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OpenSimplex in C++
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opensimplex.cpp
/* OpenSimplex Noise in C++
* Ported by Patrick Chieppe from C#
* Original at https://gist.github.com/digitalshadow/134a3a02b67cecd72181
*
* This is free and unencumbered software released into the public domain.
*
* Anyone is free to copy, modify, publish, use, compile, sell, or
* distribute this software, either in source code form or as a compiled
* binary, for any purpose, commercial or non-commercial, and by any
* means.
*
* In jurisdictions that recognize copyright laws, the author or authors
* of this software dedicate any and all copyright interest in the
* software to the public domain. We make this dedication for the benefit
* of the public at large and to the detriment of our heirs and
* successors. We intend this dedication to be an overt act of
* relinquishment in perpetuity of all present and future rights to this
* software under copyright law.
*
* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
* EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
* MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.
* IN NO EVENT SHALL THE AUTHORS BE LIABLE FOR ANY CLAIM, DAMAGES OR
* OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE,
* ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
* OTHER DEALINGS IN THE SOFTWARE.
*
* For more information, please refer to <http://unlicense.org/>
*/
#include "opensimplex.hpp"
#include <vector>
namespace opensimplex {
namespace {
constexpr double STRETCH_2D = -0.211324865405187; //(1/sqrt(2+1)-1)/2;
constexpr double STRETCH_3D = -1.0 / 6.0; //(1/sqrt(3+1)-1)/3;
constexpr double STRETCH_4D = -0.138196601125011; //(1/sqrt(4+1)-1)/4;
constexpr double SQUISH_2D = 0.366025403784439; //(sqrt(2+1)-1)/2;
constexpr double SQUISH_3D = 1.0 / 3.0; //(sqrt(3+1)-1)/3;
constexpr double SQUISH_4D = 0.309016994374947; //(sqrt(4+1)-1)/4;
constexpr double NORM_2D = 1.0 / 47.0;
constexpr double NORM_3D = 1.0 / 103.0;
constexpr double NORM_4D = 1.0 / 30.0;
inline int32_t FastFloor(double x)
{
int32_t xi = (int32_t)x;
return x < xi ? xi - 1 : xi;
}
} // namespace
OpenSimplex::Contribution2::Contribution2()
{}
OpenSimplex::Contribution2::Contribution2(double multiplier, int32_t xsb, int32_t ysb)
: xsb {xsb},
ysb {ysb},
dx {-xsb - multiplier * SQUISH_2D},
dy {-ysb - multiplier * SQUISH_2D}
{}
OpenSimplex::Contribution3::Contribution3()
{}
OpenSimplex::Contribution3::Contribution3(double multiplier, int32_t xsb, int32_t ysb, int32_t zsb)
: xsb {xsb},
ysb {ysb},
zsb {zsb},
dx {-xsb - multiplier * SQUISH_3D},
dy {-ysb - multiplier * SQUISH_3D},
dz {-zsb - multiplier * SQUISH_3D}
{}
OpenSimplex::Contribution4::Contribution4()
{}
OpenSimplex::Contribution4::Contribution4(double multiplier, int32_t xsb, int32_t ysb, int32_t zsb, int32_t wsb)
: xsb {xsb},
ysb {ysb},
zsb {zsb},
wsb {wsb},
dx {-xsb - multiplier * SQUISH_4D},
dy {-ysb - multiplier * SQUISH_4D},
dz {-zsb - multiplier * SQUISH_4D},
dw {-wsb - multiplier * SQUISH_4D}
{}
OpenSimplex::Lookups::Lookups()
{
const std::array<std::array<int32_t, 9>, 2> base2D {{
{{ 1, 1, 0, 1, 0, 1, 0, 0, 0 }},
{{ 1, 1, 0, 1, 0, 1, 2, 1, 1 }}
}};
const std::array<int32_t, 24> p2D {{ 0, 0, 1, -1, 0, 0, -1, 1, 0, 2, 1, 1, 1, 2, 2, 0, 1, 2, 0, 2, 1, 0, 0, 0 }};
const std::array<int32_t, 24> lookupPairs2D {{ 0, 1, 1, 0, 4, 1, 17, 0, 20, 2, 21, 2, 22, 5, 23, 5, 26, 4, 39, 3, 42, 4, 43, 3 }};
std::array<Contribution2*, p2D.size() / 4> contributions2D;
