diff options
Diffstat (limited to 'thirdparty')
| -rw-r--r-- | thirdparty/README.md | 5 | ||||
| -rw-r--r-- | thirdparty/misc/open-simplex-noise-LICENSE | 25 | ||||
| -rw-r--r-- | thirdparty/misc/open-simplex-noise-no-allocate.patch | 133 | ||||
| -rw-r--r-- | thirdparty/misc/open-simplex-noise.c | 2254 | ||||
| -rw-r--r-- | thirdparty/misc/open-simplex-noise.h | 58 |
5 files changed, 2475 insertions, 0 deletions
diff --git a/thirdparty/README.md b/thirdparty/README.md index 55f6a71179..71053de016 100644 --- a/thirdparty/README.md +++ b/thirdparty/README.md @@ -356,6 +356,11 @@ Collection of single-file libraries used in Godot components. * Upstream: https://github.com/ivanfratric/polypartition (`src/polypartition.cpp`) * Version: TBD, class was renamed * License: MIT +- `open-simplex-noise.{c,h}` + * Upstream: https://github.com/smcameron/open-simplex-noise-in-c + * Version: git (0d555e7, 2015) + * License: Unlicense + ### modules diff --git a/thirdparty/misc/open-simplex-noise-LICENSE b/thirdparty/misc/open-simplex-noise-LICENSE new file mode 100644 index 0000000000..a84c395662 --- /dev/null +++ b/thirdparty/misc/open-simplex-noise-LICENSE @@ -0,0 +1,25 @@ +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> + diff --git a/thirdparty/misc/open-simplex-noise-no-allocate.patch b/thirdparty/misc/open-simplex-noise-no-allocate.patch new file mode 100644 index 0000000000..fc3abe7d00 --- /dev/null +++ b/thirdparty/misc/open-simplex-noise-no-allocate.patch @@ -0,0 +1,133 @@ +diff -u orig/open-simplex-noise.c misc/open-simplex-noise.c +--- orig/open-simplex-noise.c 2018-09-14 11:11:40.049810000 +0200 ++++ misc/open-simplex-noise.c 2018-09-14 11:09:39.726457000 +0200 +@@ -13,6 +13,11 @@ + * of any particular randomization library, so results + * will be the same when ported to other languages. + */ ++ ++// -- GODOT start -- ++// Modified to work without allocating memory, also removed some unused function. ++// -- GODOT end -- ++ + #include <math.h> + #include <stdlib.h> + #include <stdint.h> +@@ -34,11 +39,12 @@ + + #define DEFAULT_SEED (0LL) + +-struct osn_context { ++// -- GODOT start -- ++/*struct osn_context { + int16_t *perm; + int16_t *permGradIndex3D; +-}; +- ++};*/ ++// -- GODOT end -- + #define ARRAYSIZE(x) (sizeof((x)) / sizeof((x)[0])) + + /* +@@ -126,7 +132,9 @@ + int xi = (int) x; + return x < xi ? xi - 1 : xi; + } +- ++ ++// -- GODOT start -- ++/* + static int allocate_perm(struct osn_context *ctx, int nperm, int ngrad) + { + if (ctx->perm) +@@ -154,18 +162,21 @@ + memcpy(ctx->perm, p, sizeof(*ctx->perm) * nelements); + + for (i = 0; i < 256; i++) { +- /* Since 3D has 24 gradients, simple bitmask won't work, so precompute modulo array. */ ++ // Since 3D has 24 gradients, simple bitmask won't work, so precompute modulo array. + ctx->permGradIndex3D[i] = (int16_t)((ctx->perm[i] % (ARRAYSIZE(gradients3D) / 3)) * 3); + } + return 0; + } ++*/ ++// -- GODOT end -- + + /* + * Initializes using a permutation array generated from a 64-bit seed. + * Generates a proper permutation (i.e. doesn't merely perform N successive pair + * swaps on a base array). Uses a simple 64-bit LCG. + */ +-int open_simplex_noise(int64_t seed, struct osn_context **ctx) ++// -- GODOT start -- ++int open_simplex_noise(int64_t seed, struct osn_context *ctx) + { + int rc; + int16_t source[256]; +@@ -174,20 +185,9 @@ + int16_t *permGradIndex3D; + int r; + +- *ctx = (struct osn_context *) malloc(sizeof(**ctx)); +- if (!(*ctx)) +- return -ENOMEM; +- (*ctx)->perm = NULL; +- (*ctx)->permGradIndex3D = NULL; +- +- rc = allocate_perm(*ctx, 256, 256); +- if (rc) { +- free(*ctx); +- return rc; +- } +- +- perm = (*ctx)->perm; +- permGradIndex3D = (*ctx)->permGradIndex3D; ++ perm = ctx->perm; ++ permGradIndex3D = ctx->permGradIndex3D; ++// -- GODOT end -- + + for (i = 0; i < 256; i++) + source[i] = (int16_t) i; +@@ -206,6 +206,8 @@ + return 0; + } + ++// -- GODOT start -- ++/* + void open_simplex_noise_free(struct osn_context *ctx) + { + if (!ctx) +@@ -220,6 +222,8 @@ + } + free(ctx); + } ++*/ ++// -- GODOT end -- + + /* 2D OpenSimplex (Simplectic) Noise. */ + double open_simplex_noise2(struct