,
xl, yl, zl);
} else {
return triLinearInterpolationNoEase(
v000, v100, v010, v110,
v001, v101, v011, v111,
xl, yl, zl);
}
}
float noise2d_perlin(float x, float y, s32 seed,
int octaves, float persistence, bool eased)
{
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, eased);
f *= 2.0;
g *= persistence;
}
return a;
}
float noise2d_perlin_abs(float x, float y, s32 seed,
int octaves, float persistence, bool eased)
{
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, eased));
f *= 2.0;
g *= persistence;
}
return a;
}
float noise3d_perlin(float x, float y, float z, s32 seed,
int octaves, float persistence, bool eased)
{
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, eased);
f *= 2.0;
g *= persistence;
}
return a;
}
float noise3d_perlin_abs(float x, float y, float z, s32 seed,
int octaves, float persistence, bool eased)
{
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, eased));
f *= 2.0;
g *= persistence;
}
return a;
}
float contour(float v)
{
v = fabs(v);
if (v >= 1.0)
return 0.0;
return (1.0 - v);
}
///////////////////////// [ New noise ] ////////////////////////////
float NoisePerlin2D(NoiseParams *np, float x, float y, s32 seed)
{
float a = 0;
float f = 1.0;
float g = 1.0;
x /= np->spread.X;
y /= np->spread.Y;
seed += np->seed;
for (size_t i = 0; i < np->octaves; i++) {
float noiseval = noise2d_gradient(x * f, y * f, seed + i,
np->flags & (NOISE_FLAG_DEFAULTS | NOISE_FLAG_EASED));
if (np->flags & NOISE_FLAG_ABSVALUE)
noiseval = fabs(noiseval);
a += g * noiseval;
f *= np->lacunarity;
g *= np->persist;
}
return np->offset + a * np->scale;
}
float NoisePerlin3D(NoiseParams *np, float x, float y, float z, s32 seed)
{
float a = 0;
float f = 1.0;
float g = 1.0;
x /= np->spread.X;
y /= np->spread.Y;
z /= np->spread.Z;
seed += np->seed;
for (size_t i = 0; i < np->octaves; i++) {
float noiseval = noise3d_gradient(x * f, y * f, z * f, seed + i,
np->flags & NOISE_FLAG_EASED);
if (np->flags & NOISE_FLAG_ABSVALUE)
noiseval = fabs(noiseval);
a += g * noiseval;
f *= np->lacunarity;
g *= np->persist;
}
return np->offset + a * np->scale;
}
Noise::Noise(NoiseParams *np_, s32 seed, u32 sx, u32 sy, u32 sz)
{
memcpy(&np, np_, sizeof(np));
this->seed = seed;
this->sx = sx;
this->sy = sy;
this->sz = sz;
this->persist_buf = NULL;
this->gradient_buf = NULL;
this->result = NULL;
allocBuffers();
}
Noise::~Noise()
{
delete[] gradient_buf;
delete[] persist_buf;
delete[] noise_buf;
delete[] result;
}
void Noise::allocBuffers()
{
if (sx < 1)
sx = 1;
if (sy < 1)
sy = 1;
if (sz < 1)
sz = 1;
this->noise_buf = NULL;
resizeNoiseBuf(sz > 1);
delete[] gradient_buf;
delete[] persist_buf;
delete[] result;
try {
size_t bufsize = sx * sy * sz;
this->persist_buf = NULL;
this->gradient_buf = new float[bufsize];
this->result = new float[bufsize];
} catch (std::bad_alloc &e) {
throw InvalidNoiseParamsException();
}
}
void Noise::setSize(u32 sx, u32 sy, u32 sz)
{
this->sx = sx;
this->sy = sy;
this->sz = sz;
allocBuffers();
}
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)
{
//maximum possible spread value factor
float ofactor = (np.lacunarity > 1.0) ?
pow(np.lacunarity, np.octaves - 1) :
np.lacunarity;
// noise lattice point count
// (int)(sz * spread * ofactor) is # of lattice points crossed due to length
float num_noise_points_x = sx * ofactor / np.spread.X;
float num_noise_points_y = sy * ofactor / np.spread.Y;
float num_noise_points_z = sz * ofactor / np.spread.Z;
// protect against obviously invalid parameters
if (num_noise_points_x > 1000000000.f ||
num_noise_points_y > 1000000000.f ||
num_noise_points_z > 1000000000.f)
throw InvalidNoiseParamsException();
// + 2 for the two initial endpoints
// + 1 for potentially crossing a boundary due to offset
size_t nlx = (size_t)ceil(num_noise_points_x) + 3;
size_t nly = (size_t)ceil(num_noise_points_y) + 3;
size_t nlz = is3d ? (size_t)ceil(num_noise_points_z) + 3 : 1;
delete[] noise_buf;
try {
noise_buf = new float[nlx * nly * nlz];
} catch (std::bad_alloc &e) {
throw InvalidNoiseParamsException();
}
}
/*
* 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,
s32 seed)
{
float v00, v01, v10, v11, u, v, orig_u;
u32 index, i, j, noisex, noisey;
u32 nlx, nly;
s32 x0, y0;
bool eased = np.flags & (NOISE_FLAG_DEFAULTS | NOISE_FLAG_EASED);
Interp2dFxn interpolate = eased ?
