From 16a67035d039222b95cab7d1b41007a7df0961b5 Mon Sep 17 00:00:00 2001 From: MarcEricMartel <74071476+MarcEricMartel@users.noreply.github.com> Date: Sat, 2 Apr 2022 15:26:55 -0400 Subject: [PATCH] Changements pour v143 et autres corrections. --- SQCSim2021/SQCSim2021.vcxproj | 12 +- SQCSim2021/SQCSim2021.vcxproj.filters | 8 +- SQCSim2021/chunk.cpp | 25 +- SQCSim2021/chunk.h | 2 + SQCSim2021/define.h | 6 +- SQCSim2021/engine.cpp | 8 +- SQCSim2021/opensimplex.cpp | 2542 +++++++++++++++++ SQCSim2021/opensimplex.h | 51 + SQCSim2021/perlin.cpp | 262 -- SQCSim2021/perlin.h | 60 - SQCSim2021/world.cpp | 11 +- SQCSim2021/world.h | 15 +- SQCSim2021/x64/Debug/SQCSim2021.exe.recipe | 11 + .../SQCSim2021.tlog/SQCSim2021.lastbuildstate | 2 + .../SQCSim2021.tlog/clang-cl.command.1.tlog | Bin 0 -> 9442 bytes .../SQCSim2021.tlog/clang-cl.read.1.tlog | Bin 0 -> 1014910 bytes .../SQCSim2021.tlog/clang-cl.write.1.tlog | Bin 0 -> 4484 bytes .../SQCSim2021.tlog/lld-link.command.1.tlog | Bin 0 -> 3700 bytes .../SQCSim2021.tlog/lld-link.read.2.tlog | Bin 0 -> 8886 bytes .../SQCSim2021.tlog/lld-link.write.1.tlog | Bin 0 -> 2120 bytes .../SQCSim2021.tlog/SQCSim2021.lastbuildstate | 4 +- .../clang-cl.1032.delete.1.tlog | Bin 7458 -> 0 bytes .../clang-cl.1032.write.1.tlog | Bin 3400 -> 0 bytes .../clang-cl.11724.delete.1.tlog | Bin 7434 -> 0 bytes .../clang-cl.13204.delete.1.tlog | Bin 7498 -> 0 bytes .../clang-cl.14816.delete.1.tlog | Bin 7426 -> 0 bytes .../clang-cl.16024.delete.1.tlog | Bin 7434 -> 0 bytes .../clang-cl.16472.delete.1.tlog | Bin 7426 -> 0 bytes .../clang-cl.18832.delete.1.tlog | Bin 7482 -> 0 bytes .../clang-cl.19712.delete.1.tlog | Bin 7434 -> 0 bytes .../clang-cl.24092.delete.1.tlog | Bin 7442 -> 0 bytes .../clang-cl.25324.delete.1.tlog | Bin 7426 -> 0 bytes .../clang-cl.26840.delete.1.tlog | Bin 7418 -> 0 bytes .../clang-cl.31424.delete.1.tlog | Bin 7490 -> 0 bytes .../clang-cl.33888.delete.1.tlog | Bin 7482 -> 0 bytes .../clang-cl.34004.delete.1.tlog | Bin 7434 -> 0 bytes .../clang-cl.34284.delete.1.tlog | Bin 7434 -> 0 bytes .../clang-cl.36512.delete.1.tlog | Bin 7418 -> 0 bytes .../clang-cl.7912.delete.1.tlog | Bin 7434 -> 0 bytes .../SQCSim2021.tlog/clang-cl.command.1.tlog | Bin 9822 -> 10414 bytes .../SQCSim2021.tlog/clang-cl.read.1.tlog | Bin 988046 -> 1028398 bytes .../SQCSim2021.tlog/lld-link.command.1.tlog | Bin 3988 -> 4164 bytes .../SQCSim2021.tlog/lld-link.delete.1.tlog | Bin 2514 -> 0 bytes .../SQCSim2021.tlog/lld-link.read.1.tlog | Bin 10424 -> 0 bytes .../SQCSim2021.tlog/lld-link.write.1.tlog | Bin 2082 -> 2200 bytes .../SQCSim2021.vcxproj.FileListAbsolute.txt | 0 x64/Debug/DevIL.dll | Bin 0 -> 1762304 bytes x64/Debug/ILU.dll | Bin 0 -> 109568 bytes x64/Debug/ILUT.dll | Bin 0 -> 36352 bytes x64/Debug/SQCSim2021.exe | Bin 0 -> 477696 bytes x64/Debug/glew32.dll | Bin 0 -> 422912 bytes x64/Debug/irrKlang.dll | Bin 0 -> 585216 bytes x64/Debug/openal32.dll | Bin 0 -> 669696 bytes x64/Debug/sfml-graphics-d-2.dll | Bin 0 -> 1840128 bytes x64/Debug/sfml-network-d-2.dll | Bin 0 -> 434688 bytes x64/Debug/sfml-system-d-2.dll | Bin 0 -> 238080 bytes x64/Debug/sfml-window-d-2.dll | Bin 0 -> 433664 bytes 57 files changed, 2655 insertions(+), 364 deletions(-) create mode 100644 SQCSim2021/opensimplex.cpp create mode 100644 SQCSim2021/opensimplex.h delete mode 100644 SQCSim2021/perlin.cpp delete mode 100644 SQCSim2021/perlin.h create mode 100644 SQCSim2021/x64/Debug/SQCSim2021.exe.recipe create mode 100644 SQCSim2021/x64/Debug/SQCSim2021.tlog/SQCSim2021.lastbuildstate create mode 100644 SQCSim2021/x64/Debug/SQCSim2021.tlog/clang-cl.command.1.tlog create mode 100644 SQCSim2021/x64/Debug/SQCSim2021.tlog/clang-cl.read.1.tlog create mode 100644 SQCSim2021/x64/Debug/SQCSim2021.tlog/clang-cl.write.1.tlog create mode 100644 SQCSim2021/x64/Debug/SQCSim2021.tlog/lld-link.command.1.tlog create mode 100644 SQCSim2021/x64/Debug/SQCSim2021.tlog/lld-link.read.2.tlog create mode 100644 SQCSim2021/x64/Debug/SQCSim2021.tlog/lld-link.write.1.tlog delete mode 100644 SQCSim2021/x64/Release/SQCSim2021.tlog/clang-cl.1032.delete.1.tlog delete mode 100644 SQCSim2021/x64/Release/SQCSim2021.tlog/clang-cl.1032.write.1.tlog delete mode 100644 SQCSim2021/x64/Release/SQCSim2021.tlog/clang-cl.11724.delete.1.tlog delete mode 100644 SQCSim2021/x64/Release/SQCSim2021.tlog/clang-cl.13204.delete.1.tlog delete mode 100644 SQCSim2021/x64/Release/SQCSim2021.tlog/clang-cl.14816.delete.1.tlog delete mode 100644 SQCSim2021/x64/Release/SQCSim2021.tlog/clang-cl.16024.delete.1.tlog delete mode 100644 SQCSim2021/x64/Release/SQCSim2021.tlog/clang-cl.16472.delete.1.tlog delete mode 100644 SQCSim2021/x64/Release/SQCSim2021.tlog/clang-cl.18832.delete.1.tlog delete mode 100644 SQCSim2021/x64/Release/SQCSim2021.tlog/clang-cl.19712.delete.1.tlog delete mode 100644 SQCSim2021/x64/Release/SQCSim2021.tlog/clang-cl.24092.delete.1.tlog delete mode 100644 SQCSim2021/x64/Release/SQCSim2021.tlog/clang-cl.25324.delete.1.tlog delete mode 100644 SQCSim2021/x64/Release/SQCSim2021.tlog/clang-cl.26840.delete.1.tlog delete mode 100644 SQCSim2021/x64/Release/SQCSim2021.tlog/clang-cl.31424.delete.1.tlog delete mode 100644 SQCSim2021/x64/Release/SQCSim2021.tlog/clang-cl.33888.delete.1.tlog delete mode 100644 SQCSim2021/x64/Release/SQCSim2021.tlog/clang-cl.34004.delete.1.tlog delete mode 100644 SQCSim2021/x64/Release/SQCSim2021.tlog/clang-cl.34284.delete.1.tlog delete mode 100644 SQCSim2021/x64/Release/SQCSim2021.tlog/clang-cl.36512.delete.1.tlog delete mode 100644 SQCSim2021/x64/Release/SQCSim2021.tlog/clang-cl.7912.delete.1.tlog delete mode 100644 SQCSim2021/x64/Release/SQCSim2021.tlog/lld-link.delete.1.tlog delete mode 100644 SQCSim2021/x64/Release/SQCSim2021.tlog/lld-link.read.1.tlog create mode 100644 SQCSim2021/x64/Release/SQCSim2021.vcxproj.FileListAbsolute.txt create mode 100644 x64/Debug/DevIL.dll create mode 100644 x64/Debug/ILU.dll create mode 100644 x64/Debug/ILUT.dll create mode 100644 x64/Debug/SQCSim2021.exe create mode 100644 x64/Debug/glew32.dll create mode 100644 x64/Debug/irrKlang.dll create mode 100644 x64/Debug/openal32.dll create mode 100644 x64/Debug/sfml-graphics-d-2.dll create mode 100644 x64/Debug/sfml-network-d-2.dll create mode 100644 x64/Debug/sfml-system-d-2.dll create mode 100644 x64/Debug/sfml-window-d-2.dll diff --git a/SQCSim2021/SQCSim2021.vcxproj b/SQCSim2021/SQCSim2021.vcxproj index 6283299..8a66eba 100644 --- a/SQCSim2021/SQCSim2021.vcxproj +++ b/SQCSim2021/SQCSim2021.vcxproj @@ -29,7 +29,7 @@ - + @@ -49,7 +49,7 @@ - + @@ -72,13 +72,13 @@ Application true Unicode - v142 + ClangCL Application true Unicode - v142 + ClangCL Application @@ -117,8 +117,8 @@ true - $(ProjectDir)\external\irrKlang-1.6.0\include$(MSBuildProjectDirectory)$(MSBuildProjectDirectory);external\devil178\include;external\sfml23\include;$(IncludePath) - external\devil178\lib;external\sfml23\lib;$(LibraryPath);D:\Repos\SQCSim2021\SQCSim2021\external\irrKlang-1.6.0\lib\Win32-visualStudio + external\irrKlang-64bit-1.6.0\include;external\devil180\include;external\sfml251\include;external\glew210\include;$(IncludePath) + external\devil180\lib\x64\Release;external\glew210\lib\Release\x64;external\sfml251\lib;$(LibraryPath);external\irrKlang-64bit-1.6.0\lib\Winx64-visualStudio false diff --git a/SQCSim2021/SQCSim2021.vcxproj.filters b/SQCSim2021/SQCSim2021.vcxproj.filters index 124abf1..4b2e6c9 100644 --- a/SQCSim2021/SQCSim2021.vcxproj.filters +++ b/SQCSim2021/SQCSim2021.vcxproj.filters @@ -68,10 +68,10 @@ Fichiers d%27en-tête - + Fichiers d%27en-tête - + Fichiers d%27en-tête @@ -121,10 +121,10 @@ Fichiers sources - + Fichiers sources - + Fichiers sources diff --git a/SQCSim2021/chunk.cpp b/SQCSim2021/chunk.cpp index c524112..2a98568 100644 --- a/SQCSim2021/chunk.cpp +++ b/SQCSim2021/chunk.cpp @@ -7,24 +7,24 @@ Chunk::Chunk(unsigned int x, unsigned int y) : m_posX(x), m_posY(y) { std::ifstream input(pos.str(), std::fstream::binary); if (input.fail()) { - Perlin perlin = Perlin(8, 45.f, 7.f, PERLIN_SEED); + OpenSimplexNoise::Noise simplex = OpenSimplexNoise::Noise(PERLIN_SEED); m_blocks.Reset(BTYPE_AIR); for (int ix = 0; ix < CHUNK_SIZE_X; ++ix) // Montagnes for (int iz = 0; iz < CHUNK_SIZE_Z; ++iz) { float xnoiz, ynoiz; - xnoiz = (double)(ix + x * CHUNK_SIZE_X) / (double)UINT16_MAX; - ynoiz = (double)(iz + y * CHUNK_SIZE_Z) / (double)UINT16_MAX; - float height = (perlin.Get(xnoiz, ynoiz)) * 20.f + 5.f; + xnoiz = (double)(ix + x * CHUNK_SIZE_X) / 256.; + ynoiz = (double)(iz + y * CHUNK_SIZE_Z) / 256.; + float height = (simplex.eval(xnoiz, ynoiz)) * 60.f + 5.f; for (int iy = 0; iy <= (int)height % CHUNK_SIZE_Y; ++iy) SetBlock(ix, iy, iz, BTYPE_METAL, nullptr); } for (int ix = 0; ix < CHUNK_SIZE_X; ++ix) // Collines for (int iz = 0; iz < CHUNK_SIZE_Z; ++iz) { float xnoiz, ynoiz; - xnoiz = (double)(ix + x * CHUNK_SIZE_X) / (double)UINT16_MAX; - ynoiz = (double)(iz + y * CHUNK_SIZE_Z) / (double)UINT16_MAX; - float height = perlin.Get(xnoiz, ynoiz) * 5.f + 24.f; + xnoiz = (double)(ix + x * CHUNK_SIZE_X) / 64.; + ynoiz = (double)(iz + y * CHUNK_SIZE_Z) / 64.; + float height = simplex.eval(xnoiz, ynoiz) * 5.f + 24.f; for (int iy = 0; iy <= (int)height % CHUNK_SIZE_Y; ++iy) { if (GetBlock(ix, iy, iz) == BTYPE_AIR) SetBlock(ix, iy, iz, BTYPE_GRASS, nullptr); @@ -32,7 +32,7 @@ Chunk::Chunk(unsigned int x, unsigned int y) : m_posX(x), m_posY(y) { } for (int ix = 0; ix < CHUNK_SIZE_X; ++ix) // "Lacs" for (int iz = 0; iz < CHUNK_SIZE_Z; ++iz) { - for (int iy = 0; iy < 13; ++iy) { + for (int iy = 0; iy < 16; ++iy) { if (GetBlock(ix, iy, iz) == BTYPE_AIR) SetBlock(ix, iy, iz, BTYPE_ICE, nullptr); } @@ -40,15 +40,14 @@ Chunk::Chunk(unsigned int x, unsigned int y) : m_posX(x), m_posY(y) { for (int ix = 0; ix < CHUNK_SIZE_X; ++ix) // "Arbres" for (int iz = 0; iz < CHUNK_SIZE_Z; ++iz) { float xnoiz, ynoiz; - xnoiz = (double)(iz * CHUNK_SIZE_Y + x * CHUNK_SIZE_X) / (double)UINT16_MAX; - ynoiz = (double)(ix * CHUNK_SIZE_Y + y * CHUNK_SIZE_Z) / (double)UINT16_MAX; - bool tree = (int)(abs(perlin.Get(xnoiz, ynoiz)) * 17933.f) % CHUNK_SIZE_Y > 126 ? true : false; - + xnoiz = (double)(iz * CHUNK_SIZE_Y + x * CHUNK_SIZE_X) / 256.; + ynoiz = (double)(ix * CHUNK_SIZE_Y + y * CHUNK_SIZE_Z) / 256.; + bool tree = (int)(abs(simplex.eval(xnoiz, ynoiz)) * 17933.f) % CHUNK_SIZE_Y > 126 ? true : false; for (int iy = 0; iy < CHUNK_SIZE_Y - 10; ++iy) if (GetBlock(ix, iy, iz) == BTYPE_AIR) if (GetBlock(ix, iy - 1, iz) == BTYPE_GRASS) if (tree) { - for (int i = 0; i < (int)(abs(perlin.Get(xnoiz, ynoiz))) % 3 + 1; ++i) + for (int i = 0; i < (int)(abs(simplex.eval(xnoiz, ynoiz) * 65)) % 42 + 1; ++i) SetBlock(ix, iy + i, iz, BTYPE_DIRT, nullptr); break; } diff --git a/SQCSim2021/chunk.h b/SQCSim2021/chunk.h index 5c0add3..f4d58b1 100644 --- a/SQCSim2021/chunk.h +++ b/SQCSim2021/chunk.h @@ -5,6 +5,8 @@ #include "array2d.h" #include "vertexbuffer.h" #include "blockinfo.h" +#include "perlin.h" +#include "opensimplex.h" class World; diff --git a/SQCSim2021/define.h b/SQCSim2021/define.h index 63987e3..f3f0d93 100644 --- a/SQCSim2021/define.h +++ b/SQCSim2021/define.h @@ -36,8 +36,8 @@ #endif #ifdef NDEBUG -#define WORLD_SIZE_X 128 -#define WORLD_SIZE_Y 128 +#define WORLD_SIZE_X 64 +#define WORLD_SIZE_Y 64 #define FRAMES_RENDER_CHUNKS 1 #define FRAMES_UPDATE_CHUNKS 1 @@ -47,7 +47,7 @@ #define THREADS_UPDATE_CHUNKS 8 #define THREADS_DELETE_CHUNKS 10 -#define VIEW_DISTANCE 1024 +#define VIEW_DISTANCE 512 #define TEXTURE_SIZE 512 #define MAX_BULLETS 512 #endif diff --git a/SQCSim2021/engine.cpp b/SQCSim2021/engine.cpp index 65099e9..204d89e 100644 --- a/SQCSim2021/engine.cpp +++ b/SQCSim2021/engine.cpp @@ -186,12 +186,14 @@ int Engine::GetFps(float elapsedTime) const { return 1 / elapsedTime; } void Engine::Render(float elapsedTime) { static float gameTime = elapsedTime; + static float pollTime = 0; static float bulletTime = 0; static BlockType bloc = 1; if (elapsedTime > 0.1f) return; gameTime += elapsedTime; + pollTime += elapsedTime; Transformation all; Transformation skybox; @@ -205,9 +207,13 @@ void Engine::Render(float elapsedTime) { if (bulletTime > 0.f) bulletTime -= elapsedTime; if (bulletTime < 0.f) bulletTime = 0.f; + if (pollTime >= .005f) { m_player.ApplyPhysics(m_player.GetInput(m_keyW, m_keyS, m_keyA, m_keyD, m_keySpace, (bloc == BTYPE_LAST && bulletTime <= 0.f && m_mouseL), elapsedTime), m_world, elapsedTime, &m_audio); m_audio.Update3DAudio(m_player.GetPOV(), m_player.GetDirection(), m_player.GetVelocity()); // Ajustement du positionnement 3D avec les coordonnées du joueur et // son vecteur de vélocité (pour l'effet Doppler) + pollTime = 0; + } + m_player.ApplyTransformation(all); m_player.ApplyTransformation(skybox, false); // Version d'ApplyTransformation qui ne tient compte que de la rotation @@ -252,7 +258,7 @@ void Engine::Render(float elapsedTime) { m_bullets[x] = nullptr; } - m_world.Update(m_renderCount, m_bullets, m_player, all, m_shader01, m_textureAtlas, m_perlin, m_blockinfo); + m_world.Update(m_renderCount, m_bullets, m_player, all, m_shader01, m_textureAtlas, m_blockinfo); if (m_isSkybox) m_skybox.Render(skybox); diff --git a/SQCSim2021/opensimplex.cpp b/SQCSim2021/opensimplex.cpp new file mode 100644 index 0000000..a64d31f --- /dev/null +++ b/SQCSim2021/opensimplex.cpp @@ -0,0 +1,2542 @@ +#include "opensimplex.h" + +#include +namespace OpenSimplexNoise +{ + using namespace std; + + Noise::Noise() + : m_stretch2d(-0.211324865405187) //(1/Math.sqrt(2+1)-1)/2; + , m_squish2d(0.366025403784439) //(Math.sqrt(2+1)-1)/2; + , m_stretch3d(-1.0 / 6) //(1/Math.sqrt(3+1)-1)/3; + , m_squish3d(1.0 / 3) //(Math.sqrt(3+1)-1)/3; + , m_stretch4d(-0.138196601125011) //(1/Math.sqrt(4+1)-1)/4; + , m_squish4d(0.309016994374947) //(Math.sqrt(4+1)-1)/4; + , m_norm2d(47) + , m_norm3d(103) + , m_norm4d(30) + , m_defaultSeed(0) + , m_perm{0} + , m_permGradIndex3d{0} + , m_gradients2d{ 5, 2, 2, 5, + -5, 2, -2, 5, + 5, -2, 2, -5, + -5, -2, -2, -5, } + , m_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, } + , m_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, } + { + } + + Noise::Noise(int64_t seed) + : Noise() + { + short source[256]; + for (short i = 0; i < 256; i++) + { + source[i] = i; + } + seed = seed * 6364136223846793005l + 1442695040888963407l; + seed = seed * 6364136223846793005l + 1442695040888963407l; + seed = seed * 6364136223846793005l + 1442695040888963407l; + for (int i = 255; i >= 0; i--) + { + seed = seed * 6364136223846793005l + 1442695040888963407l; + int r = static_cast((seed + 31) % (i + 1)); + if (r < 0) + { + r += (i + 1); + } + m_perm[i] = source[r]; + m_permGradIndex3d[i] = static_cast((m_perm[i] % (m_gradients3d.size() / 3)) * 3); + source[r] = source[i]; + } + } + + double Noise::eval(double x, double y) const + { + //Place input coordinates onto grid. + double stretchOffset = (x + y) * m_stretch2d; + double xs = x + stretchOffset; + double ys = y + stretchOffset; + + //Floor to get grid coordinates of rhombus (stretched square) super-cell origin. + int xsb = static_cast(floor(xs)); + int ysb = static_cast(floor(ys)); + + //Skew out to get actual coordinates of rhombus origin. We'll need these later. + double squishOffset = (xsb + ysb) * m_squish2d; + double xb = xsb + squishOffset; + double yb = ysb + squishOffset; + + //Compute grid coordinates relative to rhombus origin. + double xins = xs - xsb; + double yins = ys - ysb; + + //Sum those together to get a value that determines which region we're in. + double inSum = xins + yins; + + //Positions relative to origin point. + double dx0 = x - xb; + double dy0 = y - yb; + + //We'll be defining these inside the next block and using them afterwards. + double dx_ext, dy_ext; + int xsv_ext, ysv_ext; + + double value = 0; + + //Contribution (1,0) + double dx1 = dx0 - 1 - m_squish2d; + double dy1 = dy0 - 0 - m_squish2d; + double attn1 = 2 - dx1 * dx1 - dy1 * dy1; + if (attn1 > 0) + { + attn1 *= attn1; + value += attn1 * attn1 * extrapolate(xsb + 1, ysb + 0, dx1, dy1); + } + + //Contribution (0,1) + double dx2 = dx0 - 0 - m_squish2d; + double dy2 = dy0 - 1 - m_squish2d; + double attn2 = 2 - dx2 * dx2 - dy2 * dy2; + if (attn2 > 0) + { + attn2 *= attn2; + value += attn2 * attn2 * extrapolate(xsb + 0, ysb + 1, dx2, dy2); + } + + if (inSum <= 1) + { //We're inside the triangle (2-Simplex) at (0,0) + double zins = 1 - inSum; + if (zins > xins || zins > yins) + { //(0,0) is one of the closest two triangular vertices + if (xins > yins) + { + xsv_ext = xsb + 1; + ysv_ext = ysb - 1; + dx_ext = dx0 - 1; + dy_ext = dy0 + 1; + } + else + { + xsv_ext = xsb - 1; + ysv_ext = ysb + 1; + dx_ext = dx0 + 1; + dy_ext = dy0 - 1; + } + } + else + { //(1,0) and (0,1) are the closest two vertices. + xsv_ext = xsb + 1; + ysv_ext = ysb + 1; + dx_ext = dx0 - 1 - 2 * m_squish2d; + dy_ext = dy0 - 1 - 2 * m_squish2d; + } + } + else + { //We're inside the triangle (2-Simplex) at (1,1) + double zins = 2 - inSum; + if (zins < xins || zins < yins) + { //(0,0) is one of the closest two triangular vertices + if (xins > yins) + { + xsv_ext = xsb + 2; + ysv_ext = ysb + 0; + dx_ext = dx0 - 2 - 2 * m_squish2d; + dy_ext = dy0 + 0 - 2 * m_squish2d; + } + else + { + xsv_ext = xsb + 0; + ysv_ext = ysb + 2; + dx_ext = dx0 + 0 - 2 * m_squish2d; + dy_ext = dy0 - 2 - 2 * m_squish2d; + } + } + else + { //(1,0) and (0,1) are the closest two vertices. + dx_ext = dx0; + dy_ext = dy0; + xsv_ext = xsb; + ysv_ext = ysb; + } + xsb += 1; + ysb += 1; + dx0 = dx0 - 1 - 2 * m_squish2d; + dy0 = dy0 - 1 - 2 * m_squish2d; + } + + //Contribution (0,0) or (1,1) + double attn0 = 2 - dx0 * dx0 - dy0 * dy0; + if (attn0 > 0) + { + attn0 *= attn0; + value += attn0 * attn0 * extrapolate(xsb, ysb, dx0, dy0); + } + + //Extra Vertex + double attn_ext = 2 - dx_ext * dx_ext - dy_ext * dy_ext; + if (attn_ext > 0) + { + attn_ext *= attn_ext; + value += attn_ext * attn_ext * extrapolate(xsv_ext, ysv_ext, dx_ext, dy_ext); + } + + return value / m_norm2d; + } + + double Noise::eval(double x, double y, double z) const + { + //Place input coordinates on simplectic honeycomb. + double stretchOffset = (x + y + z) * m_stretch3d; + double xs = x + stretchOffset; + double ys = y + stretchOffset; + double zs = z + stretchOffset; + + //static_cast(floor to get simplectic honeycomb coordinates of rhombohedron (stretched cube) super-cell origin. + int xsb = static_cast(floor(xs)); + int ysb = static_cast(floor(ys)); + int zsb = static_cast(floor(zs)); + + //Skew out to get actual coordinates of rhombohedron origin. We'll need these later. + double squishOffset = (xsb + ysb + zsb) * m_squish3d; + double xb = xsb + squishOffset; + double yb = ysb + squishOffset; + double zb = zsb + squishOffset; + + //Compute simplectic honeycomb coordinates relative to rhombohedral origin. + double xins = xs - xsb; + double yins = ys - ysb; + double zins = zs - zsb; + + //Sum those together to get a value that determines which region we're in. + double inSum = xins + yins + zins; + + //Positions relative to origin point. + double dx0 = x - xb; + double dy0 = y - yb; + double dz0 = z - zb; + + //We'll be defining these inside the next block and using them afterwards. + double dx_ext0, dy_ext0, dz_ext0; + double dx_ext1, dy_ext1, dz_ext1; + int xsv_ext0, ysv_ext0, zsv_ext0; + int xsv_ext1, ysv_ext1, zsv_ext1; + + double value = 0; + if (inSum <= 1) + { //We're inside the tetrahedron (3-Simplex) at (0,0,0) + +//Determine which two of (0,0,1), (0,1,0), (1,0,0) are closest. + char aPoint = 0x01; + double aScore = xins; + char bPoint = 0x02; + double bScore = yins; + if (aScore >= bScore && zins > bScore) + { + bScore = zins; + bPoint = 0x04; + } + else if (aScore < bScore && zins > aScore) + { + aScore = zins; + aPoint = 0x04; + } + + //Now we determine the two lattice points not part of the tetrahedron that may contribute. + //This depends on the closest two tetrahedral vertices, including (0,0,0) + double wins = 1 - inSum; + if (wins > aScore || wins > bScore) + { //(0,0,0) is one of the closest two tetrahedral vertices. + char c = (bScore > aScore ? bPoint : aPoint); //Our other closest vertex is the closest out of a and b. + + if ((c & 0x01) == 0) + { + xsv_ext0 = xsb - 1; + xsv_ext1 = xsb; + dx_ext0 = dx0 + 1; + dx_ext1 = dx0; + } + else + { + xsv_ext0 = xsv_ext1 = xsb + 1; + dx_ext0 = dx_ext1 = dx0 - 1; + } + + if ((c & 0x02) == 0) + { + ysv_ext0 = ysv_ext1 = ysb; + dy_ext0 = dy_ext1 = dy0; + if ((c & 0x01) == 0) + { + ysv_ext1 -= 1; + dy_ext1 += 1; + } + else + { + ysv_ext0 -= 1; + dy_ext0 += 1; + } + } + else + { + ysv_ext0 = ysv_ext1 = ysb + 1; + dy_ext0 = dy_ext1 = dy0 - 1; + } + + if ((c & 0x04) == 0) + { + zsv_ext0 = zsb; + zsv_ext1 = zsb - 1; + dz_ext0 = dz0; + dz_ext1 = dz0 + 1; + } + else + { + zsv_ext0 = zsv_ext1 = zsb + 1; + dz_ext0 = dz_ext1 = dz0 - 1; + } + } + else + { //(0,0,0) is not one of the closest two tetrahedral vertices. + char c = static_cast(aPoint | bPoint); //Our two extra vertices are determined by the closest two. + + if ((c & 0x01) == 0) + { + xsv_ext0 = xsb; + xsv_ext1 = xsb - 1; + dx_ext0 = dx0 - 2 * m_squish3d; + dx_ext1 = dx0 + 1 - m_squish3d; + } + else + { + xsv_ext0 = xsv_ext1 = xsb + 1; + dx_ext0 = dx0 - 1 - 2 * m_squish3d; + dx_ext1 = dx0 - 1 - m_squish3d; + } + + if ((c & 0x02) == 0) + { + ysv_ext0 = ysb; + ysv_ext1 = ysb - 1; + dy_ext0 = dy0 - 2 * m_squish3d; + dy_ext1 = dy0 + 1 - m_squish3d; + } + else + { + ysv_ext0 = ysv_ext1 = ysb + 1; + dy_ext0 = dy0 - 1 - 2 * m_squish3d; + dy_ext1 = dy0 - 1 - m_squish3d; + } + + if ((c & 0x04) == 0) + { + zsv_ext0 = zsb; + zsv_ext1 = zsb - 1; + dz_ext0 = dz0 - 2 * m_squish3d; + dz_ext1 = dz0 + 1 - m_squish3d; + } + else + { + zsv_ext0 = zsv_ext1 = zsb + 1; + dz_ext0 = dz0 - 1 - 2 * m_squish3d; + dz_ext1 = dz0 - 1 - m_squish3d; + } + } + + //Contribution (0,0,0) + double attn0 = 2 - dx0 * dx0 - dy0 * dy0 - dz0 * dz0; + if (attn0 > 0) + { + attn0 *= attn0; + value += attn0 * attn0 * extrapolate(xsb + 0, ysb + 0, zsb + 0, dx0, dy0, dz0); + } + + //Contribution (1,0,0) + double dx1 = dx0 - 1 - m_squish3d; + double dy1 = dy0 - 0 - m_squish3d; + double dz1 = dz0 - 0 - m_squish3d; + double attn1 = 2 - dx1 * dx1 - dy1 * dy1 - dz1 * dz1; + if (attn1 > 0) + { + attn1 *= attn1; + value += attn1 * attn1 * extrapolate(xsb + 1, ysb + 0, zsb + 0, dx1, dy1, dz1); + } + + //Contribution (0,1,0) + double dx2 = dx0 - 0 - m_squish3d; + double dy2 = dy0 - 1 - m_squish3d; + double dz2 = dz1; + double attn2 = 2 - dx2 * dx2 - dy2 * dy2 - dz2 * dz2; + if (attn2 > 0) + { + attn2 *= attn2; + value += attn2 * attn2 * extrapolate(xsb + 0, ysb + 1, zsb + 0, dx2, dy2, dz2); + } + + //Contribution (0,0,1) + double dx3 = dx2; + double dy3 = dy1; + double dz3 = dz0 - 1 - m_squish3d; + double attn3 = 2 - dx3 * dx3 - dy3 * dy3 - dz3 * dz3; + if (attn3 > 0) + { + attn3 *= attn3; + value += attn3 * attn3 * extrapolate(xsb + 0, ysb + 0, zsb + 1, dx3, dy3, dz3); + } + } + else if (inSum >= 2) + { //We're inside the tetrahedron (3-Simplex) at (1,1,1) + +//Determine which two tetrahedral vertices are the closest, out of (1,1,0), (1,0,1), (0,1,1) but not (1,1,1). + char aPoint = 0x06; + double aScore = xins; + char bPoint = 0x05; + double bScore = yins; + if (aScore <= bScore && zins < bScore) + { + bScore = zins; + bPoint = 0x03; + } + else if (aScore > bScore && zins < aScore) + { + aScore = zins; + aPoint = 0x03; + } + + //Now we determine the two lattice points not part of the tetrahedron that may contribute. + //This depends on the closest two tetrahedral vertices, including (1,1,1) + double wins = 3 - inSum; + if (wins < aScore || wins < bScore) + { //(1,1,1) is one of the closest two tetrahedral vertices. + char c = (bScore < aScore ? bPoint : aPoint); //Our other closest vertex is the closest out of a and b. + + if ((c & 0x01) != 0) + { + xsv_ext0 = xsb + 2; + xsv_ext1 = xsb + 1; + dx_ext0 = dx0 - 2 - 3 * m_squish3d; + dx_ext1 = dx0 - 1 - 3 * m_squish3d; + } + else + { + xsv_ext0 = xsv_ext1 = xsb; + dx_ext0 = dx_ext1 = dx0 - 3 * m_squish3d; + } + + if ((c & 0x02) != 0) + { + ysv_ext0 = ysv_ext1 = ysb + 1; + dy_ext0 = dy_ext1 = dy0 - 1 - 3 * m_squish3d; + if ((c & 0x01) != 0) + { + ysv_ext1 += 1; + dy_ext1 -= 1; + } + else + { + ysv_ext0 += 1; + dy_ext0 -= 1; + } + } + else + { + ysv_ext0 = ysv_ext1 = ysb; + dy_ext0 = dy_ext1 = dy0 - 3 * m_squish3d; + } + + if ((c & 0x04) != 0) + { + zsv_ext0 = zsb + 1; + zsv_ext1 = zsb + 2; + dz_ext0 = dz0 - 1 - 3 * m_squish3d; + dz_ext1 = dz0 - 2 - 3 * m_squish3d; + } + else + { + zsv_ext0 = zsv_ext1 = zsb; + dz_ext0 = dz_ext1 = dz0 - 3 * m_squish3d; + } + } + else + { //(1,1,1) is not one of the closest two tetrahedral vertices. + char c = static_cast(aPoint & bPoint); //Our two extra vertices are determined by the closest two. + + if ((c & 0x01) != 0) + { + xsv_ext0 = xsb + 1; + xsv_ext1 = xsb + 2; + dx_ext0 = dx0 - 1 - m_squish3d; + dx_ext1 = dx0 - 2 - 2 * m_squish3d; + } + else + { + xsv_ext0 = xsv_ext1 = xsb; + dx_ext0 = dx0 - m_squish3d; + dx_ext1 = dx0 - 2 * m_squish3d; + } + + if ((c & 0x02) != 0) + { + ysv_ext0 = ysb + 1; + ysv_ext1 = ysb + 2; + dy_ext0 = dy0 - 1 - m_squish3d; + dy_ext1 = dy0 - 2 - 2 * m_squish3d; + } + else + { + ysv_ext0 = ysv_ext1 = ysb; + dy_ext0 = dy0 - m_squish3d; + dy_ext1 = dy0 - 2 * m_squish3d; + } + + if ((c & 0x04) != 0) + { + zsv_ext0 = zsb + 1; + zsv_ext1 = zsb + 2; + dz_ext0 = dz0 - 1 - m_squish3d; + dz_ext1 = dz0 - 2 - 2 * m_squish3d; + } + else + { + zsv_ext0 = zsv_ext1 = zsb; + dz_ext0 = dz0 - m_squish3d; + dz_ext1 = dz0 - 2 * m_squish3d; + } + } + + //Contribution (1,1,0) + double dx3 = dx0 - 1 - 2 * m_squish3d; + double dy3 = dy0 - 1 - 2 * m_squish3d; + double dz3 = dz0 - 0 - 2 * m_squish3d; + double attn3 = 2 - dx3 * dx3 - dy3 * dy3 - dz3 * dz3; + if (attn3 > 0) + { + attn3 *= attn3; + value += attn3 * attn3 * extrapolate(xsb + 1, ysb + 1, zsb + 0, dx3, dy3, dz3); + } + + //Contribution (1,0,1) + double dx2 = dx3; + double dy2 = dy0 - 0 - 2 * m_squish3d; + double dz2 = dz0 - 1 - 2 * m_squish3d; + double attn2 = 2 - dx2 * dx2 - dy2 * dy2 - dz2 * dz2; + if (attn2 > 0) + { + attn2 *= attn2; + value += attn2 * attn2 * extrapolate(xsb + 1, ysb + 0, zsb + 1, dx2, dy2, dz2); + } + + //Contribution (0,1,1) + double dx1 = dx0 - 0 - 2 * m_squish3d; + double dy1 = dy3; + double dz1 = dz2; + double attn1 = 2 - dx1 * dx1 - dy1 * dy1 - dz1 * dz1; + if (attn1 > 0) + { + attn1 *= attn1; + value += attn1 * attn1 * extrapolate(xsb + 0, ysb + 1, zsb + 1, dx1, dy1, dz1); + } + + //Contribution (1,1,1) + dx0 = dx0 - 1 - 3 * m_squish3d; + dy0 = dy0 - 1 - 3 * m_squish3d; + dz0 = dz0 - 1 - 3 * m_squish3d; + double attn0 = 2 - dx0 * dx0 - dy0 * dy0 - dz0 * dz0; + if (attn0 > 0) + { + attn0 *= attn0; + value += attn0 * attn0 * extrapolate(xsb + 1, ysb + 1, zsb + 1, dx0, dy0, dz0); + } + } + else + { //We're inside the octahedron (Rectified 3-Simplex) in between. + double aScore; + char aPoint; + bool aIsFurtherSide; + double bScore; + char bPoint; + bool bIsFurtherSide; + + //Decide between point (0,0,1) and (1,1,0) as closest + double p1 = xins + yins; + if (p1 > 1) + { + aScore = p1 - 1; + aPoint = 0x03; + aIsFurtherSide = true; + } + else + { + aScore = 1 - p1; + aPoint = 0x04; + aIsFurtherSide = false; + } + + //Decide between point (0,1,0) and (1,0,1) as closest + double p2 = xins + zins; + if (p2 > 1) + { + bScore = p2 - 1; + bPoint = 0x05; + bIsFurtherSide = true; + } + else + { + bScore = 1 - p2; + bPoint = 0x02; + bIsFurtherSide = false; + } + + //The closest out of the two (1,0,0) and (0,1,1) will replace the furthest out of the two decided above, if closer. + double p3 = yins + zins; + if (p3 > 1) + { + double score = p3 - 1; + if (aScore <= bScore && aScore < score) + { + aScore = score; + aPoint = 0x06; + aIsFurtherSide = true; + } + else if (aScore > bScore && bScore < score) + { + bScore = score; + bPoint = 0x06; + bIsFurtherSide = true; + } + } + else + { + double score = 1 - p3; + if (aScore <= bScore && aScore < score) + { + aScore = score; + aPoint = 0x01; + aIsFurtherSide = false; + } + else if (aScore > bScore && bScore < score) + { + bScore = score; + bPoint = 0x01; + bIsFurtherSide = false; + } + } + + //Where each of the two closest points are determines how the extra two vertices are calculated. + if (aIsFurtherSide == bIsFurtherSide) + { + if (aIsFurtherSide) + { //Both closest points on (1,1,1) side + +//One of the two extra points is (1,1,1) + dx_ext0 = dx0 - 1 - 3 * m_squish3d; + dy_ext0 = dy0 - 1 - 3 * m_squish3d; + dz_ext0 = dz0 - 1 - 3 * m_squish3d; + xsv_ext0 = xsb + 1; + ysv_ext0 = ysb + 1; + zsv_ext0 = zsb + 1; + + //Other extra point is based on the shared axis. + char c = static_cast(aPoint & bPoint); + if ((c & 0x01) != 0) + { + dx_ext1 = dx0 - 2 - 2 * m_squish3d; + dy_ext1 = dy0 - 2 * m_squish3d; + dz_ext1 = dz0 - 2 * m_squish3d; + xsv_ext1 = xsb + 2; + ysv_ext1 = ysb; + zsv_ext1 = zsb; + } + else if ((c & 0x02) != 0) + { + dx_ext1 = dx0 - 2 * m_squish3d; + dy_ext1 = dy0 - 2 - 2 * m_squish3d; + dz_ext1 = dz0 - 2 * m_squish3d; + xsv_ext1 = xsb; + ysv_ext1 = ysb + 2; + zsv_ext1 = zsb; + } + else + { + dx_ext1 = dx0 - 2 * m_squish3d; + dy_ext1 = dy0 - 2 * m_squish3d; + dz_ext1 = dz0 - 2 - 2 * m_squish3d; + xsv_ext1 = xsb; + ysv_ext1 = ysb; + zsv_ext1 = zsb + 2; + } + } + else + {//Both closest points on (0,0,0) side + + //One of the two extra points is (0,0,0) + dx_ext0 = dx0; + dy_ext0 = dy0; + dz_ext0 = dz0; + xsv_ext0 = xsb; + ysv_ext0 = ysb; + zsv_ext0 = zsb; + + //Other extra point is based on the omitted axis. + char c = static_cast(aPoint | bPoint); + if ((c & 0x01) == 0) + { + dx_ext1 = dx0 + 1 - m_squish3d; + dy_ext1 = dy0 - 1 - m_squish3d; + dz_ext1 = dz0 - 1 - m_squish3d; + xsv_ext1 = xsb - 1; + ysv_ext1 = ysb + 1; + zsv_ext1 = zsb + 1; + } + else if ((c & 0x02) == 0) + { + dx_ext1 = dx0 - 1 - m_squish3d; + dy_ext1 = dy0 + 1 - m_squish3d; + dz_ext1 = dz0 - 1 - m_squish3d; + xsv_ext1 = xsb + 1; + ysv_ext1 = ysb - 1; + zsv_ext1 = zsb + 1; + } + else + { + dx_ext1 = dx0 - 1 - m_squish3d; + dy_ext1 = dy0 - 1 - m_squish3d; + dz_ext1 = dz0 + 1 - m_squish3d; + xsv_ext1 = xsb + 1; + ysv_ext1 = ysb + 1; + zsv_ext1 = zsb - 1; + } + } + } + else + { //One point on (0,0,0) side, one point on (1,1,1) side + char c1, c2; + if (aIsFurtherSide) + { + c1 = aPoint; + c2 = bPoint; + } + else + { + c1 = bPoint; + c2 = aPoint; + } + + //One contribution is a permutation of (1,1,-1) + if ((c1 & 0x01) == 0) + { + dx_ext0 = dx0 + 1 - m_squish3d; + dy_ext0 = dy0 - 1 - m_squish3d; + dz_ext0 = dz0 - 1 - m_squish3d; + xsv_ext0 = xsb - 1; + ysv_ext0 = ysb + 1; + zsv_ext0 = zsb + 1; + } + else if ((c1 & 