osn_context *ctx, double x, double y) +diff -u orig/open-simplex-noise.h misc/open-simplex-noise.h +--- orig/open-simplex-noise.h 2018-09-14 11:11:19.659807000 +0200 ++++ misc/open-simplex-noise.h 2018-09-14 11:10:05.006460000 +0200 +@@ -35,11 +35,18 @@ + extern "C" { + #endif + +-struct osn_context; ++// -- GODOT start -- ++// Modified to work without allocating memory, also removed some unused function. + +-int open_simplex_noise(int64_t seed, struct osn_context **ctx); ++struct osn_context { ++ int16_t perm[256]; ++ int16_t permGradIndex3D[256]; ++}; ++ ++int open_simplex_noise(int64_t seed, struct osn_context *ctx); ++//int open_simplex_noise_init_perm(struct osn_context *ctx, int16_t p[], int nelements); ++// -- GODOT end -- + void open_simplex_noise_free(struct osn_context *ctx); +-int open_simplex_noise_init_perm(struct osn_context *ctx, int16_t p[], int nelements); + double open_simplex_noise2(struct osn_context *ctx, double x, double y); + double open_simplex_noise3(struct osn_context *ctx, double x, double y, double z); + double open_simplex_noise4(struct osn_context *ctx, double x, double y, double z, double w); diff --git a/thirdparty/misc/open-simplex-noise.c b/thirdparty/misc/open-simplex-noise.c new file mode 100644 index 0000000000..42f2fbb5be --- /dev/null +++ b/thirdparty/misc/open-simplex-noise.c @@ -0,0 +1,2254 @@ +/* + * OpenSimplex (Simplectic) Noise in C. + * Ported by Stephen M. Cameron from Kurt Spencer's java implementation + * + * v1.1 (October 5, 2014) + * - Added 2D and 4D implementations. + * - Proper gradient sets for all dimensions, from a + * dimensionally-generalizable scheme with an actual + * rhyme and reason behind it. + * - Removed default permutation array in favor of + * default seed. + * - Changed seed-based constructor to be independent + * of any particular randomization library, so results + * will be the same when ported to other languages. + */ + +// -- GODOT start -- +// Modified to work without allocating memory, also removed some unused function. +// -- GODOT end -- + +#include <math.h> +#include <stdlib.h> +#include <stdint.h> +#include <string.h> +#include <errno.h> + +#include "open-simplex-noise.h" + +#define STRETCH_CONSTANT_2D (-0.211324865405187) /* (1 / sqrt(2 + 1) - 1 ) / 2; */ +#define SQUISH_CONSTANT_2D (0.366025403784439) /* (sqrt(2 + 1) -1) / 2; */ +#define STRETCH_CONSTANT_3D (-1.0 / 6.0) /* (1 / sqrt(3 + 1) - 1) / 3; */ +#define SQUISH_CONSTANT_3D (1.0 / 3.0) /* (sqrt(3+1)-1)/3; */ +#define STRETCH_CONSTANT_4D (-0.138196601125011) /* (1 / sqrt(4 + 1) - 1) / 4; */ +#define SQUISH_CONSTANT_4D (0.309016994374947) /* (sqrt(4 + 1) - 1) / 4; */ + +#define NORM_CONSTANT_2D (47.0) +#define NORM_CONSTANT_3D (103.0) +#define NORM_CONSTANT_4D (30.0) + +#define DEFAULT_SEED (0LL) + +// -- GODOT start -- +/*struct osn_context { + int16_t *perm; + int16_t *permGradIndex3D; +};*/ +// -- GODOT end -- +#define ARRAYSIZE(x) (sizeof((x)) / sizeof((x)[0])) + +/* + * Gradients for 2D. They approximate the directions to the + * vertices of an octagon from the center. + */ +static const int8_t gradients2D[] = { + 5, 2, 2, 5, + -5, 2, -2, 5, + 5, -2, 2, -5, + -5, -2, -2, -5, +}; + +/* + * Gradients for 3D. They approximate the directions to the + * vertices of a rhombicuboctahedron from the center, skewed so + * that the triangular and square facets can be inscribed inside + * circles of the same radius. + */ +static const signed char 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, +}; + +/* + * Gradients for 4D. They approximate the directions to the + * vertices of a disprismatotesseractihexadecachoron from the center, + * skewed so that the tetrahedral and cubic facets can be inscribed inside + * spheres of the same radius. + */ +static const signed char 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, +}; + +static double extrapolate2(struct osn_context *ctx, int xsb, int ysb, double dx, double dy) +{ + int16_t *perm = ctx->perm; + int index = perm[(perm[xsb & 0xFF] + ysb) & 0xFF] & 0x0E; + return gradients2D[index] * dx + + gradients2D[index + 1] * dy; +} + +static double extrapolate3(struct