for (size_t i = 0; i < p2D.size(); i += 4) {
auto baseSet = base2D[p2D[i]];
Contribution2* previous = nullptr;
Contribution2* current = nullptr;
for (size_t k = 0; k < baseSet.size(); k += 3) {
current = new Contribution2(baseSet[k], baseSet[k + 1], baseSet[k + 2]);
if (!previous) {
contributions2D[i / 4] = current;
} else {
previous->Next = current;
}
previous = current;
}
current->Next = new Contribution2(p2D[i + 1], p2D[i + 2], p2D[i + 3]);
}
for (size_t i = 0; i < lookupPairs2D.size(); i += 2) {
lookup2D[lookupPairs2D[i]] = contributions2D[lookupPairs2D[i + 1]];
}
const std::array<std::vector<int32_t>, 3> base3D {{
{{ 0, 0, 0, 0, 1, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 1 }},
{{ 2, 1, 1, 0, 2, 1, 0, 1, 2, 0, 1, 1, 3, 1, 1, 1 }},
{{ 1, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 1, 2, 1, 1, 0, 2, 1, 0, 1, 2, 0, 1, 1 }}
}};
const std::array<int32_t, 216> p3D {{ 0, 0, 1, -1, 0, 0, 1, 0, -1, 0, 0, -1, 1, 0, 0, 0, 1, -1, 0, 0, -1, 0, 1, 0, 0, -1, 1, 0, 2, 1, 1, 0, 1, 1, 1, -1, 0, 2, 1, 0, 1, 1, 1, -1, 1, 0, 2, 0, 1, 1, 1, -1, 1, 1, 1, 3, 2, 1, 0, 3, 1, 2, 0, 1, 3, 2, 0, 1, 3, 1, 0, 2, 1, 3, 0, 2, 1, 3, 0, 1, 2, 1, 1, 1, 0, 0, 2, 2, 0, 0, 1, 1, 0, 1, 0, 2, 0, 2, 0, 1, 1, 0, 0, 1, 2, 0, 0, 2, 2, 0, 0, 0, 0, 1, 1, -1, 1, 2, 0, 0, 0, 0, 1, -1, 1, 1, 2, 0, 0, 0, 0, 1, 1, 1, -1, 2, 3, 1, 1, 1, 2, 0, 0, 2, 2, 3, 1, 1, 1, 2, 2, 0, 0, 2, 3, 1, 1, 1, 2, 0, 2, 0, 2, 1, 1, -1, 1, 2, 0, 0, 2, 2, 1, 1, -1, 1, 2, 2, 0, 0, 2, 1, -1, 1, 1, 2, 0, 0, 2, 2, 1, -1, 1, 1, 2, 0, 2, 0, 2, 1, 1, 1, -1, 2, 2, 0, 0, 2, 1, 1, 1, -1, 2, 0, 2, 0 }};
const std::array<int32_t, 144> lookupPairs3D {{ 0, 2, 1, 1, 2, 2, 5, 1, 6, 0, 7, 0, 32, 2, 34, 2, 129, 1, 133, 1, 160, 5, 161, 5, 518, 0, 519, 0, 546, 4, 550, 4, 645, 3, 647, 3, 672, 5, 673, 5, 674, 4, 677, 3, 678, 4, 679, 3, 680, 13, 681, 13, 682, 12, 685, 14, 686, 12, 687, 14, 712, 20, 714, 18, 809, 21, 813, 23, 840, 20, 841, 21, 1198, 19, 1199, 22, 1226, 18, 1230, 19, 1325, 23, 1327, 22, 1352, 15, 1353, 17, 1354, 15, 1357, 17, 1358, 16, 1359, 16, 1360, 11, 1361, 10, 1362, 11, 1365, 10, 1366, 9, 1367, 9, 1392, 11, 1394, 11, 1489, 10, 1493, 10, 1520, 8, 1521, 8, 1878, 9, 1879, 9, 1906, 7, 1910, 7, 2005, 6, 2007, 6, 2032, 8, 2033, 8, 2034, 7, 2037, 6, 2038, 7, 2039, 6 }};
std::array<Contribution3*, p3D.size() / 9> contributions3D;
for (size_t i = 0; i < p3D.size(); i += 9) {
auto baseSet = base3D[p3D[i]];
Contribution3* previous {nullptr};
Contribution3* current {nullptr};
for (size_t k = 0; k < baseSet.size(); k += 4) {
current = new Contribution3(baseSet[k], baseSet[k + 1], baseSet[k + 2], baseSet[k + 3]);
if (!previous) {
contributions3D[i / 9] = current;
} else {
previous->Next = current;
}
previous = current;
}
current->Next = new Contribution3(p3D[i + 1], p3D[i + 2], p3D[i + 3], p3D[i + 4]);
current->Next->Next = new Contribution3(p3D[i + 5], p3D[i + 6], p3D[i + 7], p3D[i + 8]);
}
for (size_t i = 0; i < lookupPairs3D.size(); i += 2) {
lookup3D[lookupPairs3D[i]] = contributions3D[lookupPairs3D[i + 1]];
}
const std::array<std::vector<int32_t>, 4> base4D {{
{{ 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 1 }},
{{ 3, 1, 1, 1, 0, 3, 1, 1, 0, 1, 3, 1, 0, 1, 1, 3, 0, 1, 1, 1, 4, 1, 1, 1, 1 }},
{{ 1, 1, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 1, 2, 1, 1, 0, 0, 2, 1, 0, 1, 0, 2, 1, 0, 0, 1, 2, 0, 1, 1, 0, 2, 0, 1, 0, 1, 2, 0, 0, 1, 1 }},
{{ 3, 1, 1, 1, 0, 3, 1, 1, 0, 1, 3, 1, 0, 1, 1, 3, 0, 1, 1, 1, 2, 1, 1, 0, 0, 2, 1, 0, 1, 0, 2, 1, 0, 0, 1, 2, 0, 1, 1, 0, 2, 0, 1, 0, 1, 2, 0, 0, 1, 1 }}