0x02) == 0) + { + dx_ext0 = dx0 - 1 - m_squish3d; + dy_ext0 = dy0 + 1 - m_squish3d; + dz_ext0 = dz0 - 1 - m_squish3d; + xsv_ext0 = xsb + 1; + ysv_ext0 = ysb - 1; + zsv_ext0 = zsb + 1; + } + else + { + dx_ext0 = dx0 - 1 - m_squish3d; + dy_ext0 = dy0 - 1 - m_squish3d; + dz_ext0 = dz0 + 1 - m_squish3d; + xsv_ext0 = xsb + 1; + ysv_ext0 = ysb + 1; + zsv_ext0 = zsb - 1; + } + + //One contribution is a permutation of (0,0,2) + dx_ext1 = dx0 - 2 * m_squish3d; + dy_ext1 = dy0 - 2 * m_squish3d; + dz_ext1 = dz0 - 2 * m_squish3d; + xsv_ext1 = xsb; + ysv_ext1 = ysb; + zsv_ext1 = zsb; + if ((c2 & 0x01) != 0) + { + dx_ext1 -= 2; + xsv_ext1 += 2; + } + else if ((c2 & 0x02) != 0) + { + dy_ext1 -= 2; + ysv_ext1 += 2; + } + else + { + dz_ext1 -= 2; + zsv_ext1 += 2; + } + } + + //Contribution (1,0,0) + double dx1 = dx0 - 1 - m_squish3d; + double dy1 = dy0 - 0 - m_squish3d; + double dz1 = dz0 - 0 - m_squish3d; + double attn1 = 2 - dx1 * dx1 - dy1 * dy1 - dz1 * dz1; + if (attn1 > 0) + { + attn1 *= attn1; + value += attn1 * attn1 * extrapolate(xsb + 1, ysb + 0, zsb + 0, dx1, dy1, dz1); + } + + //Contribution (0,1,0) + double dx2 = dx0 - 0 - m_squish3d; + double dy2 = dy0 - 1 - m_squish3d; + double dz2 = dz1; + double attn2 = 2 - dx2 * dx2 - dy2 * dy2 - dz2 * dz2; + if (attn2 > 0) + { + attn2 *= attn2; + value += attn2 * attn2 * extrapolate(xsb + 0, ysb + 1, zsb + 0, dx2, dy2, dz2); + } + + //Contribution (0,0,1) + double dx3 = dx2; + double dy3 = dy1; + double dz3 = dz0 - 1 - m_squish3d; + double attn3 = 2 - dx3 * dx3 - dy3 * dy3 - dz3 * dz3; + if (attn3 > 0) + { + attn3 *= attn3; + value += attn3 * attn3 * extrapolate(xsb + 0, ysb + 0, zsb + 1, dx3, dy3, dz3); + } + + //Contribution (1,1,0) + double dx4 = dx0 - 1 - 2 * m_squish3d; + double dy4 = dy0 - 1 - 2 * m_squish3d; + double dz4 = dz0 - 0 - 2 * m_squish3d; + double attn4 = 2 - dx4 * dx4 - dy4 * dy4 - dz4 * dz4; + if (attn4 > 0) + { + attn4 *= attn4; + value += attn4 * attn4 * extrapolate(xsb + 1, ysb + 1, zsb + 0, dx4, dy4, dz4); + } + + //Contribution (1,0,1) + double dx5 = dx4; + double dy5 = dy0 - 0 - 2 * m_squish3d; + double dz5 = dz0 - 1 - 2 * m_squish3d; + double attn5 = 2 - dx5 * dx5 - dy5 * dy5 - dz5 * dz5; + if (attn5 > 0) + { + attn5 *= attn5; + value += attn5 * attn5 * extrapolate(xsb + 1, ysb + 0, zsb + 1, dx5, dy5, dz5); + } + + //Contribution (0,1,1) + double dx6 = dx0 - 0 - 2 * m_squish3d; + double dy6 = dy4; + double dz6 = dz5; + double attn6 = 2 - dx6 * dx6 - dy6 * dy6 - dz6 * dz6; + if (attn6 > 0) + { + attn6 *= attn6; + value += attn6 * attn6 * extrapolate(xsb + 0, ysb + 1, zsb + 1, dx6, dy6, dz6); + } + } + + //First extra vertex + double attn_ext0 = 2 - dx_ext0 * dx_ext0 - dy_ext0 * dy_ext0 - dz_ext0 * dz_ext0; + if (attn_ext0 > 0) + { + attn_ext0 *= attn_ext0; + value += attn_ext0 * attn_ext0 * extrapolate(xsv_ext0, ysv_ext0, zsv_ext0, dx_ext0, dy_ext0, dz_ext0); + } + + //Second extra vertex + double attn_ext1 = 2 - dx_ext1 * dx_ext1 - dy_ext1 * dy_ext1 - dz_ext1 * dz_ext1; + if (attn_ext1 > 0) + { + attn_ext1 *= attn_ext1; + value += attn_ext1 * attn_ext1 * extrapolate(xsv_ext1, ysv_ext1, zsv_ext1, dx_ext1, dy_ext1, dz_ext1); + } + + return value / m_norm3d; + } + + double Noise::eval(double x, double y, double z, double w) const + { + //Place input coordinates on simplectic honeycomb. + double stretchOffset = (x + y + z + w) * m_stretch4d; + double xs = x + stretchOffset; + double ys = y + stretchOffset; + double zs = z + stretchOffset; + double ws = w + stretchOffset; + + //static_cast(floor to get simplectic honeycomb coordinates of rhombo-hypercube super-cell origin. + int xsb = static_cast(floor(xs)); + int ysb = static_cast(floor(ys)); + int zsb = static_cast(floor(zs)); + int wsb = static_cast(floor(ws)); + + //Skew out to get actual coordinates of stretched rhombo-hypercube origin. We'll need these later. + double squishOffset = (xsb + ysb + zsb + wsb) * m_squish4d; + double xb = xsb + squishOffset; + double yb = ysb + squishOffset; + double zb = zsb + squishOffset; + double wb = wsb + squishOffset; + + //Compute simplectic honeycomb coordinates relative to rhombo-hypercube origin. + double xins = xs - xsb; + double yins = ys - ysb; + double zins = zs - zsb; + double wins = ws - wsb; + + //Sum those together to get a value that determines which region we're in. + double inSum = xins + yins + zins + wins; + + //Positions relative to origin point. + double dx0 = x - xb; + double dy0 = y - yb; + double dz0 = z - zb; + double dw0 = w - wb; + + //We'll be defining these inside the next block and using them afterwards. + double dx_ext0, dy_ext0, dz_ext0, dw_ext0; + double dx_ext1, dy_ext1, dz_ext1, dw_ext1; + double dx_ext2, dy_ext2, dz_ext2, dw_ext2; + int xsv_ext0, ysv_ext0, zsv_ext0, wsv_ext0; + int xsv_ext1, ysv_ext1, zsv_ext1, wsv_ext1; + int xsv_ext2, ysv_ext2, zsv_ext2, wsv_ext2; + + double value = 0; + if (inSum <= 1) + { //We're inside the pentachoron (4-Simplex) at (0,0,0,0) + +//Determine which two of (0,0,0,1), (0,0,1,0), (0,1,0,0), (1,0,0,0) are closest. + char aPoint = 0x01; + double aScore = xins; + char bPoint = 0x02; + double bScore = yins; + if (aScore >= bScore && zins > bScore) + { + bScore = zins; + bPoint = 0x04; + } + else if (aScore < bScore && zins > aScore) + { + aScore = zins; + aPoint = 0x04; + } + if (aScore >= bScore && wins > bScore) + { + bScore = wins; + bPoint = 0x08; + } + else if (aScore < bScore && wins > aScore) + { + aScore = wins; + aPoint = 0x08; + } + + //Now we determine the three lattice points not part of the pentachoron that may contribute. + //This depends on the closest two pentachoron vertices, including (0,0,0,0) + double uins = 1 - inSum; + if (uins > aScore || uins > bScore) + { //(0,0,0,0) is one of the closest two pentachoron vertices. + char c = (bScore > aScore ? bPoint : aPoint); //Our other closest vertex is the closest out of a and b. + if ((c & 0x01) == 0) + { + xsv_ext0 = xsb - 1; + xsv_ext1 = xsv_ext2 = xsb; + dx_ext0 = dx0 + 1; + dx_ext1 = dx_ext2 = dx0; + } + else + { + xsv_ext0 = xsv_ext1 = xsv_ext2 = xsb + 1; + dx_ext0 = dx_ext1 = dx_ext2 = dx0 - 1; + } + + if ((c & 0x02) == 0) + { + ysv_ext0 = ysv_ext1 = ysv_ext2 = ysb; + dy_ext0 = dy_ext1 = dy_ext2 = dy0; + if ((c & 0x01) == 0x01) + { + ysv_ext0 -= 1; + dy_ext0 += 1; + } + else + { + ysv_ext1 -= 1; + dy_ext1 += 1; + } + } + else + { + ysv_ext0 = ysv_ext1 = ysv_ext2 = ysb + 1; + dy_ext0 = dy_ext1 = dy_ext2 = dy0 - 1; + } + + if ((c & 0x04) == 0) + { + zsv_ext0 = zsv_ext1 = zsv_ext2 = zsb; + dz_ext0 = dz_ext1 = dz_ext2 = dz0; + if ((c & 0x03) != 0) + { + if ((c & 0x03) == 0x03) + { + zsv_ext0 -= 1; + dz_ext0 += 1; + } + else + { + zsv_ext1 -= 1; + dz_ext1 += 1; + } + } + else + { + zsv_ext2 -= 1; + dz_ext2 += 1; + } + } + else + { + zsv_ext0 = zsv_ext1 = zsv_ext2 = zsb + 1; + dz_ext0 = dz_ext1 = dz_ext2 = dz0 - 1; + } + + if ((c & 0x08) == 0) + { + wsv_ext0 = wsv_ext1 = wsb; + wsv_ext2 = wsb - 1; + dw_ext0 = dw_ext1 = dw0; + dw_ext2 = dw0 + 1; + } + else + { + wsv_ext0 = wsv_ext1 = wsv_ext2 = wsb + 1; + dw_ext0 = dw_ext1 = dw_ext2 = dw0 - 1; + } + } + else + { //(0,0,0,0) is not one of the closest two pentachoron vertices. + char c = static_cast(aPoint | bPoint); //Our three extra vertices are determined by the closest two. + + if ((c & 0x01) == 0) + { + xsv_ext0 = xsv_ext2 = xsb; + xsv_ext1 = xsb - 1; + dx_ext0 = dx0 - 2 * m_squish4d; + dx_ext1 = dx0 + 1 - m_squish4d; + dx_ext2 = dx0 - m_squish4d; + } + else + { + xsv_ext0 = xsv_ext1 = xsv_ext2 = xsb + 1; + dx_ext0 = dx0 - 1 - 2 * m_squish4d; + dx_ext1 = dx_ext2 = dx0 - 1 - m_squish4d; + } + + if ((c & 0x02) == 0) + { + ysv_ext0 = ysv_ext1 = ysv_ext2 = ysb; + dy_ext0 = dy0 - 2 * m_squish4d; + dy_ext1 = dy_ext2 = dy0 - m_squish4d; + if ((c & 0x01) == 0x01) + { + ysv_ext1 -= 1; + dy_ext1 += 1; + } + else + { + ysv_ext2 -= 1; + dy_ext2 += 1; + } + } + else + { + ysv_ext0 = ysv_ext1 = ysv_ext2 = ysb + 1; + dy_ext0 = dy0 - 1 - 2 * m_squish4d; + dy_ext1 = dy_ext2 = dy0 - 1 - m_squish4d; + } + + if ((c & 0x04) == 0) + { + zsv_ext0 = zsv_ext1 = zsv_ext2 = zsb; + dz_ext0 = dz0 - 2 * m_squish4d; + dz_ext1 = dz_ext2 = dz0 - m_squish4d; + if ((c & 0x03) == 0x03) + { + zsv_ext1 -= 1; + dz_ext1 += 1; + } + else + { + zsv_ext2 -= 1; + dz_ext2 += 1; + } + } + else + { + zsv_ext0 = zsv_ext1 = zsv_ext2 = zsb + 1; + dz_ext0 = dz0 - 1 - 2 * m_squish4d; + dz_ext1 = dz_ext2 = dz0 - 1 - m_squish4d; + } + + if ((c & 0x08) == 0) + { + wsv_ext0 = wsv_ext1 = wsb; + wsv_ext2 = wsb - 1; + dw_ext0 = dw0 - 2 * m_squish4d; + dw_ext1 = dw0 - m_squish4d; + dw_ext2 = dw0 + 1 - m_squish4d; + } + else + { + wsv_ext0 = wsv_ext1 = wsv_ext2 = wsb + 1; + dw_ext0 = dw0 - 1 - 2 * m_squish4d; + dw_ext1 = dw_ext2 = dw0 - 1 - m_squish4d; + } + } + + //Contribution (0,0,0,0) + double attn0 = 2 - dx0 * dx0 - dy0 * dy0 - dz0 * dz0 - dw0 * dw0; + if (attn0 > 0) + { + attn0 *= attn0; + value += attn0 * attn0 * extrapolate(xsb + 0, ysb + 0, zsb + 0, wsb + 0, dx0, dy0, dz0, dw0); + } + + //Contribution (1,0,0,0) + double dx1 = dx0 - 1 - m_squish4d; + double dy1 = dy0 - 0 - m_squish4d; + double dz1 = dz0 - 0 - m_squish4d; + double dw1 = dw0 - 0 - m_squish4d; + double attn1 = 2 - dx1 * dx1 - dy1 * dy1 - dz1 * dz1 - dw1 * dw1; + if (attn1 > 0) + { + attn1 *= attn1; + value += attn1 * attn1 * extrapolate(xsb + 1, ysb + 0, zsb + 0, wsb + 0, dx1, dy1, dz1, dw1); + } + + //Contribution (0,1,0,0) + double dx2 = dx0 - 0 - m_squish4d; + double dy2 = dy0 - 1 - m_squish4d; + double dz2 = dz1; + double dw2 = dw1; + double attn2 = 2 - dx2 * dx2 - dy2 * dy2 - dz2 * dz2 - dw2 * dw2; + if (attn2 > 0) + { + attn2 *= attn2; + value += attn2 * attn2 * extrapolate(xsb + 0, ysb + 1, zsb + 0, wsb + 0, dx2, dy2, dz2, dw2); + } + + //Contribution (0,0,1,0) + double dx3 = dx2; + double dy3 = dy1; + double dz3 = dz0 - 1 - m_squish4d; + double dw3 = dw1; + double attn3 = 2 - dx3 * dx3 - dy3 * dy3 - dz3 * dz3 - dw3 * dw3; + if (attn3 > 0) + { + attn3 *= attn3; + value += attn3 * attn3 * extrapolate(xsb + 0, ysb + 0, zsb + 1, wsb + 0, dx3, dy3, dz3, dw3); + } + + //Contribution (0,0,0,1) + double dx4 = dx2; + double dy4 = dy1; + double dz4 = dz1; + double dw4 = dw0 - 1 - m_squish4d; + double attn4 = 2 - dx4 * dx4 - dy4 * dy4 - dz4 * dz4 - dw4 * dw4; + if (attn4 > 0) + { + attn4 *= attn4; + value += attn4 * attn4 * extrapolate(xsb + 0, ysb + 0, zsb + 0, wsb + 1, dx4, dy4, dz4, dw4); + } + } + else if (inSum >= 3) + { //We're inside the pentachoron (4-Simplex) at (1,1,1,1) +//Determine which two of (1,1,1,0), (1,1,0,1), (1,0,1,1), (0,1,1,1) are closest. + char aPoint = 0x0E; + double aScore = xins; + char bPoint = 0x0D; + double bScore = yins; + if (aScore <= bScore && zins < bScore) + { + bScore = zins; + bPoint = 0x0B; + } + else if (aScore > bScore && zins < aScore) + { + aScore = zins; + aPoint = 0x0B; + } + if (aScore <= bScore && wins < bScore) + { + bScore = wins; + bPoint = 0x07; + } + else if (aScore > bScore && wins < aScore) + { + aScore = wins; + aPoint = 0x07; + } + + //Now we determine the three lattice points not part of the pentachoron that may contribute. + //This depends on the closest two pentachoron vertices, including (0,0,0,0) + double uins = 4 - inSum; + if (uins < aScore || uins < bScore) + { //(1,1,1,1) is one of the closest two pentachoron vertices. + char c = (bScore < aScore ? bPoint : aPoint); //Our other closest vertex is the closest out of a and b. + + if ((c & 0x01) != 0) + { + xsv_ext0 = xsb + 2; + xsv_ext1 = xsv_ext2 = xsb + 1; + dx_ext0 = dx0 - 2 - 4 * m_squish4d; + dx_ext1 = dx_ext2 = dx0 - 1 - 4 * m_squish4d; + } + else + { + xsv_ext0 = xsv_ext1 = xsv_ext2 = xsb; + dx_ext0 = dx_ext1 = dx_ext2 = dx0 - 4 * m_squish4d; + } + + if ((c & 0x02) != 0) + { + ysv_ext0 = ysv_ext1 = ysv_ext2 = ysb + 1; + dy_ext0 = dy_ext1 = dy_ext2 = dy0 - 1 - 4 * m_squish4d; + if ((c & 0x01) != 0) + { + ysv_ext1 += 1; + dy_ext1 -= 1; + } + else + { + ysv_ext0 += 1; + dy_ext0 -= 1; + } + } + else + { + ysv_ext0 = ysv_ext1 = ysv_ext2 = ysb; + dy_ext0 = dy_ext1 = dy_ext2 = dy0 - 4 * m_squish4d; + } + + if ((c & 0x04) != 0) + { + zsv_ext0 = zsv_ext1 = zsv_ext2 = zsb + 1; + dz_ext0 = dz_ext1 = dz_ext2 = dz0 - 1 - 4 * m_squish4d; + if ((c & 0x03) != 0x03) + { + if ((c & 0x03) == 0) + { + zsv_ext0 += 1; + dz_ext0 -= 1; + } + else + { + zsv_ext1 += 1; + dz_ext1 -= 1; + } + } + else + { + zsv_ext2 += 1; + dz_ext2 -= 1; + } + } + else + { + zsv_ext0 = zsv_ext1 = zsv_ext2 = zsb; + dz_ext0 = dz_ext1 = dz_ext2 = dz0 - 4 * m_squish4d; + } + + if ((c & 0x08) != 0) + { + wsv_ext0 = wsv_ext1 = wsb + 1; + wsv_ext2 = wsb + 2; + dw_ext0 = dw_ext1 = dw0 - 1 - 4 * m_squish4d; + dw_ext2 = dw0 - 2 - 4 * m_squish4d; + } + else + { + wsv_ext0 = wsv_ext1 = wsv_ext2 = wsb; + dw_ext0 = dw_ext1 = dw_ext2 = dw0 - 4 * m_squish4d; + } + } + else + { //(1,1,1,1) is not one of the closest two pentachoron vertices. + char c = static_cast(aPoint & bPoint); //Our three extra vertices are determined by the closest two. + + if ((c & 0x01) != 0) + { + xsv_ext0 = xsv_ext2 = xsb + 1; + xsv_ext1 = xsb + 2; + dx_ext0 = dx0 - 1 - 2 * m_squish4d; + dx_ext1 = dx0 - 2 - 3 * m_squish4d; + dx_ext2 = dx0 - 1 - 3 * m_squish4d; + } + else + { + xsv_ext0 = xsv_ext1 = xsv_ext2 = xsb; + dx_ext0 = dx0 - 2 * m_squish4d; + dx_ext1 = dx_ext2 = dx0 - 3 * m_squish4d; + } + + if ((c & 0x02) != 0) + { + ysv_ext0 = ysv_ext1 = ysv_ext2 = ysb + 1; + dy_ext0 = dy0 - 1 - 2 * m_squish4d; + dy_ext1 = dy_ext2 = dy0 - 1 - 3 * m_squish4d; + if ((c & 0x01) != 0) + { + ysv_ext2 += 1; + dy_ext2 -= 1; + } + else + { + ysv_ext1 += 1; + dy_ext1 -= 1; + } + } + else + { + ysv_ext0 = ysv_ext1 = ysv_ext2 = ysb; + dy_ext0 = dy0 - 2 * m_squish4d; + dy_ext1 = dy_ext2 = dy0 - 3 * m_squish4d; + } + + if ((c & 0x04) != 0) + { + zsv_ext0 = zsv_ext1 = zsv_ext2 = zsb + 1; + dz_ext0 = dz0 - 1 - 2 * m_squish4d; + dz_ext1 = dz_ext2 = dz0 - 1 - 3 * m_squish4d; + if ((c & 0x03) != 0) + { + zsv_ext2 += 1; + dz_ext2 -= 1; + } + else + { + zsv_ext1 += 1; + dz_ext1 -= 1; + } + } + else + { + zsv_ext0 = zsv_ext1 = zsv_ext2 = zsb; + dz_ext0 = dz0 - 2 * m_squish4d; + dz_ext1 = dz_ext2 = dz0 - 3 * m_squish4d; + } + + if ((c & 0x08) != 0) + { + wsv_ext0 = wsv_ext1 = wsb + 1; + wsv_ext2 = wsb + 2; + dw_ext0 = dw0 - 1 - 2 * m_squish4d; + dw_ext1 = dw0 - 1 - 3 * m_squish4d; + dw_ext2 = dw0 - 2 - 3 * m_squish4d; + } + else + { + wsv_ext0 = wsv_ext1 = wsv_ext2 = wsb; + dw_ext0 = dw0 - 2 * m_squish4d; + dw_ext1 = dw_ext2 = dw0 - 3 * m_squish4d; + } + } + + //Contribution (1,1,1,0) + double dx4 = dx0 - 1 - 3 * m_squish4d; + double dy4 = dy0 - 1 - 3 * m_squish4d; + double dz4 = dz0 - 1 - 3 * m_squish4d; + double dw4 = dw0 - 3 * m_squish4d; + double attn4 = 2 - dx4 * dx4 - dy4 * dy4 - dz4 * dz4 - dw4 * dw4; + if (attn4 > 0) + { + attn4 *= attn4; + value += attn4 * attn4 * extrapolate(xsb + 1, ysb + 1, zsb + 1, wsb + 0, dx4, dy4, dz4, dw4); + } + + //Contribution (1,1,0,1) + double dx3 = dx4; + double dy3 = dy4; + double dz3 = dz0 - 3 * m_squish4d; + double dw3 = dw0 - 1 - 3 * m_squish4d; + double attn3 = 2 - dx3 * dx3 - dy3 * dy3 - dz3 * dz3 - dw3 * dw3; + if (attn3 > 0) + { + attn3 *= attn3; + value += attn3 * attn3 * extrapolate(xsb + 1, ysb + 1, zsb + 0, wsb + 1, dx3, dy3, dz3, dw3); + } + + //Contribution (1,0,1,1) + double dx2 = dx4; + double dy2 = dy0 - 3 * m_squish4d; + double dz2 = dz4; + double dw2 = dw3; + double attn2 = 2 - dx2 * dx2 - dy2 * dy2 - dz2 * dz2 - dw2 * dw2; + if (attn2 > 0) + { + attn2 *= attn2; + value += attn2 * attn2 * extrapolate(xsb + 1, ysb + 0, zsb + 1, wsb + 1, dx2, dy2, dz2, dw2); + } + + //Contribution (0,1,1,1) + double dx1 = dx0 - 3 * m_squish4d; + double dz1 = dz4; + double dy1 = dy4; + double dw1 = dw3; + double attn1 = 2 - dx1 * dx1 - dy1 * dy1 - dz1 * dz1 - dw1 * dw1; + if (attn1 > 0) + { + attn1 *= attn1; + value += attn1 * attn1 * extrapolate(xsb + 0, ysb + 1, zsb + 1, wsb + 1, dx1, dy1, dz1, dw1); + } + + //Contribution (1,1,1,1) + dx0 = dx0 - 1 - 4 * m_squish4d; + dy0 = dy0 - 1 - 4 * m_squish4d; + dz0 = dz0 - 1 - 4 * m_squish4d; + dw0 = dw0 - 1 - 4 * m_squish4d; + double attn0 = 2 - dx0 * dx0 - dy0 * dy0 - dz0 * dz0 - dw0 * dw0; + if (attn0 > 0) + { + attn0 *= attn0; + value += attn0 * attn0 * extrapolate(xsb + 1, ysb + 1, zsb + 1, wsb + 1, dx0, dy0, dz0, dw0); + } + } + else if (inSum <= 2) + { //We're inside the first dispentachoron (Rectified 4-Simplex) + double aScore; + char aPoint; + bool aIsBiggerSide = true; + double bScore; + char bPoint; + bool bIsBiggerSide = true; + + //Decide between (1,1,0,0) and (0,0,1,1) + if (xins + yins > zins + wins) + { + aScore = xins + yins; + aPoint = 0x03; + } + else + { + aScore = zins + wins; + aPoint = 0x0C; + } + + //Decide between (1,0,1,0) and (0,1,0,1) + if (xins + zins > yins + wins) + { + bScore = xins + zins; + bPoint = 0x05; + } + else + { + bScore = yins + wins; + bPoint = 0x0A; + } + + //Closer between (1,0,0,1) and (0,1,1,0) will replace the further of a and b, if closer. + if (xins + wins > yins + zins) + { + double score = xins + wins; + if (aScore >= bScore && score > bScore) + { + bScore = score; + bPoint = 0x09; + } + else if (aScore < bScore && score > aScore) + { + aScore = score; + aPoint = 0x09; + } + } + else + { + double score = yins + zins; + if (aScore >= bScore && score > bScore) + { + bScore = score; + bPoint = 0x06; + } + else if (aScore < bScore && score > aScore) + { + aScore = score; + aPoint = 0x06; + } + } + + //Decide if (1,0,0,0) is closer. + double p1 = 2 - inSum + xins; + if (aScore >= bScore && p1 > bScore) + { + bScore = p1; + bPoint = 0x01; + bIsBiggerSide = false; + } + else if (aScore < bScore && p1 > aScore) + { + aScore = p1; + aPoint = 0x01; + aIsBiggerSide = false; + } + + //Decide if (0,1,0,0) is closer. + double p2 = 2 - inSum + yins; + if (aScore >= bScore && p2 > bScore) + { + bScore = p2; + bPoint = 0x02; + bIsBiggerSide = false; + } + else if (aScore < bScore && p2 > aScore) + { + aScore = p2; + aPoint = 0x02; + aIsBiggerSide = false; + } + + //Decide if (0,0,1,0) is closer. + double p3 = 2 - inSum + zins; + if (aScore >= bScore && p3 > bScore) + { + bScore = p3; + bPoint = 0x04; + bIsBiggerSide = false; + } + else if (aScore < bScore && p3 > aScore) + { + aScore = p3; + aPoint = 0x04; + aIsBiggerSide = false; + } + + //Decide if (0,0,0,1) is closer. + double p4 = 2 - inSum + wins; + if (aScore >= bScore && p4 > bScore) + { + bScore = p4; + bPoint = 0x08; + bIsBiggerSide = false; + } + else if (aScore < bScore && p4 > aScore) + { + aScore = p4; + aPoint = 0x08; + aIsBiggerSide = false; + } + + //Where each of the two closest points are determines how the extra three vertices are calculated. + if (aIsBiggerSide == bIsBiggerSide) + { + if (aIsBiggerSide) + { //Both closest points on the bigger side + char c1 = static_cast(aPoint | bPoint); + char c2 = static_cast(aPoint & bPoint); + if ((c1 & 0x01) == 0) + { + xsv_ext0 = xsb; + xsv_ext1 = xsb - 1; + dx_ext0 = dx0 - 3 * m_squish4d; + dx_ext1 = dx0 + 1 - 2 * m_squish4d; + } + else + { + xsv_ext0 = xsv_ext1 = xsb + 1; + dx_ext0 = dx0 - 1 - 3 * m_squish4d; + dx_ext1 = dx0 - 1 - 2 * m_squish4d; + } + + if ((c1 & 0x02) == 0) + { + ysv_ext0 = ysb; + ysv_ext1 = ysb - 1; + dy_ext0 = dy0 - 3 * m_squish4d; + dy_ext1 = dy0 + 1 - 2 * m_squish4d; + } + else + { + ysv_ext0 = ysv_ext1 = ysb + 1; + dy_ext0 = dy0 - 1 - 3 * m_squish4d; + dy_ext1 = dy0 - 1 - 2 * m_squish4d; + } + + if ((c1 & 0x04) == 0) + { + zsv_ext0 = zsb; + zsv_ext1 = zsb - 1; + dz_ext0 = dz0 - 3 * m_squish4d; + dz_ext1 = dz0 + 1 - 2 * m_squish4d; + } + else + { + zsv_ext0 = zsv_ext1 = zsb + 1; + dz_ext0 = dz0 - 1 - 3 * m_squish4d; + dz_ext1 = dz0 - 1 - 2 * m_squish4d; + } + + if ((c1 & 0x08) == 0) + { + wsv_ext0 = wsb; + wsv_ext1 = wsb - 1; + dw_ext0 = dw0 - 3 * m_squish4d; + dw_ext1 = dw0 + 1 - 2 * m_squish4d; + } + else + { + wsv_ext0 = wsv_ext1 = wsb + 1; + dw_ext0 = dw0 - 1 - 3 * m_squish4d; + dw_ext1 = dw0 - 1 - 2 * m_squish4d; + } + + //One combination is a permutation of (0,0,0,2) based on c2 + xsv_ext2 = xsb; + ysv_ext2 = ysb; + zsv_ext2 = zsb; + wsv_ext2 = wsb; + dx_ext2 = dx0 - 2 * m_squish4d; + dy_ext2 = dy0 - 2 * m_squish4d; + dz_ext2 = dz0 - 2 * m_squish4d; + dw_ext2 = dw0 - 2 * m_squish4d; + if ((c2 & 0x01) != 0) + { + xsv_ext2 += 2; + dx_ext2 -= 2; + } + else if ((c2 & 0x02) != 0) + { + ysv_ext2 += 2; + dy_ext2 -= 2; + } + else if ((c2 & 0x04) != 0) + { + zsv_ext2 += 2; + dz_ext2 -= 2; + } + else + { + wsv_ext2 += 2; + dw_ext2 -= 2; + } + + } + else + { //Both closest points on the smaller side + //One of the two extra points is (0,0,0,0) + xsv_ext2 = xsb; + ysv_ext2 = ysb; + zsv_ext2 = zsb; + wsv_ext2 = wsb; + dx_ext2 = dx0; + dy_ext2 = dy0; + dz_ext2 = dz0; + dw_ext2 = dw0; + + //Other two points are based on the omitted axes. + char c = static_cast(aPoint | bPoint); + + if ((c & 0x01) == 0) + { + xsv_ext0 = xsb - 1; + xsv_ext1 = xsb; + dx_ext0 = dx0 + 1 - m_squish4d; + dx_ext1 = dx0 - m_squish4d; + } + else + { + xsv_ext0 = xsv_ext1 = xsb + 1; + dx_ext0 = dx_ext1 = dx0 - 1 - m_squish4d; + } + + if ((c & 0x02) == 0) + { + ysv_ext0 = ysv_ext1 = ysb; + dy_ext0 = dy_ext1 = dy0 - m_squish4d; + if ((c & 0x01) == 0x01) + { + ysv_ext0 -= 1; + dy_ext0 += 1; + } + else + { + ysv_ext1 -= 1; + dy_ext1 += 1; + } + } + else + { + ysv_ext0 = ysv_ext1 = ysb + 1; + dy_ext0 = dy_ext1 = dy0 - 1 - m_squish4d; + } + + if ((c & 0x04) == 0) + { + zsv_ext0 = zsv_ext1 = zsb; + dz_ext0 = dz_ext1 = dz0 - m_squish4d; + if ((c & 0x03) == 0x03) + { + zsv_ext0 -= 1; + dz_ext0 += 1; + } + else + { + zsv_ext1 -= 1; + dz_ext1 += 1; + } + } + else + { + zsv_ext0 = zsv_ext1 = zsb + 1; + dz_ext0 = dz_ext1 = dz0 - 1 - m_squish4d; + } + + if ((c & 0x08) == 0) + { + wsv_ext0 = wsb; + wsv_ext1 = wsb - 1; + dw_ext0 = dw0 - m_squish4d; + dw_ext1 = dw0 + 1 - m_squish4d; + } + else + { + wsv_ext0 = wsv_ext1 = wsb + 1; + dw_ext0 = dw_ext1 = dw0 - 1 - m_squish4d; + } + + } + } + else + { //One point on each "side" + char c1, c2; + if (aIsBiggerSide) + { + c1 = aPoint; + c2 = bPoint; + } + else + { + c1 = bPoint; + c2 = aPoint; + } + + //Two contributions are the bigger-sided point with each 0 replaced with -1. + if ((c1 & 0x01) == 0) + { + xsv_ext0 = xsb - 1; + xsv_ext1 = xsb; + dx_ext0 = dx0 + 1 - m_squish4d; + dx_ext1 = dx0 - m_squish4d; + } + else + { + xsv_ext0 = xsv_ext1 = xsb + 1; + dx_ext0 = dx_ext1 = dx0 - 1 - m_squish4d; + } + + if ((c1 & 0x02) == 0) + { + ysv_ext0 = ysv_ext1 = ysb; + dy_ext0 = dy_ext1 = dy0 - m_squish4d; + if ((c1 & 0x01) == 0x01) + { + ysv_ext0 -= 1; + dy_ext0 += 1; + } + else + { + ysv_ext1 -= 1; + dy_ext1 += 1; + } + } + else + { + ysv_ext0 = ysv_ext1 = ysb + 1; + dy_ext0 = dy_ext1 = dy0 - 1 - m_squish4d; + } + + if ((c1 & 0x04) == 0) + { + zsv_ext0 = zsv_ext1 = zsb; + dz_ext0 = dz_ext1 = dz0 - m_squish4d; + if ((c1 & 0x03) == 0x03) + { + zsv_ext0 -= 1; + dz_ext0 += 1; + } + else + { + zsv_ext1 -= 1; + dz_ext1 += 1; + } + } + else + { + zsv_ext0 = zsv_ext1 = zsb + 1; + dz_ext0 = dz_ext1 = dz0 - 1 - m_squish4d; + } + + if ((c1 & 0x08) == 0) + { + wsv_ext0 = wsb; + wsv_ext1 = wsb - 1; + dw_ext0 = dw0 - m_squish4d; + dw_ext1 = dw0 + 1 - m_squish4d; + } + else + { + wsv_ext0 = wsv_ext1 = wsb + 1; + dw_ext0 = dw_ext1 = dw0 - 1 - m_squish4d; + } + + //One contribution is a permutation of (0,0,0,2) based on the smaller-sided point + xsv_ext2 = xsb; + ysv_ext2 = ysb; + zsv_ext2 = zsb; + wsv_ext2 = wsb; + dx_ext2 = dx0 - 2 * m_squish4d; + dy_ext2 = dy0 - 2 * m_squish4d; + dz_ext2 = dz0 - 2 * m_squish4d; + dw_ext2 = dw0 - 2 * m_squish4d; + if ((c2 & 0x01) != 0) + { + xsv_ext2 += 2; + dx_ext2 -= 2; + } + else if ((c2 & 0x02) != 0) + { + ysv_ext2 += 2; + dy_ext2 -= 2; + } + else if ((c2 & 0x04) != 0) + { + zsv_ext2 += 2; + dz_ext2 -= 2; + } + else + { + wsv_ext2 += 2; + dw_ext2 -= 2; + } + } + + //Contribution (1,0,0,0) + double dx1 = dx0 - 1 - m_squish4d; + double dy1 = dy0 - 0 - m_squish4d; + double dz1 = dz0 - 0 - m_squish4d; + double dw1 = dw0 - 0 - m_squish4d; + double attn1 = 2 - dx1 * dx1 - dy1 * dy1 - dz1 * dz1 - dw1 * dw1; + if (attn1 > 0) + { + attn1 *= attn1; + value += attn1 * attn1 * extrapolate(xsb + 1, ysb + 0, zsb + 0, wsb + 0, dx1, dy1, dz1, dw1); + } + + //Contribution (0,1,0,0) + double dx2 = dx0 - 0 - m_squish4d; + double dy2 = dy0 - 1 - m_squish4d; + double dz2 = dz1; + double dw2 = dw1; + double attn2 = 2 - dx2 * dx2 - dy2 * dy2 - dz2 * dz2 - dw2 * dw2; + if (attn2 > 0) + { + attn2 *= attn2; + value += attn2 * attn2 * extrapolate(xsb + 0, ysb + 1, zsb + 0, wsb + 0, dx2, dy2, dz2, dw2); + } + + //Contribution (0,0,1,0) + double dx3 = dx2; + double dy3 = dy1; + double dz3 = dz0 - 1 - m_squish4d; + double dw3 = dw1; + double attn3 = 2 - dx3 * dx3 - dy3 * dy3 - dz3 * dz3 - dw3 * dw3; + if (attn3 > 0) + { + attn3 *= attn3; + value += attn3 * attn3 * extrapolate(xsb + 0, ysb + 0, zsb + 1, wsb + 0, dx3, dy3, dz3, dw3); + } + + //Contribution (0,0,0,1) + double dx4 = dx2; + double dy4 = dy1; + double dz4 = dz1; + double dw4 = dw0 - 1 - m_squish4d; + double attn4 = 2 - dx4 * dx4 - dy4 * dy4 - dz4 * dz4 - dw4 * dw4; + if (attn4 > 0) + { + attn4 *= attn4; + value += attn4 * attn4 * extrapolate(xsb + 0, ysb + 0, zsb + 0, wsb + 1, dx4, dy4, dz4, dw4); + } + + //Contribution (1,1,0,0) + double dx5 = dx0 - 1 - 2 * m_squish4d; + double dy5 = dy0 - 1 - 2 * m_squish4d; + double dz5 = dz0 - 0 - 2 * m_squish4d; + double dw5 = dw0 - 0 - 2 * m_squish4d; + double attn5 = 2 - dx5 * dx5 - dy5 * dy5 - dz5 * dz5 - dw5 * dw5; + if (attn5 > 0) + { + attn5 *= attn5; + value += attn5 * attn5 * extrapolate(xsb + 1, ysb + 1, zsb + 0, wsb + 0, dx5, dy5, dz5, dw5); + } + + //Contribution (1,0,1,0) + double dx6 = dx0 - 1 - 2 * m_squish4d; + double dy6 = dy0 - 0 - 2 * m_squish4d; + double dz6 = dz0 - 1 - 2 * m_squish4d; + double dw6 = dw0 - 0 - 2 * m_squish4d; + double attn6 = 2 - dx6 * dx6 - dy6 * dy6 - dz6 * dz6 - dw6 * dw6; + if (attn6 > 0) + { + attn6 *= attn6; + value += attn6 * attn6 * extrapolate(xsb + 1, ysb + 0, zsb + 1, wsb + 0, dx6, dy6, dz6, dw6); + } + + //Contribution (1,0,0,1) + double dx7 = dx0 - 1 - 2 * m_squish4d; + double dy7 = dy0 - 0 - 2 * m_squish4d; + double dz7 = dz0 - 0 - 2 * m_squish4d; + double dw7 = dw0 - 1 - 2 * m_squish4d; + double attn7 = 2 - dx7 * dx7 - dy7 * dy7 - dz7 * dz7 - dw7 * dw7; + if (attn7 > 0) + { + attn7 *= attn7; + value += attn7 * attn7 * extrapolate(xsb + 1, ysb + 0, zsb + 0, wsb + 1, dx7, dy7, dz7, dw7); + } + + //Contribution (0,1,1,0) + double dx8 = dx0 - 0 - 2 * m_squish4d; + double dy8 = dy0 - 1 - 2 * m_squish4d; + double dz8 = dz0 - 1 - 2 * m_squish4d; + double dw8 = dw0 - 0 - 2 * m_squish4d; + double attn8 = 2 - dx8 * dx8 - dy8 * dy8 - dz8 * dz8 - dw8 * dw8; + if (attn8 > 0) + { + attn8 *= attn8; + value += attn8 * attn8 * extrapolate(xsb + 0, ysb + 1, zsb + 1, wsb + 0, dx8, dy8, dz8, dw8); + } + + //Contribution (0,1,0,1) + double dx9 = dx0 - 0 - 2 * m_squish4d; + double dy9 = dy0 - 1 - 2 * m_squish4d; + double dz9 = dz0 - 0 - 2 * m_squish4d; + double dw9 = dw0 - 1 - 2 * m_squish4d; + double attn9 = 2 - dx9 * dx9 - dy9 * dy9 - dz9 * dz9 - dw9 * dw9; + if (attn9 > 0) + { + attn9 *= attn9; + value += attn9 * attn9 * extrapolate(xsb + 0, ysb + 1, zsb + 0, wsb + 1, dx9, dy9, dz9, dw9); + } + + //Contribution (0,0,1,1) + double dx10 = dx0 - 0 - 2 * m_squish4d; + double dy10 = dy0 - 0 - 2 * m_squish4d; + double dz10 = dz0 - 1 - 2 * m_squish4d; + double dw10 = dw0 - 1 - 2 * m_squish4d; + double attn10 = 2 - dx10 * dx10 - dy10 * dy10 - dz10 * dz10 - dw10 * dw10; + if (attn10 > 0) + { + attn10 *= attn10; + value += attn10 * attn10 * extrapolate(xsb + 0, ysb + 0, zsb + 1, wsb + 1, dx10, dy10, dz10, dw10); + } + } + else + { //We're inside the second dispentachoron (Rectified 4-Simplex) + double aScore; + char aPoint; + bool aIsBiggerSide = true; + double bScore; + char bPoint; + bool bIsBiggerSide = true; + + //Decide between (0,0,1,1) and (1,1,0,0) + if (xins + yins < zins + wins) + { + aScore = xins + yins; + aPoint = 0x0C; + } + else + { + aScore = zins + wins; + aPoint = 0x03; + } + + //Decide between (0,1,0,1) and (1,0,1,0) + if (xins + zins < yins + wins) + { + bScore = xins + zins; + bPoint = 0x0A; + } + else + { + bScore = yins + wins; + bPoint = 0x05; + } + + //Closer between (0,1,1,0) and (1,0,0,1) will replace the further of a and b, if closer. + if (xins + wins < yins + zins) + { + double score = xins + wins; + if (aScore <= bScore && score < bScore) + { + bScore = score; + bPoint = 0x06; + } + else if (aScore > bScore && score < aScore) + { + aScore = score; + aPoint = 0x06; + } + } + else + { + double score = yins + zins; + if (aScore <= bScore && score < bScore) + { + bScore = score; + bPoint = 0x09; + } + else if (aScore > bScore && score < aScore) + { + aScore = score; + aPoint = 0x09; + } + } + + //Decide if (0,1,1,1) is closer. + double p1 = 3 - inSum + xins; + if (aScore <= bScore && p1 < bScore) + { + bScore = p1; + bPoint = 0x0E; + bIsBiggerSide = false; + } + else if (aScore > bScore && p1 < aScore) + { + aScore = p1; + aPoint = 0x0E; + aIsBiggerSide = false; + } + + //Decide if (1,0,1,1) is closer. + double p2 = 3 - inSum + yins; + if (aScore <= bScore && p2 < bScore) + { + bScore = p2; + bPoint = 0x0D; + bIsBiggerSide = false; + } + else if (aScore > bScore && p2 < aScore) + { + aScore = p2; + aPoint = 0x0D; + aIsBiggerSide = false; + } + + //Decide if (1,1,0,1) is closer. + double p3 = 3 - inSum + zins; + if (aScore <= bScore && p3 < bScore) + { + bScore = p3; + bPoint = 0x0B; + bIsBiggerSide = false; + } + else if (aScore > bScore && p3 < aScore) + { + aScore = p3; + aPoint = 0x0B; + aIsBiggerSide = false; + } + + //Decide if (1,1,1,0) is closer. + double p4 = 3 - inSum + wins; + if (aScore <= bScore && p4 < bScore) + { + bScore = p4; + bPoint = 0x07; + bIsBiggerSide = false; + } + else if (aScore > bScore && p4 < aScore) + { + aScore = p4; + aPoint = 0x07; + aIsBiggerSide = false; + } + + //Where each of the two closest points are determines how the extra three vertices are calculated. + if (aIsBiggerSide == bIsBiggerSide) + { + if (aIsBiggerSide) + { //Both closest points on the bigger side + char c1 = static_cast(aPoint & bPoint); + char c2 = static_cast(aPoint | bPoint); + + //Two contributions are permutations of (0,0,0,1) and (0,0,0,2) based on c1 + xsv_ext0 = xsv_ext1 = xsb; + ysv_ext0 = ysv_ext1 = ysb; + zsv_ext0 = zsv_ext1 = zsb; + wsv_ext0 = wsv_ext1 = wsb; + dx_ext0 = dx0 - m_squish4d; + dy_ext0 = dy0 - m_squish4d; + dz_ext0 = dz0 - m_squish4d; + dw_ext0 = dw0 - m_squish4d; + dx_ext1 = dx0 - 2 * m_squish4d; + dy_ext1 = dy0 - 2 * m_squish4d; + dz_ext1 = dz0 - 2 * m_squish4d; + dw_ext1 = dw0 - 2 * m_squish4d; + if ((c1 & 0x01) != 0) + { + xsv_ext0 += 1; + dx_ext0 -= 1; + xsv_ext1 += 2; + dx_ext1 -= 2; + } + else if ((c1 & 0x02) != 0) + { + ysv_ext0 += 1; + dy_ext0 -= 1; + ysv_ext1 += 2; + dy_ext1 -= 2; + } + else if ((c1 & 0x04) != 0) + { + zsv_ext0 += 1; + dz_ext0 -= 1; + zsv_ext1 += 2; + dz_ext1 -= 2; + } + else + { + wsv_ext0 += 1; + dw_ext0 -= 1; + wsv_ext1 += 2; + dw_ext1 -= 2; + } + + //One contribution is a permutation of (1,1,1,-1) based on c2 + xsv_ext2 = xsb + 1; + ysv_ext2 = ysb + 1; + zsv_ext2 = zsb + 1; + wsv_ext2 = wsb + 1; + dx_ext2 = dx0 - 1 - 2 * m_squish4d; + dy_ext2 = dy0 - 1 - 2 * m_squish4d; + dz_ext2 = dz0 - 1 - 2 * m_squish4d; + dw_ext2 = dw0 - 1 - 2 * m_squish4d; + if ((c2 & 0x01) == 0) + { + xsv_ext2 -= 2; + dx_ext2 += 2; + } + else if ((c2 & 0x02) == 0) + { + ysv_ext2 -= 2; + dy_ext2 += 2; + } + else if ((c2 & 0x04) == 0) + { + zsv_ext2 -= 2; + dz_ext2 += 2; + } + else + { + wsv_ext2 -= 2; + dw_ext2 += 2; + } + } + else + { //Both closest points on the smaller side + //One of the two extra points is (1,1,1,1) + xsv_ext2 = xsb + 1; + ysv_ext2 = ysb + 1; + zsv_ext2 = zsb + 1; + wsv_ext2 = wsb + 1; + dx_ext2 = dx0 - 1 - 4 * m_squish4d; + dy_ext2 = dy0 - 1 - 4 * m_squish4d; + dz_ext2 = dz0 - 1 - 4 * m_squish4d; + dw_ext2 = dw0 - 1 - 4 * m_squish4d; + + //Other two points are based on the shared axes. + char c = static_cast(aPoint & bPoint); + + if ((c & 0x01) != 0) + { + xsv_ext0 = xsb + 2; + xsv_ext1 = xsb + 1; + dx_ext0 = dx0 - 2 - 3 * m_squish4d; + dx_ext1 = dx0 - 1 - 3 * m_squish4d; + } + else + { + xsv_ext0 = xsv_ext1 = xsb; + dx_ext0 = dx_ext1 = dx0 - 3 * m_squish4d; + } + + if ((c & 0x02) != 0) + { + ysv_ext0 = ysv_ext1 = ysb + 1; + dy_ext0 = dy_ext1 = dy0 - 1 - 3 * m_squish4d; + if ((c & 0x01) == 0) + { + ysv_ext0 += 1; + dy_ext0 -= 1; + } + else + { + ysv_ext1 += 1; + dy_ext1 -= 1; + } + } + else + { + ysv_ext0 = ysv_ext1 = ysb; + dy_ext0 = dy_ext1 = dy0 - 3 * m_squish4d; + } + + if ((c & 0x04) != 0) + { + zsv_ext0 = zsv_ext1 = zsb + 1; + dz_ext0 = dz_ext1 = dz0 - 1 - 3 * m_squish4d; + if ((c & 0x03) == 0) + { + zsv_ext0 += 1; + dz_ext0 -= 1; + } + else + { + zsv_ext1 += 1; + dz_ext1 -= 1; + } + } + else + { + zsv_ext0 = zsv_ext1 = zsb; + dz_ext0 = dz_ext1 = dz0 - 3 * m_squish4d; + } + + if ((c & 0x08) != 0) + { + wsv_ext0 = wsb + 1; + wsv_ext1 = wsb + 2; + dw_ext0 = dw0 - 1 - 3 * m_squish4d; + dw_ext1 = dw0 - 2 - 3 * m_squish4d; + } + else + { + wsv_ext0 = wsv_ext1 = wsb; + dw_ext0 = dw_ext1 = dw0 - 3 * m_squish4d; + } + } + } + else + { //One point on each "side" + char c1, c2; + if (aIsBiggerSide) + { + c1 = aPoint; + c2 = bPoint; + } + else + { + c1 = bPoint; + c2 = aPoint; + } + + //Two contributions are the bigger-sided point with each 1 replaced with 2. + if ((c1 & 0x01) != 0) + { + xsv_ext0 = xsb + 2; + xsv_ext1 = xsb + 1; + dx_ext0 = dx0 - 2 - 3 * m_squish4d; + dx_ext1 = dx0 - 1 - 3 * m_squish4d; + } + else + { + xsv_ext0 = xsv_ext1 = xsb; + dx_ext0 = dx_ext1 = dx0 - 3 * m_squish4d; + } + + if ((c1 & 0x02) != 0) + { + ysv_ext0 = ysv_ext1 = ysb + 1; + dy_ext0 = dy_ext1 = dy0 - 1 - 3 * m_squish4d; + if ((c1 & 0x01) == 0) + { + ysv_ext0 += 1; + dy_ext0 -= 1; + } + else + { + ysv_ext1 += 1; + dy_ext1 -= 1; + } + } + else + { + ysv_ext0 = ysv_ext1 = ysb; + dy_ext0 = dy_ext1 = dy0 - 3 * m_squish4d; + } + + if ((c1 & 0x04) != 0) + { + zsv_ext0 = zsv_ext1 = zsb + 1; + dz_ext0 = dz_ext1 = dz0 - 1 - 3 * m_squish4d; + if ((c1 & 0x03) == 0) + { + zsv_ext0 += 1; + dz_ext0 -= 1; + } + else + { + zsv_ext1 += 1; + dz_ext1 -= 1; + } + } + else + { + zsv_ext0 = zsv_ext1 = zsb; + dz_ext0 = dz_ext1 = dz0 - 3 * m_squish4d; + } + + if ((c1 & 0x08) != 0) + { + wsv_ext0 = wsb + 1; + wsv_ext1 = wsb + 2; + dw_ext0 = dw0 - 1 - 3 * m_squish4d; + dw_ext1 = dw0 - 2 - 3 * m_squish4d; + } + else + { + wsv_ext0 = wsv_ext1 = wsb; + dw_ext0 = dw_ext1 = dw0 - 3 * m_squish4d; + } + + //One contribution is a permutation of (1,1,1,-1) based on the smaller-sided point + xsv_ext2 = xsb + 1; + ysv_ext2 = ysb + 1; + zsv_ext2 = zsb + 1; + wsv_ext2 = wsb + 1; + dx_ext2 = dx0 - 1 - 2 * m_squish4d; + dy_ext2 = dy0 - 1 - 2 * m_squish4d; + dz_ext2 = dz0 - 1 - 2 * m_squish4d; + dw_ext2 = dw0 - 1 - 2 * m_squish4d; + if ((c2 & 0x01) == 0) + { + xsv_ext2 -= 2; + dx_ext2 += 2; + } + else if ((c2 & 0x02) == 0) + { + ysv_ext2 -= 2; + dy_ext2 += 2; + } + else if ((c2 & 0x04) == 0) + { + zsv_ext2 -= 2; + dz_ext2 += 2; + } + else + { + wsv_ext2 -= 2; + dw_ext2 += 2; + } + } + + //Contribution (1,1,1,0) + double dx4 = dx0 - 1 - 3 * m_squish4d; + double dy4 = dy0 - 1 - 3 * m_squish4d; + double dz4 = dz0 - 1 - 3 * m_squish4d; + double dw4 = dw0 - 3 * m_squish4d; + double attn4 = 2 - dx4 * dx4 - dy4 * dy4 - dz4 * dz4 - dw4 * dw4; + if (attn4 > 0) + { + attn4 *= attn4; + value += attn4 * attn4 * extrapolate(xsb + 1, ysb + 1, zsb + 1, wsb + 0, dx4, dy4, dz4, dw4); + } + + //Contribution (1,1,0,1) + double dx3 = dx4; + double dy3 = dy4; + double dz3 = dz0 - 3 * m_squish4d; + double dw3 = dw0 - 1 - 3 * m_squish4d; + double attn3 = 2 - dx3 * dx3 - dy3 * dy3 - dz3 * dz3 - dw3 * dw3; + if (attn3 > 0) + { + attn3 *= attn3; + value += attn3 * attn3 * extrapolate(xsb + 1, ysb + 1, zsb + 0, wsb + 1, dx3, dy3, dz3, dw3); + } + + //Contribution (1,0,1,1) + double dx2 = dx4; + double dy2 = dy0 - 3 * m_squish4d; + double dz2 = dz4; + double dw2 = dw3; + double attn2 = 2 - dx2 * dx2 - dy2 * dy2 - dz2 * dz2 - dw2 * dw2; + if (attn2 > 0) + { + attn2 *= attn2; + value += attn2 * attn2 * extrapolate(xsb + 1, ysb + 0, zsb + 1, wsb + 1, dx2, dy2, dz2, dw2); + } + + //Contribution (0,1,1,1) + double dx1 = dx0 - 3 * m_squish4d; + double dz1 = dz4; + double dy1 = dy4; + double dw1 = dw3; + double attn1 = 2 - dx1 * dx1 - dy1 * dy1 - dz1 * dz1 - dw1 * dw1; + if (attn1 > 0) + { + attn1 *= attn1; + value += attn1 * attn1 * extrapolate(xsb + 0, ysb + 1, zsb + 1, wsb + 1, dx1, dy1, dz1, dw1); + } + + //Contribution (1,1,0,0) + double dx5 = dx0 - 1 - 2 * m_squish4d; + double dy5 = dy0 - 1 - 2 * m_squish4d; + double dz5 = dz0 - 0 - 2 * m_squish4d; + double dw5 = dw0 - 0 - 2 * m_squish4d; + double attn5 = 2 - dx5 * dx5 - dy5 * dy5 - dz5 * dz5 - dw5 * dw5; + if (attn5 > 0) + { + attn5 *= attn5; + value += attn5 * attn5 * extrapolate(xsb + 1, ysb + 1, zsb + 0, wsb + 0, dx5, dy5, dz5, dw5); + } + + //Contribution (1,0,1,0) + double dx6 = dx0 - 1 - 2 * m_squish4d; + double dy6 = dy0 - 0 - 2 * m_squish4d; + double dz6 = dz0 - 1 - 2 * m_squish4d; + double dw6 = dw0 - 0 - 2 * m_squish4d; + double attn6 = 2 - dx6 * dx6 - dy6 * dy6 - dz6 * dz6 - dw6 * dw6; + if (attn6 > 0) + { + attn6 *= attn6; + value += attn6 * attn6 * extrapolate(xsb + 1, ysb + 0, zsb + 1, wsb + 0, dx6, dy6, dz6, dw6); + } + + //Contribution (1,0,0,1) + double dx7 = dx0 - 1 - 2 * m_squish4d; + double dy7 = dy0 - 0 - 2 * m_squish4d; + double dz7 = dz0 - 0 - 2 * m_squish4d; + double dw7 = dw0 - 1 - 2 * m_squish4d; + double attn7 = 2 - dx7 * dx7 - dy7 * dy7 - dz7 * dz7 - dw7 * dw7; + if (attn7 > 0) + { + attn7 *= attn7; + value += attn7 * attn7 * extrapolate(xsb + 1, ysb + 0, zsb + 0, wsb + 1, dx7, dy7, dz7, dw7); + } + + //Contribution (0,1,1,0) + double dx8 = dx0 - 0 - 2 * m_squish4d; + double dy8 = dy0 - 1 - 2 * m_squish4d; + double dz8 = dz0 - 1 - 2 * m_squish4d; + double dw8 = dw0 - 0 - 2 * m_squish4d; + double attn8 = 2 - dx8 * dx8 - dy8 * dy8 - dz8 * dz8 - dw8 * dw8; + if (attn8 > 0) + { + attn8 *= attn8; + value += attn8 * attn8 * extrapolate(xsb + 0, ysb + 1, zsb + 1, wsb + 0, dx8, dy8, dz8, dw8); + } + + //Contribution (0,1,0,1) + double dx9 = dx0 - 0 - 2 * m_squish4d; + double dy9 = dy0 - 1 - 2 * m_squish4d; + double dz9 = dz0 - 0 - 2 * m_squish4d; + double dw9 = dw0 - 1 - 2 * m_squish4d; + double attn9 = 2 - dx9 * dx9 - dy9 * dy9 - dz9 * dz9 - dw9 * dw9; + if (attn9 > 0) + { + attn9 *= attn9; + value += attn9 * attn9 * extrapolate(xsb + 0, ysb + 1, zsb + 0, wsb + 1, dx9, dy9, dz9, dw9); + } + + //Contribution (0,0,1,1) + double dx10 = dx0 - 0 - 2 * m_squish4d; + double dy10 = dy0 - 0 - 2 * m_squish4d; + double dz10 = dz0 - 1 - 2 * m_squish4d; + double dw10 = dw0 - 1 - 2 * m_squish4d; + double attn10 = 2 - dx10 * dx10 - dy10 * dy10 - dz10 * dz10 - dw10 * dw10; + if (attn10 > 0) + { + attn10 *= attn10; + value += attn10 * attn10 * extrapolate(xsb + 0, ysb + 0, zsb + 1, wsb + 1, dx10, dy10, dz10, dw10); + } + } + + //First extra vertex + double attn_ext0 = 2 - dx_ext0 * dx_ext0 - dy_ext0 * dy_ext0 - dz_ext0 * dz_ext0 - dw_ext0 * dw_ext0; + if (attn_ext0 > 0) + { + attn_ext0 *= attn_ext0; + value += attn_ext0 * attn_ext0 * extrapolate(xsv_ext0, ysv_ext0, zsv_ext0, wsv_ext0, dx_ext0, dy_ext0, dz_ext0, dw_ext0); + } + + //Second extra vertex + double attn_ext1 = 2 - dx_ext1 * dx_ext1 - dy_ext1 * dy_ext1 - dz_ext1 * dz_ext1 - dw_ext1 * dw_ext1; + if (attn_ext1 > 0) + { + attn_ext1 *= attn_ext1; + value += attn_ext1 * attn_ext1 * extrapolate(xsv_ext1, ysv_ext1, zsv_ext1, wsv_ext1, dx_ext1, dy_ext1, dz_ext1, dw_ext1); + } + + //Third extra vertex + double attn_ext2 = 2 - dx_ext2 * dx_ext2 - dy_ext2 * dy_ext2 - dz_ext2 * dz_ext2 - dw_ext2 * dw_ext2; + if (attn_ext2 > 0) + { + attn_ext2 *= attn_ext2; + value += attn_ext2 * attn_ext2 * extrapolate(xsv_ext2, ysv_ext2, zsv_ext2, wsv_ext2, dx_ext2, dy_ext2, dz_ext2, dw_ext2); + } + + return value / m_norm4d; + } + + double Noise::extrapolate(int xsb, int ysb, double dx, double dy) const + { + int index = m_perm[(m_perm[xsb & 0xFF] + ysb) & 0xFF] & 0x0E; + return m_gradients2d[index] * dx + + m_gradients2d[index + 1] * dy; + } + + double Noise::extrapolate(int xsb, int ysb, int zsb, double dx, double dy, double dz) const + { + int index = m_permGradIndex3d[(m_perm[(m_perm[xsb & 0xFF] + ysb) & 0xFF] + zsb) & 0xFF]; + return m_gradients3d[index] * dx + + m_gradients3d[index + 1] * dy + + m_gradients3d[index + 2] * dz; + } + + double Noise::extrapolate(int xsb, int ysb, int zsb, int wsb, double dx, double dy, double dz, double dw) const + { + int index = m_perm[(m_perm[(m_perm[(m_perm[xsb & 0xFF] + ysb) & 0xFF] + zsb) & 0xFF] + wsb) & 0xFF] & 0xFC; + return m_gradients4d[index] * dx + + m_gradients4d[index + 1] * dy + + m_gradients4d[index + 2] * dz + + m_gradients4d[index + 3] * dw; + } + +} \ No newline at end of file diff --git a/SQCSim2021/opensimplex.h