123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899100101102103104105106107108109110111112113114115116117118119120121122123124125126127128129130131132133134135136137138139140141142143144145146147148149150151152153154155156157158159160161162163164165166167168169170171172173174175176177178179180181182183184185186187188189190191192193194195196197198199200201202203204205206207208209210211212213214215216217218219220221222223224225226227228229230231232233234235236237238239240241242243244245246247248249250251252253254255256257258259260261262263264265266267268269270271272273274275276277278279280281282283284285286287288289290291292293294295296297298299300301302303304305306307308309310311312313314315316317318319320321322323324325326327328329330331332333334335336337338339340341342343344345346347348349350351352353354355356357358359360361362363364365366367368369370371372373374375376377378379380381382383384385386387388389390391392393394395396397398399400401402403404405406407408409410411412413414415416417418419420421422423424425426427428429430431432433434435436437438439440441442443444445446447448449450451452453454455456457458459460461462463464465466467468469470471472473474475476477478479480481482483484485486487488489490491492493494495496497498499500501502503504505506507508509510511512513514515516517518519520521522523524525526527528529530531532533534535536537538539540541542543544545546547548549550551552553554555556557558559560561562563564565566567568569570571572573574575576577578579580581582583584585586587588589590591592593594595596597598599600601602603604605606607608609610611612613614615616617618619620621622623624625626627628629630631632633634635636637638639640641642643644645646647648649650651652653654655656657658659660661662663664665666667668669670671672673674675676677678679680681682683684685686687688689690691692693694695696697698699700701702703704705706707708709710711712713714715716717718719720721722723724725726727728729730731732733 |
- /*
- * 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 <cmath>
- #include "noise.h"
- #include <iostream>
- #include <cstring> // 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
- // Unsigned magic seed prevents undefined behavior.
- #define NOISE_MAGIC_SEED 1013U
- 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)");
- // We have to cast to s64 because otherwise this could overflow,
- // and signed overflow is undefined behavior.
- u32 bound = (s64)max - (s64)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,
- bool eased)
- {
- // Inlining will optimize this branch out when possible
- if (eased) {
- x = easeCurve(x);
- y = easeCurve(y);
- }
- float u = linearInterpolation(v00, v10, x);
- float v = linearInterpolation(v01, v11, x);
- return linearInterpolation(u, v, y);
- }
- inline float triLinearInterpolation(
- float v000, float v100, float v010, float v110,
- float v001, float v101, float v011, float v111,
- float x, float y, float z,
- bool eased)
- {
- // Inlining will optimize this branch out when possible
- if (eased) {
- x = easeCurve(x);
- y = easeCurve(y);
- z = easeCurve(z);
- }
- float u = biLinearInterpolation(v000, v100, v010, v110, x, y, false);
- float v = biLinearInterpolation(v001, v101, v011, v111, x, y, false);
- 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
- return biLinearInterpolation(v00, v10, v01, v11, xl, yl, eased);
- }
- 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
- return triLinearInterpolation(
- v000, v100, v010, v110,
- v001, v101, v011, v111,
- xl, yl, zl,
- eased);
- }
- 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 contour(float v)
- {
- v = std::fabs(v);
- if (v >= 1.0)
- return 0.0;
- return (1.0 - v);
- }
- ///////////////////////// [ New noise ] ////////////////////////////
- float NoisePerlin2D(const 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 = std::fabs(noiseval);
- a += g * noiseval;
- f *= np->lacunarity;
- g *= np->persist;
- }
- return np->offset + a * np->scale;
- }
- float NoisePerlin3D(const 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 = std::fabs(noiseval);
- a += g * noiseval;
- f *= np->lacunarity;
- g *= np->persist;
- }
- return np->offset + a * np->scale;
- }
- Noise::Noise(const NoiseParams *np_, s32 seed, u32 sx, u32 sy, u32 sz)
- {
- np = *np_;
- this->seed = seed;
- this->sx = sx;
- this->sy = sy;
- this->sz = sz;
- 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();
- // Protect against an octave having a spread < 1, causing broken noise values
- if (np.spread.X / ofactor < 1.0f ||
- np.spread.Y / ofactor < 1.0f ||
- np.spread.Z / ofactor < 1.0f) {
- errorstream << "A noise parameter has too many octaves: "
- << np.octaves << " octaves" << std::endl;
- throw InvalidNoiseParamsException("A noise parameter has too many octaves");
- }
- // + 2 for the two initial endpoints
- // + 1 for potentially crossing a boundary due to offset
- size_t nlx = (size_t)std::ceil(num_noise_points_x) + 3;
- size_t nly = (size_t)std::ceil(num_noise_points_y) + 3;
- size_t nlz = is3d ? (size_t)std::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);
- x0 = std::floor(x);
- y0 = std::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++] =
- biLinearInterpolation(v00, v10, v01, v11, u, v, eased);
- 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;
- bool eased = np.flags & NOISE_FLAG_EASED;
- x0 = std::floor(x);
- y0 = std::floor(y);
- z0 = std::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++] = triLinearInterpolation(
- v000, v100, v010, v110,
- v001, v101, v011, v111,
- u, v, w,
- eased);
- 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 (std::fabs(np.offset - 0.f) > 0.00001 || std::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 (std::fabs(np.offset - 0.f) > 0.00001 || std::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,
- const 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] * std::fabs(gradient_buf[i]);
- gmap[i] *= persistence_map[i];
- }
- } else {
- for (size_t i = 0; i != bufsize; i++)
- result[i] += g * std::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];
- }
- }
- }
|