}};
const std::array<int32_t, 1280> p4D {{ 0, 0, 1, -1, 0, 0, 0, 1, 0, -1, 0, 0, 1, 0, 0, -1, 0, 0, -1, 1, 0, 0, 0, 0, 1, -1, 0, 0, 0, 1, 0, -1, 0, 0, -1, 0, 1, 0, 0, 0, -1, 1, 0, 0, 0, 0, 1, -1, 0, 0, -1, 0, 0, 1, 0, 0, -1, 0, 1, 0, 0, 0, -1, 1, 0, 2, 1, 1, 0, 0, 1, 1, 1, -1, 0, 1, 1, 1, 0, -1, 0, 2, 1, 0, 1, 0, 1, 1, -1, 1, 0, 1, 1, 0, 1, -1, 0, 2, 0, 1, 1, 0, 1, -1, 1, 1, 0, 1, 0, 1, 1, -1, 0, 2, 1, 0, 0, 1, 1, 1, -1, 0, 1, 1, 1, 0, -1, 1, 0, 2, 0, 1, 0, 1, 1, -1, 1, 0, 1, 1, 0, 1, -1, 1, 0, 2, 0, 0, 1, 1, 1, -1, 0, 1, 1, 1, 0, -1, 1, 1, 1, 4, 2, 1, 1, 0, 4, 1, 2, 1, 0, 4, 1, 1, 2, 0, 1, 4, 2, 1, 0, 1, 4, 1, 2, 0, 1, 4, 1, 1, 0, 2, 1, 4, 2, 0, 1, 1, 4, 1, 0, 2, 1, 4, 1, 0, 1, 2, 1, 4, 0, 2, 1, 1, 4, 0, 1, 2, 1, 4, 0, 1, 1, 2, 1, 2, 1, 1, 0, 0, 3, 2, 1, 0, 0, 3, 1, 2, 0, 0, 1, 2, 1, 0, 1, 0, 3, 2, 0, 1, 0, 3, 1, 0, 2, 0, 1, 2, 0, 1, 1, 0, 3, 0, 2, 1, 0, 3, 0, 1, 2, 0, 1, 2, 1, 0, 0, 1, 3, 2, 0, 0, 1, 3, 1, 0, 0, 2, 1, 2, 0, 1, 0, 1, 3, 0, 2, 0, 1, 3, 0, 1, 0, 2, 1, 2, 0, 0, 1, 1, 3, 0, 0, 2, 1, 3, 0, 0, 1, 2, 2, 3, 1, 1, 1, 0, 2, 1, 1, 1, -1, 2, 2, 0, 0, 0, 2, 3, 1, 1, 0, 1, 2, 1, 1, -1, 1, 2, 2, 0, 0, 0, 2, 3, 1, 0, 1, 1, 2, 1, -1, 1, 1, 2, 2, 0, 0, 0, 2, 3, 1, 1, 1, 0, 2, 1, 1, 1, -1, 2, 0, 2, 0, 0, 2, 3, 1, 1, 0, 1, 2, 1, 1, -1, 1, 2, 0, 2, 0, 0, 2, 3, 0, 1, 1, 1, 2, -1, 1, 1, 1, 2, 0, 2, 0, 0, 2, 3, 1, 1, 1, 0, 2, 1, 1, 1, -1, 2, 0, 0, 2, 0, 2, 3, 1, 0, 1, 1, 2, 1, -1, 1, 1, 2, 0, 0, 2, 0, 2, 3, 0, 1, 1, 1, 2, -1, 1, 1, 1, 2, 0, 0, 2, 0, 2, 3, 1, 1, 0, 1, 2, 1, 1, -1, 1, 2, 0, 0, 0, 2, 2, 3, 1, 0, 1, 1, 2, 1, -1, 1, 1, 2, 0, 0, 0, 2, 2, 3, 0, 1, 1, 1, 2, -1, 1, 1, 1, 2, 0, 0, 0, 2, 2, 1, 1, 1, -1, 0, 1, 1, 1, 0, -1, 0, 0, 0, 0, 0, 2, 1, 1, -1, 1, 0, 1, 1, 0, 1, -1, 0, 0, 0, 0, 0, 2, 1, -1, 1, 1, 0, 1, 0, 1, 1, -1, 0, 0, 0, 0, 0, 2, 1, 1, -1, 0, 1, 1, 1, 0, -1, 1, 0, 0, 0, 0, 0, 2, 1, -1, 1, 0, 1, 1, 0, 1, -1, 1, 0, 0, 0, 0, 0, 2, 1, -1, 0, 1, 1, 1, 0, -1, 1, 1, 0, 0, 0, 0, 0, 2, 1, 1, 1, -1, 0, 1, 1, 1, 0, -1, 2, 2, 0, 0, 0, 2, 1, 1, -1, 1, 0, 1, 1, 0, 1, -1, 2, 2, 0, 0, 0, 2, 1, 1, -1, 0, 1, 1, 1, 0, -1, 1, 2, 2, 0, 0, 0, 2, 1, 1, 1, -1, 0, 1, 1, 1, 0, -1, 2, 0, 2, 0, 0, 2, 1, -1, 1, 1, 0, 1, 0, 1, 1, -1, 2, 0, 2, 0, 0, 2, 1, -1, 1, 0, 1, 1, 0, 1, -1, 1, 2, 0, 2, 0, 0, 2, 1, 1, -1, 1, 0, 1, 1, 0, 1, -1, 2, 0, 0, 2, 0, 2, 1, -1, 1, 1, 0, 1, 0, 1, 1, -1, 2, 0, 0, 2, 0, 2, 1, -1, 0, 1, 1, 1, 0, -1, 1, 1, 2, 0, 0, 2, 0, 2, 1, 1, -1, 0, 1, 1, 1, 0, -1, 1, 2, 0, 0, 0, 2, 2, 1, -1, 1, 0, 1, 1, 0, 1, -1, 1, 2, 0, 0, 0, 2, 2, 1, -1, 0, 1, 1, 1, 0, -1, 1, 1, 2, 0, 0, 0, 2, 3, 1, 1, 0, 0, 0, 2, 2, 0, 0, 0, 2, 1, 1, 1, -1, 3, 1, 0, 1, 0, 0, 2, 0, 2, 0, 0, 2, 1, 1, 1, -1, 3, 1, 0, 0, 1, 0, 2, 0, 0, 2, 0, 2, 1, 1, 1, -1, 3, 1, 1, 0, 0, 0, 2, 2, 0, 0, 0, 2, 1, 1, -1, 1, 3, 1, 0, 1, 0, 0, 2, 0, 2, 0, 0, 2, 1, 1, -1, 1, 3, 1, 0, 0, 0, 1, 2, 0, 0, 0, 2, 2, 1, 1, -1, 1, 3, 1, 1, 0, 0, 0, 2, 2, 0, 0, 0, 2, 1, -1, 1, 1, 3, 1, 0, 0, 1, 0, 2, 0, 0, 2, 0, 2, 1, -1, 1, 1, 3, 1, 0, 0, 0, 1, 2, 0, 0, 0, 2, 2, 1, -1, 1, 1, 3, 1, 0, 1, 0, 0, 2, 0, 2, 0, 0, 2, -1, 1, 1, 1, 3, 1, 0, 0, 1, 0, 2, 0, 0, 2, 0, 2, -1, 1, 1, 1, 3, 1, 0, 0, 0, 1, 2, 0, 0, 0, 2, 2, -1, 1, 1, 1, 3, 3, 2, 1, 0, 0, 3, 1, 2, 0, 0, 4, 1, 1, 1, 1, 3, 3, 2, 0, 1, 0, 3, 1, 0, 2, 0, 4, 1, 1, 1, 1, 3, 3, 0, 2, 1, 0, 3, 0, 1, 2, 0, 4, 1, 1, 1, 1, 3, 3, 2, 0, 0, 1, 3, 1, 0, 0, 2, 4, 1, 1, 1, 1, 3, 3, 0, 2, 0, 1, 3, 0, 1, 0, 2, 4, 1, 1, 1, 1, 3, 3, 0, 0, 2, 1, 3, 0, 0, 1, 2, 4, 1, 1, 1, 1, 3, 3, 2, 1, 0, 0, 3, 1, 2, 0, 0, 2, 1, 1, 1, -1, 3, 3, 2, 0, 1, 