b/SQCSim2021/opensimplex.h new file mode 100644 index 0000000..4b1b1f4 --- /dev/null +++ b/SQCSim2021/opensimplex.h @@ -0,0 +1,51 @@ +/** + Open Simple Noise for C++ + + Port to C++ from https://gist.github.com/KdotJPG/b1270127455a94ac5d19 + by Rickard Lundberg, 2019. +*/ +#ifndef _OPENSIMPLEX_H__ +#define _OPENSIMPLEX_H__ + +#include +#include + +namespace OpenSimplexNoise +{ + class Noise + { + public: + Noise(); + Noise(int64_t seed); + //2D Open Simplex Noise. + double eval(const double x, const double y) const; + //3D Open Simplex Noise. + double eval(double x, double y, double z) const; + //4D Open Simplex Noise. + double eval(double x, double y, double z, double w) const; + private: + const double m_stretch2d; + const double m_squish2d; + const double m_stretch3d; + const double m_squish3d; + const double m_stretch4d; + const double m_squish4d; + + const double m_norm2d; + const double m_norm3d; + const double m_norm4d; + + const long m_defaultSeed; + + std::array m_perm; + std::array m_permGradIndex3d; + std::array m_gradients2d; + std::array m_gradients3d; + std::array m_gradients4d; + double extrapolate(int xsb, int ysb, double dx, double dy) const; + double extrapolate(int xsb, int ysb, int zsb, double dx, double dy, double dz) const; + double extrapolate(int xsb, int ysb, int zsb, int wsb, double dx, double dy, double dz, double dw) const; + }; +} + +#endif // _OPENSIMPLEX_H__ \ No newline at end of file diff --git a/SQCSim2021/perlin.cpp b/SQCSim2021/perlin.cpp deleted file mode 100644 index 6e62717..0000000 --- a/SQCSim2021/perlin.cpp +++ /dev/null @@ -1,262 +0,0 @@ -/* coherent noise function over 1, 2 or 3 dimensions */ -/* (copyright Ken Perlin) */ - -#include -#include -#include - -#include "perlin.h" - -#define B SAMPLE_SIZE -#define BM (SAMPLE_SIZE-1) - -#define N 0x1000 -#define NP 12 /* 2^N */ -#define NM 0xfff - -#define s_curve(t) ( t * t * (3.0f - 2.0f * t) ) -#define lerp(t, a, b) ( a + t * (b - a) ) - -#define setup(i,b0,b1,r0,r1)\ - t = vec[i] + N;\ -b0 = ((int)t) & BM;\ -b1 = (b0+1) & BM;\ -r0 = t - (int)t;\ -r1 = r0 - 1.0f; - -float Perlin::noise1(float arg) -{ - int bx0, bx1; - float rx0, rx1, sx, t, u, v, vec[1]; - - vec[0] = arg; - - if (mStart) - { - srand(mSeed); - mStart = false; - init(); - } - - setup(0, bx0,bx1, rx0,rx1); - - sx = s_curve(rx0); - - u = rx0 * g1[ p[ bx0 ] ]; - v = rx1 * g1[ p[ bx1 ] ]; - - return lerp(sx, u, v); -} - -float Perlin::noise2(float vec[2]) -{ - int bx0, bx1, by0, by1, b00, b10, b01, b11; - float rx0, rx1, ry0, ry1, *q, sx, sy, a, b, t, u, v; - int i, j; - - if (mStart) - { - srand(mSeed); - mStart = false; - init(); - } - - setup(0,bx0,bx1,rx0,rx1); - setup(1,by0,by1,ry0,ry1); - - i = p[bx0]; - j = p[bx1]; - - b00 = p[i + by0]; - b10 = p[j + by0]; - b01 = p[i + by1]; - b11 = p[j + by1]; - - sx = s_curve(rx0); - sy = s_curve(ry0); - -#define at2(rx,ry) ( rx * q[0] + ry * q[1] ) - - q = g2[b00]; - u = at2(rx0,ry0); - q = g2[b10]; - v = at2(rx1,ry0); - a = lerp(sx, u, v); - - q = g2[b01]; - u = at2(rx0,ry1); - q = g2[b11]; - v = at2(rx1,ry1); - b = lerp(sx, u, v); - - return lerp(sy, a, b); -} - -float Perlin::noise3(float vec[3]) -{ - int bx0, bx1, by0, by1, bz0, bz1, b00, b10, b01, b11; - float rx0, rx1, ry0, ry1, rz0, rz1, *q, sy, sz, a, b, c, d, t, u, v; - int i, j; - - if (mStart) - { - srand(mSeed); - mStart = false; - init(); - } - - setup(0, bx0,bx1, rx0,rx1); - setup(1, by0,by1, ry0,ry1); - setup(2, bz0,bz1, rz0,rz1); - - i = p[ bx0 ]; - j = p[ bx1 ]; - - b00 = p[ i + by0 ]; - b10 = p[ j + by0 ]; - b01 = p[ i + by1 ]; - b11 = p[ j + by1 ]; - - t = s_curve(rx0); - sy = s_curve(ry0); - sz = s_curve(rz0); - -#define at3(rx,ry,rz) ( rx * q[0] + ry * q[1] + rz * q[2] ) - - q = g3[ b00 + bz0 ] ; u = at3(rx0,ry0,rz0); - q = g3[ b10 + bz0 ] ; v = at3(rx1,ry0,rz0); - a = lerp(t, u, v); - - q = g3[ b01 + bz0 ] ; u = at3(rx0,ry1,rz0); - q = g3[ b11 + bz0 ] ; v = at3(rx1,ry1,rz0); - b = lerp(t, u, v); - - c = lerp(sy, a, b); - - q = g3[ b00 + bz1 ] ; u = at3(rx0,ry0,rz1); - q = g3[ b10 + bz1 ] ; v = at3(rx1,ry0,rz1); - a = lerp(t, u, v); - - q = g3[ b01 + bz1 ] ; u = at3(rx0,ry1,rz1); - q = g3[ b11 + bz1 ] ; v = at3(rx1,ry1,rz1); - b = lerp(t, u, v); - - d = lerp(sy, a, b); - - return lerp(sz, c, d); -} - -void Perlin::normalize2(float v[2]) -{ - float s; - - s = (float)sqrt(v[0] * v[0] + v[1] * v[1]); - s = 1.0f/s; - v[0] = v[0] * s; - v[1] = v[1] * s; -} - -void Perlin::normalize3(float v[3]) -{ - float s; - - s = (float)sqrt(v[0] * v[0] + v[1] * v[1] + v[2] * v[2]); - s = 1.0f/s; - - v[0] = v[0] * s; - v[1] = v[1] * s; - v[2] = v[2] * s; -} - -void Perlin::init(void) -{ - int i, j, k; - - for (i = 0 ; i < B ; i++) - { - p[i] = i; - g1[i] = (float)((rand() % (B + B)) - B) / B; - for (j = 0 ; j < 2 ; j++) - g2[i][j] = (float)((rand() % (B + B)) - B) / B; - normalize2(g2[i]); - for (j = 0 ; j < 3 ; j++) - g3[i][j] = (float)((rand() % (B + B)) - B) / B; - normalize3(g3[i]); - } - - while (--i) - { - k = p[i]; - p[i] = p[j = rand() % B]; - p[j] = k; - } - - for (i = 0 ; i < B + 2 ; i++) - { - p[B + i] = p[i]; - g1[B + i] = g1[i]; - for (j = 0 ; j < 2 ; j++) - g2[B + i][j] = g2[i][j]; - for (j = 0 ; j < 3 ; j++) - g3[B + i][j] = g3[i][j]; - } - -} - - -float Perlin::perlin_noise_2D(float vec[2]) -{ - int terms = mOctaves; - //float freq = mFrequency; - float result = 0.0f; - float amp = mAmplitude; - - vec[0]*=mFrequency; - vec[1]*=mFrequency; - - for( int i=0; i - - -#define SAMPLE_SIZE 1024 - -class Perlin -{ -public: - - Perlin(int octaves,float freq,float amp,int seed); - - - float Get(float x,float y) - { - float vec[2]; - vec[0] = x; - vec[1] = y; - return perlin_noise_2D(vec); - }; - - float Get(float x,float y, float z) - { - float vec[3]; - vec[0] = x; - vec[1] = y; - vec[2] = z; - return perlin_noise_3D(vec); - }; - -private: - void init_perlin(int n,float p); - float perlin_noise_2D(float vec[2]); - float perlin_noise_3D(float vec[3]); - - float noise1(float arg); - float noise2(float vec[2]); - float noise3(float vec[3]); - void normalize2(float v[2]); - void normalize3(float v[3]); - void init(void); - - int mOctaves; - float mFrequency; - float mAmplitude; - int mSeed; - - int p[SAMPLE_SIZE + SAMPLE_SIZE + 2]; - float g3[SAMPLE_SIZE + SAMPLE_SIZE + 2][3]; - float g2[SAMPLE_SIZE + SAMPLE_SIZE + 2][2]; - float g1[SAMPLE_SIZE + SAMPLE_SIZE + 2]; - bool mStart; - -}; - -#endif diff --git a/SQCSim2021/world.cpp b/SQCSim2021/world.cpp index 5fa0880..3042df7 100644 --- a/SQCSim2021/world.cpp +++ b/SQCSim2021/world.cpp @@ -125,12 +125,12 @@ void World::GetScope(unsigned int& x, unsigned int& y) { y = m_center[1]; } -void World::Update(int& rendercount, Bullet* bullets[MAX_BULLETS], Player& player, Transformation& world, Shader& shader, TextureAtlas& atlas, Perlin& perlin, BlockInfo* blockinfo[BTYPE_LAST]) { +void World::Update(int& rendercount, Bullet* bullets[MAX_BULLETS], Player& player, Transformation& world, Shader& shader, TextureAtlas& atlas, BlockInfo* blockinfo[BTYPE_LAST]) { glStencilFunc(GL_EQUAL, 1, 0x00); glStencilOp(GL_KEEP, GL_KEEP, GL_REPLACE); atlas.Bind(); RenderWorld(rendercount, player, world, shader); - UpdateWorld(player, perlin, blockinfo); + UpdateWorld(player, blockinfo); TransposeWorld(player, bullets); shader.Disable(); glStencilFunc(GL_GREATER, 1, 0xFF); @@ -301,7 +301,7 @@ void World::RenderWorld(int& rendercount, Player& player, Transformation& world, shader.Disable(); }; -void World::UpdateWorld(Player& player, Perlin& perlin, BlockInfo* blockinfo[BTYPE_LAST]) { +void World::UpdateWorld(Player& player, BlockInfo* blockinfo[BTYPE_LAST]) { int cx = player.GetPosition().x; int cy = player.GetPosition().z; static int frameGenerate = 0; @@ -466,9 +466,10 @@ void World::UpdateWorld(Player& player, Perlin& perlin, BlockInfo* blockinfo[BTY else m_tbDeleted.pop_back(); } - for (int x = 0; x < threads; ++x) + for (int x = 0; x < threads; ++x) { delThList[x].wait(); - + delThList[x].get(); + } } int World::GettbDeleted() const { return m_tbDeleted.size(); } \ No newline at end of file diff --git a/SQCSim2021/world.h b/SQCSim2021/world.h index ab37cf7..d4b1545 100644 --- a/SQCSim2021/world.h +++ b/SQCSim2021/world.h @@ -1,20 +1,19 @@ #ifndef WORLD_H__ #define WORLD_H__ +#include +#include +#include +#include +#include #include "define.h" #include "chunk.h" #include "array2d.h" #include "vector3.h" #include "player.h" #include "transformation.h" -#include "perlin.h" #include "shader.h" #include "bullet.h" #include "textureatlas.h" -#include -#include -#include -#include -#include class Chunk; class Player; @@ -33,7 +32,7 @@ public: BlockType BlockAt(float x, float y, float z, BlockType defaultBlockType = BTYPE_AIR) const; BlockType BlockAt(const Vector3f& pos, BlockType defaultBlockType = BTYPE_AIR) const; - void Update(int& rendercount, Bullet* bullets[MAX_BULLETS], Player& player, Transformation& world, Shader& shader, TextureAtlas& atlas, Perlin& perlin, BlockInfo* blockinfo[BTYPE_LAST]); + void Update(int& rendercount, Bullet* bullets[MAX_BULLETS], Player& player, Transformation& world, Shader& shader, TextureAtlas& atlas, BlockInfo* blockinfo[BTYPE_LAST]); void GetScope(unsigned int& x, unsigned int& y); @@ -49,7 +48,7 @@ private: void UpdateChunk(int& updates, unsigned int chx, unsigned int chy, BlockInfo* blockinfo[BTYPE_LAST]); void RenderWorld(int& rendercount, Player& player, Transformation& world, Shader& shader); - void UpdateWorld(Player& player, Perlin& perlin, BlockInfo* blockinfo[BTYPE_LAST]); + void UpdateWorld(Player& player, BlockInfo* blockinfo[BTYPE_LAST]); void TransposeWorld(Player& player, Bullet* bullets[MAX_BULLETS]); }; diff --git a/SQCSim2021/x64/Debug/SQCSim2021.exe.recipe b/SQCSim2021/x64/Debug/SQCSim2021.exe.recipe new file mode 100644 index 0000000..2232cc6 --- /dev/null +++ b/SQCSim2021/x64/Debug/SQCSim2021.exe.recipe @@ -0,0 +1,11 @@ + + + + + D:\Repos\SQCSim2021\x64\Debug\SQCSim2021.exe + + + + + + \ No newline at end of file diff --git a/SQCSim2021/x64/Debug/SQCSim2021.tlog/SQCSim2021.lastbuildstate b/SQCSim2021/x64/Debug/SQCSim2021.tlog/SQCSim2021.lastbuildstate new file mode 100644 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