biLinearInterpolation : biLinearInterpolationNoEase;
x0 = floor(x);
y0 = floor(y);
u = x - (float)x0;
v = y - (float)y0;
orig_u = u;
//calculate noise point lattice
nlx = (u32)(u + sx * step_x) + 2;
nly = (u32)(v + sy * step_y) + 2;
index = 0;
for (j = 0; j != nly; j++)
for (i = 0; i != nlx; i++)
noise_buf[index++] = noise2d(x0 + i, y0 + j, seed);
//calculate interpolations
index = 0;
noisey = 0;
for (j = 0; j != sy; j++) {
v00 = noise_buf[idx(0, noisey)];
v10 = noise_buf[idx(1, noisey)];
v01 = noise_buf[idx(0, noisey + 1)];
v11 = noise_buf[idx(1, noisey + 1)];
u = orig_u;
noisex = 0;
for (i = 0; i != sx; i++) {
gradient_buf[index++] = interpolate(v00, v10, v01, v11, u, v);
u += step_x;
if (u >= 1.0) {
u -= 1.0;
noisex++;
v00 = v10;
v01 = v11;
v10 = noise_buf[idx(noisex + 1, noisey)];
v11 = noise_buf[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,
s32 seed)
{
float v000, v010, v100, v110;
float v001, v011, v101, v111;
float u, v, w, orig_u, orig_v;
u32 index, i, j, k, noisex, noisey, noisez;
u32 nlx, nly, nlz;
s32 x0, y0, z0;
Interp3dFxn interpolate = (np.flags & NOISE_FLAG_EASED) ?
triLinearInterpolation : triLinearInterpolationNoEase;
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 = (u32)(u + sx * step_x) + 2;
nly = (u32)(v + sy * step_y) + 2;
nlz = (u32)(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++)
noise_buf[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 = noise_buf[idx(0, noisey, noisez)];
v100 = noise_buf[idx(1, noisey, noisez)];
v010 = noise_buf[idx(0, noisey + 1, noisez)];
v110 = noise_buf[idx(1, noisey + 1, noisez)];
v001 = noise_buf[idx(0, noisey, noisez + 1)];
v101 = noise_buf[idx(1, noisey, noisez + 1)];
v011 = noise_buf[idx(0, noisey + 1, noisez + 1)];
v111 = noise_buf[idx(1, noisey + 1, noisez + 1)];
u = orig_u;
noisex = 0;
for (i = 0; i != sx; i++) {
gradient_buf[index++] = interpolate(
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 = noise_buf[idx(noisex + 1, noisey, noisez)];
v110 = noise_buf[idx(noisex + 1, noisey + 1, noisez)];
v001 = v101;
v011 = v111;
v101 = noise_buf[idx(noisex + 1, noisey, noisez + 1)];
v111 = noise_buf[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 *persistence_map)
{
float f = 1.0, g = 1.0;
size_t bufsize = sx * sy;
x /= np.spread.X;
y /= np.spread.Y;
memset(result, 0, sizeof(float) * bufsize);
if (persistence_map) {
if (!persist_buf)
persist_buf = new float[bufsize];
for (size_t i = 0; i != bufsize; i++)
persist_buf[i] = 1.0;
}
for (size_t oct = 0; oct < np.octaves; oct++) {
gradientMap2D(x * f, y * f,
f / np.spread.X, f / np.spread.Y,
seed + np.seed + oct);
updateResults(g, persist_buf, persistence_map, bufsize);
f *= np.lacunarity;
g *= np.persist;
}
if (fabs(np.offset - 0.f) > 0.00001 || fabs(np.scale - 1.f) > 0.00001) {
for (size_t i = 0; i != bufsize; i++)
result[i] = result[i] * np.scale + np.offset;
}
return result;
}
float *Noise::perlinMap3D(float x, float y, float z, float *persistence_map)
{
float f = 1.0, g = 1.0;
size_t bufsize = sx * sy * sz;
x /= np.spread.X;
y /= np.spread.Y;
z /= np.spread.Z;
memset(result, 0, sizeof(float) * bufsize);
if (persistence_map) {
if (!persist_buf)
persist_buf = new float[bufsize];
for (size_t i = 0; i != bufsize; i++)
persist_buf[i] = 1.0;
}
for (size_t 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);
updateResults(g, persist_buf, persistence_map, bufsize);
f *= np.lacunarity;
g *= np.persist;
}
if (fabs(np.offset - 0.f) > 0.00001 || fabs(np.scale - 1.f) > 0.00001) {
for (size_t i = 0; i != bufsize; i++)
result[i] = result[i] * np.scale + np.offset;
}
return result;
}
void Noise::updateResults(float g, float *gmap,
float *persistence_map, size_t bufsize)
{
// This looks very ugly, but it is 50-70% faster than having
// conditional statements inside the loop
if (np.flags & NOISE_FLAG_ABSVALUE) {
if (persistence_map) {
for (size_t i = 0; i != bufsize; i++) {
result[i] += gmap[i] * fabs(gradient_buf[i]);
gmap[i] *= persistence_map[i];
}
} else {
for (size_t i = 0; i != bufsize; i++)
result[i] += g * fabs(gradient_buf[i]);
}
} else {
if (persistence_map) {
for (size_t i = 0; i != bufsize; i++) {
result[i] += gmap[i] * gradient_buf[i];
gmap[i] *= persistence_map[i];
}
} else {
for (size_t i = 0; i != bufsize; i++)
result[i] += g * gradient_buf[i];
}
}
}