0, 3, 1, 0, 2, 0, 2, 1, 1, 1, -1, 3, 3, 0, 2, 1, 0, 3, 0, 1, 2, 0, 2, 1, 1, 1, -1, 3, 3, 2, 1, 0, 0, 3, 1, 2, 0, 0, 2, 1, 1, -1, 1, 3, 3, 2, 0, 0, 1, 3, 1, 0, 0, 2, 2, 1, 1, -1, 1, 3, 3, 0, 2, 0, 1, 3, 0, 1, 0, 2, 2, 1, 1, -1, 1, 3, 3, 2, 0, 1, 0, 3, 1, 0, 2, 0, 2, 1, -1, 1, 1, 3, 3, 2, 0, 0, 1, 3, 1, 0, 0, 2, 2, 1, -1, 1, 1, 3, 3, 0, 0, 2, 1, 3, 0, 0, 1, 2, 2, 1, -1, 1, 1, 3, 3, 0, 2, 1, 0, 3, 0, 1, 2, 0, 2, -1, 1, 1, 1, 3, 3, 0, 2, 0, 1, 3, 0, 1, 0, 2, 2, -1, 1, 1, 1, 3, 3, 0, 0, 2, 1, 3, 0, 0, 1, 2, 2, -1, 1, 1, 1 }};
const std::array<int32_t, 1120> lookupPairs4D {{ 0, 3, 1, 2, 2, 3, 5, 2, 6, 1, 7, 1, 8, 3, 9, 2, 10, 3, 13, 2, 16, 3, 18, 3, 22, 1, 23, 1, 24, 3, 26, 3, 33, 2, 37, 2, 38, 1, 39, 1, 41, 2, 45, 2, 54, 1, 55, 1, 56, 0, 57, 0, 58, 0, 59, 0, 60, 0, 61, 0, 62, 0, 63, 0, 256, 3, 258, 3, 264, 3, 266, 3, 272, 3, 274, 3, 280, 3, 282, 3, 2049, 2, 2053, 2, 2057, 2, 2061, 2, 2081, 2, 2085, 2, 2089, 2, 2093, 2, 2304, 9, 2305, 9, 2312, 9, 2313, 9, 16390, 1, 16391, 1, 16406, 1, 16407, 1, 16422, 1, 16423, 1, 16438, 1, 16439, 1, 16642, 8, 16646, 8, 16658, 8, 16662, 8, 18437, 6, 18439, 6, 18469, 6, 18471, 6, 18688, 9, 18689, 9, 18690, 8, 18693, 6, 18694, 8, 18695, 6, 18696, 9, 18697, 9, 18706, 8, 18710, 8, 18725, 6, 18727, 6, 131128, 0, 131129, 0, 131130, 0, 131131, 0, 131132, 0, 131133, 0, 131134, 0, 131135, 0, 131352, 7, 131354, 7, 131384, 7, 131386, 7, 133161, 5, 133165, 5, 133177, 5, 133181, 5, 133376, 9, 133377, 9, 133384, 9, 133385, 9, 133400, 7, 133402, 7, 133417, 5, 133421, 5, 133432, 7, 133433, 5, 133434, 7, 133437, 5, 147510, 4, 147511, 4, 147518, 4, 147519, 4, 147714, 8, 147718, 8, 147730, 8, 147734, 8, 147736, 7, 147738, 7, 147766, 4, 147767, 4, 147768, 7, 147770, 7, 147774, 4, 147775, 4, 149509, 6, 149511, 6, 149541, 6, 149543, 6, 149545, 5, 149549, 5, 149558, 4, 149559, 4, 149561, 5, 149565, 5, 149566, 4, 149567, 4, 149760, 9, 149761, 9, 149762, 8, 149765, 6, 149766, 8, 149767, 6, 149768, 9, 149769, 9, 149778, 8, 149782, 8, 149784, 7, 149786, 7, 149797, 6, 149799, 6, 149801, 5, 149805, 5, 149814, 4, 149815, 4, 149816, 7, 149817, 5, 149818, 7, 149821, 5, 149822, 4, 149823, 4, 149824, 37, 149825, 37, 149826, 36, 149829, 34, 149830, 36, 149831, 34, 149832, 37, 149833, 37, 149842, 36, 149846, 36, 149848, 35, 149850, 35, 149861, 34, 149863, 34, 149865, 33, 149869, 33, 149878, 32, 149879, 32, 149880, 35, 149881, 33, 149882, 35, 149885, 33, 149886, 32, 149887, 32, 150080, 49, 150082, 48, 150088, 49, 150098, 48, 150104, 47, 150106, 47, 151873, 46, 151877, 45, 151881, 46, 151909, 45, 151913, 44, 151917, 44, 152128, 49, 152129, 46, 152136, 49, 152137, 46, 166214, 43, 166215, 42, 166230, 43, 166247, 42, 166262, 41, 166263, 41, 166466, 48, 166470, 43, 166482, 48, 166486, 43, 168261, 45, 168263, 42, 168293, 45, 168295, 42, 168512, 31, 168513, 28, 168514, 31, 168517, 28, 168518, 25, 168519, 25, 280952, 40, 280953, 39, 280954, 40, 280957, 39, 280958, 38, 280959, 38, 281176, 47, 281178, 47, 281208, 40, 281210, 40, 282985, 44, 282989, 44, 283001, 39, 283005, 39, 283208, 30, 283209, 27, 283224, 30, 283241, 27, 283256, 22, 283257, 22, 297334, 41, 297335, 41, 297342, 38, 297343, 38, 297554, 29, 297558, 24, 297562, 29, 297590, 24, 297594, 21, 297598, 21, 299365, 26, 299367, 23, 299373, 26, 299383, 23, 299389, 20, 299391, 20, 299584, 31, 299585, 28, 299586, 31, 299589, 28, 299590, 25, 299591, 25, 299592, 30, 299593, 27, 299602, 29, 299606, 24, 299608, 30, 299610, 29, 299621, 26, 299623, 23, 299625, 27, 299629, 26, 299638, 24, 299639, 23, 299640, 22, 299641, 22, 299642, 21, 299645, 20, 299646, 21, 299647, 20, 299648, 61, 299649, 60, 299650, 61, 299653, 60, 299654, 59, 299655, 59, 299656, 58, 299657, 57, 299666, 55, 299670, 54, 299672, 58, 299674, 55, 299685, 52, 299687, 51, 299689, 57, 299693, 52, 299702, 54, 299703, 51, 299704, 56, 299705, 56, 299706, 53, 299709, 50, 299710, 53, 299711, 50, 299904, 61, 299906, 61, 299912, 58, 299922, 55, 299928, 58, 299930, 55, 301697, 60, 301701, 60, 301705, 57, 301733, 52, 301737, 57, 301741, 52, 301952, 79, 301953, 79, 301960, 76, 301961, 76, 316038, 59, 316039, 59, 316054, 54, 316071, 51, 316086, 54, 316087, 51, 316290, 78, 316294, 78, 316306, 73, 316310, 73, 318085, 77, 318087, 77, 318117, 70, 318119, 70, 318336, 79, 318337, 79, 318338, 78, 318341, 77, 318342, 78, 318343, 77, 430776, 56, 430777, 56, 430778, 53, 430781, 50, 430782, 53, 430783, 50, 431000, 75, 431002, 72, 431032, 75, 431034, 72, 432809, 74, 432813, 69, 432825, 74, 432829, 69, 433032, 76, 433033, 76, 433048, 75, 433065, 74, 433080, 75, 433081, 74, 447158, 71, 447159, 68, 447166, 71, 447167, 68, 447378, 73, 447382, 73, 447386, 72, 447414, 71, 447418, 72, 447422, 71, 449189, 70, 449191, 70, 449197, 69, 449207, 68, 449213, 69, 449215, 68, 449408, 67, 449409, 67, 449410, 66, 449413, 64, 449414, 66, 449415, 64, 449416, 67, 449417, 67, 449426, 66, 449430, 66, 449432, 65, 449434, 65, 449445, 64, 449447, 64, 449449, 63, 449453, 63, 449462, 62, 449463, 62, 449464, 65, 449465, 63, 449466, 65, 449469, 63, 449470, 62, 449471, 62, 449472, 19, 449473, 19, 449474, 18, 449477, 16, 449478, 18, 449479, 16, 449480, 19, 449481, 19, 449490, 18, 449494, 18, 449496, 17, 449498, 17, 449509, 16, 449511, 16, 449513, 15, 449517, 15, 449526, 14, 449527, 14, 449528, 17, 449529, 15, 449530, 17, 449533, 15, 449534, 14, 449535, 14, 449728, 19, 449729, 19, 449730, 18, 449734, 18, 449736, 19, 449737, 19, 449746, 18, 449750, 18, 449752, 17, 449754, 17, 449784, 17, 449786, 17, 451520, 19, 451521, 19, 451525, 16, 451527, 16, 451528, 19, 451529, 19, 451557, 16, 451559, 16, 451561, 15, 451565, 15, 451577, 15, 451581, 15, 451776, 19, 451777, 19, 451784, 19, 451785, 19, 465858, 18, 465861, 16, 465862, 18, 465863, 16, 465874, 18, 465878, 18, 465893, 16, 465895, 16, 465910, 14, 465911, 14, 465918, 14, 465919, 14, 466114, 18, 466118, 18, 466130, 18, 466134, 18, 467909, 16, 467911, 16, 467941, 16, 467943, 16, 468160, 13, 468161, 13, 468162, 13, 468163, 13, 468164, 13, 468165, 13, 468166, 13, 468167, 13, 580568, 17, 580570, 17, 580585, 15, 580589, 15, 580598, 14, 580599, 14, 580600, 17, 580601, 15, 580602, 17, 580605, 15, 580606, 14, 580607, 14, 580824, 17, 580826, 17, 580856, 17, 580858, 17, 582633, 15, 582637, 15, 582649, 15, 582653, 15, 582856, 12, 582857, 12, 582872, 12, 582873, 12, 582888, 12, 582889, 12, 582904, 12, 582905, 12, 596982, 14, 596983, 14, 596990, 14, 596991, 14, 597202, 11, 597206, 11, 597210, 11, 597214, 11, 597234, 11, 597238, 11, 597242, 11, 597246, 11, 599013, 10, 599015, 10, 599021, 10, 599023, 10, 599029, 10, 599031, 10, 599037, 10, 599039, 10, 599232, 13, 599233, 13, 599234, 13, 599235, 13, 599236, 13, 599237, 13, 599238, 13, 599239, 13, 599240, 12, 599241, 12, 599250, 11, 599254, 11, 599256, 12, 599257, 12, 599258, 11, 599262, 11, 599269, 10, 599271, 10, 599272, 12, 599273, 12, 599277, 10, 599279, 10, 599282, 11, 599285, 10, 599286, 11, 599287, 10, 599288, 12, 599289, 12, 599290, 11, 599293, 10, 599294, 11, 599295, 10 }};
std::array<Contribution4*, p4D.size() / 16> contributions4D;
for (size_t i = 0; i < p4D.size(); i += 16) {
auto baseSet = base4D[p4D[i]];
Contribution4* previous {nullptr};
Contribution4* current {nullptr};
for (size_t k = 0; k < baseSet.size(); k += 5) {
current = new Contribution4(baseSet[k], baseSet[k + 1], baseSet[k + 2], baseSet[k + 3], baseSet[k + 4]);
if (!previous) {
contributions4D[i / 16] = current;
} else {
previous->Next = current;
}
previous = current;
}
current->Next = new Contribution4(p4D[i + 1], p4D[i + 2], p4D[i + 3], p4D[i + 4], p4D[i + 5]);
current->Next->Next = new Contribution4(p4D[i + 6], p4D[i + 7], p4D[i + 8], p4D[i + 9], p4D[i + 10]);
current->Next->Next->Next = new Contribution4(p4D[i + 11], p4D[i + 12], p4D[i + 13], p4D[i + 14], p4D[i + 15]);
}
for (size_t i = 0; i < lookupPairs4D.size(); i += 2) {
lookup4D[lookupPairs4D[i]] = contributions4D[lookupPairs4D[i + 1]];
}
}
OpenSimplex::OpenSimplex()
: OpenSimplex(std::chrono::high_resolution_clock::now().time_since_epoch().count())
{}
OpenSimplex::OpenSimplex(long seed)
{
std::array<uint8_t, 256> source;
for (size_t i = 0; i < 256; i++) {
source[i] = static_cast<uint8_t>(i);
}
seed = seed * 6364136223846793005L + 1442695040888963407L;
seed = seed * 6364136223846793005L + 1442695040888963407L;
seed = seed * 6364136223846793005L + 1442695040888963407L;
for (int32_t i = 255; i >= 0; i--) {
seed = seed * 6364136223846793005L + 1442695040888963407L;
int32_t r = static_cast<int32_t>((seed + 31) % (i + 1));
if (r < 0) {
r += (i + 1);
}
perm[i] = source[r];
perm2D[i] = static_cast<uint8_t>(perm[i] & 0x0E);
perm3D[i] = static_cast<uint8_t>((perm[i] % 24) * 3);
perm4D[i] = static_cast<uint8_t>(perm[i] & 0xFC);
source[r] = source[i];
}
}
double OpenSimplex::compute(double x, double y) const
{
auto stretchOffset = (x + y) * STRETCH_2D;
auto xs = x + stretchOffset;
auto ys = y + stretchOffset;
auto xsb = FastFloor(xs);
auto ysb = FastFloor(ys);
auto squishOffset = (xsb + ysb) * SQUISH_2D;
auto dx0 = x - (xsb + squishOffset);
auto dy0 = y - (ysb + squishOffset);
auto xins = xs - xsb;
auto yins = ys - ysb;
auto inSum = xins + yins;
auto hash =
static_cast<int32_t>(xins - yins + 1) |
static_cast<int32_t>(inSum) << 1 |
static_cast<int32_t>(inSum + yins) << 2 |
static_cast<int32_t>(inSum + xins) << 4;
auto c = lookups.lookup2D[hash];
auto value = 0.0;
while (c) {
auto dx = dx0 + c->dx;
auto dy = dy0 + c->dy;
auto attn = 2 - dx * dx - dy * dy;
if (attn > 0) {
auto px = xsb + c->xsb;
auto py = ysb + c->ysb;
auto i = perm2D[(perm[px & 0xFF] + py) & 0xFF];
auto valuePart = gradients2D[i] * dx + gradients2D[i + 1] * dy;
attn *= attn;
value += attn * attn * valuePart;
}
c = c->Next;
}
return value * NORM_2D;
}
double OpenSimplex::compute(double x, double y, double z) const
{
auto stretchOffset = (x + y + z) * STRETCH_3D;
auto xs = x + stretchOffset;
auto ys = y + stretchOffset;
auto zs = z + stretchOffset;
auto xsb = FastFloor(xs);
auto ysb = FastFloor(ys);
auto zsb = FastFloor(zs);
auto squishOffset = (xsb + ysb + zsb) * SQUISH_3D;
auto dx0 = x - (xsb + squishOffset);
auto dy0 = y - (ysb + squishOffset);
auto dz0 = z - (zsb + squishOffset);
auto xins = xs - xsb;
auto yins = ys - ysb;
auto zins = zs - zsb;
auto inSum = xins + yins + zins;
auto hash =
static_cast<int32_t>(yins - zins + 1) |
static_cast<int32_t>(xins - yins + 1) << 1 |
static_cast<int32_t>(xins - zins + 1) << 2 |
static_cast<int32_t>(inSum) << 3 |
static_cast<int32_t>(inSum + zins) << 5 |
static_cast<int32_t>(inSum + yins) << 7 |
static_cast<int32_t>(inSum + xins) << 9;
auto c = lookups.lookup3D[hash];
auto value = 0.0;
while (c) {
auto dx = dx0 + c->dx;
auto dy = dy0 + c->dy;
auto dz = dz0 + c->dz;
auto attn = 2 - dx * dx - dy * dy - dz * dz;
if (attn > 0) {
auto px = xsb + c->xsb;
auto py = ysb + c->ysb;
auto pz = zsb + c->zsb;
auto i = perm3D[(perm[(perm[px & 0xFF] + py) & 0xFF] + pz) & 0xFF];
auto valuePart = gradients3D[i] * dx + gradients3D[i + 1] * dy + gradients3D[i + 2] * dz;
attn *= attn;
value += attn * attn * valuePart;
}
c = c->Next;
}
return value * NORM_3D;
}
double OpenSimplex::compute(double x, double y, double z, double w) const
{
auto stretchOffset = (x + y + z + w) * STRETCH_4D;
auto xs = x + stretchOffset;
auto ys = y + stretchOffset;
auto zs = z + stretchOffset;
auto ws = w + stretchOffset;
auto xsb = FastFloor(xs);
auto ysb = FastFloor(ys);
auto zsb = FastFloor(zs);
auto wsb = FastFloor(ws);
auto squishOffset = (xsb + ysb + zsb + wsb) * SQUISH_4D;
auto dx0 = x - (xsb + squishOffset);
auto dy0 = y - (ysb + squishOffset);
auto dz0 = z - (zsb + squishOffset);
auto dw0 = w - (wsb + squishOffset);
auto xins = xs - xsb;
auto yins = ys - ysb;
auto zins = zs - zsb;
auto wins = ws - wsb;
auto inSum = xins + yins + zins + wins;
auto hash =
static_cast<int32_t>(zins - wins + 1) |
static_cast<int32_t>(yins - zins + 1) << 1 |
static_cast<int32_t>(yins - wins + 1) << 2 |
static_cast<int32_t>(xins - yins + 1) << 3 |
static_cast<int32_t>(xins - zins + 1) << 4 |
static_cast<int32_t>(xins - wins + 1) << 5 |
static_cast<int32_t>(inSum) << 6 |
static_cast<int32_t>(inSum + wins) << 8 |
static_cast<int32_t>(inSum + zins) << 11 |
static_cast<int32_t>(inSum + yins) << 14 |
static_cast<int32_t>(inSum + xins) << 17;
auto c = lookups.lookup4D[hash];
auto value = 0.0;
while (c) {
auto dx = dx0 + c->dx;
auto dy = dy0 + c->dy;
auto dz = dz0 + c->dz;
auto dw = dw0 + c->dw;
auto attn = 2 - dx * dx - dy * dy - dz * dz - dw * dw;
if (attn > 0) {
auto px = xsb + c->xsb;
auto py = ysb + c->ysb;
auto pz = zsb + c->zsb;
auto pw = wsb + c->wsb;
auto i = perm4D[(perm[(perm[(perm[px & 0xFF] + py) & 0xFF] + pz) & 0xFF] + pw) & 0xFF];
auto valuePart = gradients4D[i] * dx + gradients4D[i + 1] * dy + gradients4D[i + 2] * dz + gradients4D[i + 3] * dw;
attn *= attn;
value += attn * attn * valuePart;
}
c = c->Next;
}
return value * NORM_4D;
}
const OpenSimplex::gradients_t<2> OpenSimplex::gradients2D {{
5, 2, 2, 5,
-5, 2, -2, 5,
5, -2, 2, -5,
-5, -2, -2, -5,
}};
const OpenSimplex::gradients_t<3> OpenSimplex::gradients3D {{
-11, 4, 4, -4, 11, 4, -4, 4, 11,
11, 4, 4, 4, 11, 4, 4, 4, 11,
-11, -4, 4, -4, -11, 4, -4, -4, 11,
11, -4, 4, 4, -11, 4, 4, -4, 11,
-11, 4, -4, -4, 11, -4, -4, 4, -11,
11, 4, -4, 4, 11, -4, 4, 4, -11,
-11, -4, -4, -4, -11, -4, -4, -4, -11,
11, -4, -4, 4, -11, -4, 4, -4, -11,
}};
const OpenSimplex::gradients_t<4> OpenSimplex::gradients4D {{
3, 1, 1, 1, 1, 3, 1, 1, 1, 1, 3, 1, 1, 1, 1, 3,
-3, 1, 1, 1, -1, 3, 1, 1, -1, 1, 3, 1, -1, 1, 1, 3,
3, -1, 1, 1, 1, -3, 1, 1, 1, -1, 3, 1, 1, -1, 1, 3,
-3, -1, 1, 1, -1, -3, 1, 1, -1, -1, 3, 1, -1, -1, 1, 3,
3, 1, -1, 1, 1, 3, -1, 1, 1, 1, -3, 1, 1, 1, -1, 3,
-3, 1, -1, 1, -1, 3, -1, 1, -1, 1, -3, 1, -1, 1, -1, 3,
3, -1, -1, 1, 1, -3, -1, 1, 1, -1, -3, 1, 1, -1, -1, 3,
-3, -1, -1, 1, -1, -3, -1, 1, -1, -1, -3, 1, -1, -1, -1, 3,
3, 1, 1, -1, 1, 3, 1, -1, 1, 1, 3, -1, 1, 1, 1, -3,
-3, 1, 1, -1, -1, 3, 1, -1, -1, 1, 3, -1, -1, 1, 1, -3,
3, -1, 1, -1, 1, -3, 1, -1, 1, -1, 3, -1, 1, -1, 1, -3,
-3, -1, 1, -1, -1, -3, 1, -1, -1, -1, 3, -1, -1, -1, 1, -3,
3, 1, -1, -1, 1, 3, -1, -1, 1, 1, -3, -1, 1, 1, -1, -3,
-3, 1, -1, -1, -1, 3, -1, -1, -1, 1, -3, -1, -1, 1, -1, -3,
3, -1, -1, -1, 1, -3, -1, -1, 1, -1, -3, -1, 1, -1, -1, -3,
-3, -1, -1, -1, -1, -3, -1, -1, -1, -1, -3, -1, -1, -1, -1, -3,
}};
const OpenSimplex::Lookups OpenSimplex::lookups;
} // namespace opensimplex
Raw
opensimplex.hpp
/* OpenSimplex Noise in C++
* Ported by Patrick Chieppe from C#
* Original at https://gist.github.com/digitalshadow/134a3a02b67cecd72181
*
* This is free and unencumbered software released into the public domain.
*
* Anyone is free to copy, modify, publish, use, compile, sell, or
* distribute this software, either in source code form or as a compiled
* binary, for any purpose, commercial or non-commercial, and by any
* means.
*
* In jurisdictions that recognize copyright laws, the author or authors
* of this software dedicate any and all copyright interest in the
* software to the public domain. We make this dedication for the benefit
* of the public at large and to the detriment of our heirs and
* successors. We intend this dedication to be an overt act of
* relinquishment in perpetuity of all present and future rights to this
* software under copyright law.
*
* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
* EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
* MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.
* IN NO EVENT SHALL THE AUTHORS BE LIABLE FOR ANY CLAIM, DAMAGES OR
* OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE,
* ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
* OTHER DEALINGS IN THE SOFTWARE.
*
* For more information, please refer to <http://unlicense.org/>
*/
#ifndef OPENSIMPLEX_HPP
#define OPENSIMPLEX_HPP
#include <cstdint>
#include <array>
#include <chrono>
namespace opensimplex {
namespace detail {
inline constexpr size_t c_pow(size_t base, size_t exponent)
{
return (exponent == 0
? 1
: base * c_pow(base, exponent - 1));
}
inline constexpr size_t c_sqr(size_t n)
{
return c_pow(n, 2);
}
inline constexpr size_t gradients_size(size_t dimension)
{
return c_sqr(dimension) * c_pow(2, dimension);
}
} // namespace detail
class OpenSimplex
{
public:
explicit OpenSimplex();
explicit OpenSimplex(long seed);
double compute(double x, double y) const;
double compute(double x, double y, double z) const;
double compute(double x, double y, double z, double w) const;
private:
std::array<uint8_t, 256> perm, perm2D, perm3D, perm4D;
// Static members
template<size_t n>
using gradients_t = std::array<double, detail::gradients_size(n)>;
static const gradients_t<2> gradients2D;
static const gradients_t<3> gradients3D;
static const gradients_t<4> gradients4D;
struct Contribution2
{
int32_t xsb, ysb;
double dx, dy;
Contribution2* Next {nullptr};
Contribution2();
Contribution2(double multiplier, int32_t xsb, int32_t ysb);
};
struct Contribution3
{
int32_t xsb, ysb, zsb;
double dx, dy, dz;
Contribution3* Next {nullptr};
Contribution3();
Contribution3(double multiplier, int32_t xsb, int32_t ysb, int32_t zsb);
};
struct Contribution4
{
int32_t xsb, ysb, zsb, wsb;
double dx, dy, dz, dw;
Contribution4* Next {nullptr};
Contribution4();
Contribution4(double multiplier, int32_t xsb, int32_t ysb, int32_t zsb, int32_t wsb);
};
struct Lookups
{
std::array<Contribution2*, 64> lookup2D;
std::array<Contribution3*, 2048> lookup3D;
std::array<Contribution4*, 1048576> lookup4D;
Lookups();
};
static const Lookups lookups;
};
} // namespace opensimplex
#endif
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