osn_context *ctx, int xsb, int ysb, int zsb, double dx, double dy, double dz) +{ + int16_t *perm = ctx->perm; + int16_t *permGradIndex3D = ctx->permGradIndex3D; + int index = permGradIndex3D[(perm[(perm[xsb & 0xFF] + ysb) & 0xFF] + zsb) & 0xFF]; + return gradients3D[index] * dx + + gradients3D[index + 1] * dy + + gradients3D[index + 2] * dz; +} + +static double extrapolate4(struct osn_context *ctx, int xsb, int ysb, int zsb, int wsb, double dx, double dy, double dz, double dw) +{ + int16_t *perm = ctx->perm; + int index = perm[(perm[(perm[(perm[xsb & 0xFF] + ysb) & 0xFF] + zsb) & 0xFF] + wsb) & 0xFF] & 0xFC; + return gradients4D[index] * dx + + gradients4D[index + 1] * dy + + gradients4D[index + 2] * dz + + gradients4D[index + 3] * dw; +} + +static INLINE int fastFloor(double x) { + int xi = (int) x; + return x < xi ? xi - 1 : xi; +} + +// -- GODOT start -- +/* +static int allocate_perm(struct osn_context *ctx, int nperm, int ngrad) +{ + if (ctx->perm) + free(ctx->perm); + if (ctx->permGradIndex3D) + free(ctx->permGradIndex3D); + ctx->perm = (int16_t *) malloc(sizeof(*ctx->perm) * nperm); + if (!ctx->perm) + return -ENOMEM; + ctx->permGradIndex3D = (int16_t *) malloc(sizeof(*ctx->permGradIndex3D) * ngrad); + if (!ctx->permGradIndex3D) { + free(ctx->perm); + return -ENOMEM; + } + return 0; +} + +int open_simplex_noise_init_perm(struct osn_context *ctx, int16_t p[], int nelements) +{ + int i, rc; + + rc = allocate_perm(ctx, nelements, 256); + if (rc) + return rc; + memcpy(ctx->perm, p, sizeof(*ctx->perm) * nelements); + + for (i = 0; i < 256; i++) { + // Since 3D has 24 gradients, simple bitmask won't work, so precompute modulo array. + ctx->permGradIndex3D[i] = (int16_t)((ctx->perm[i] % (ARRAYSIZE(gradients3D) / 3)) * 3); + } + return 0; +} +*/ +// -- GODOT end -- + +/* + * Initializes using a permutation array generated from a 64-bit seed. + * Generates a proper permutation (i.e. doesn't merely perform N successive pair + * swaps on a base array). Uses a simple 64-bit LCG. + */ +// -- GODOT start -- +int open_simplex_noise(int64_t seed, struct osn_context *ctx) +{ + int rc; + int16_t source[256]; + int i; + int16_t *perm; + int16_t *permGradIndex3D; + int r; + + perm = ctx->perm; + permGradIndex3D = ctx->permGradIndex3D; +// -- GODOT end -- + + for (i = 0; i < 256; i++) + source[i] = (int16_t) i; + seed = seed * 6364136223846793005LL + 1442695040888963407LL; + seed = seed * 6364136223846793005LL + 1442695040888963407LL; + seed = seed * 6364136223846793005LL + 1442695040888963407LL; + for (i = 255; i >= 0; i--) { + seed = seed * 6364136223846793005LL + 1442695040888963407LL; + r = (int)((seed + 31) % (i + 1)); + if (r < 0) + r += (i + 1); + perm[i] = source[r]; + permGradIndex3D[i] = (short)((perm[i] % (ARRAYSIZE(gradients3D) / 3)) * 3); + source[r] = source[i]; + } + return 0; +} + +// -- GODOT start -- +/* +void open_simplex_noise_free(struct osn_context *ctx) +{ + if (!ctx) + return; + if (ctx->perm) { + free(ctx->perm); + ctx->perm = NULL; + } + if (ctx->permGradIndex3D) { + free(ctx->permGradIndex3D); + ctx->permGradIndex3D = NULL; + } + free(ctx); +} +*/ +// -- GODOT end -- + +/* 2D OpenSimplex (Simplectic) Noise. */ +double open_simplex_noise2(struct osn_context *ctx, double x, double y) +{ + + /* Place input coordinates onto grid. */ + double stretchOffset = (x + y) * STRETCH_CONSTANT_2D; + double xs = x + stretchOffset; + double ys = y + stretchOffset; + + /* Floor to get grid coordinates of rhombus (stretched square) super-cell origin. */ + int xsb = fastFloor(xs); + int ysb = fastFloor(ys); + + /* Skew out to get actual coordinates of rhombus origin. We'll need these later. */ + double squishOffset = (xsb + ysb) * SQUISH_CONSTANT_2D; + 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 dx1; + double dy1; + double attn1; + double dx2; + double dy2; + double attn2; + double zins; + double attn0; + double attn_ext; + + double value = 0; + + /* Contribution (1,0) */ + dx1 = dx0 - 1 - SQUISH_CONSTANT_2D; + dy1 = dy0 - 0 - SQUISH_CONSTANT_2D; + attn1 = 2 - dx1 * dx1 - dy1 * dy1; + if (attn1 > 0) { + attn1 *= attn1; + value += attn1 * attn1 * extrapolate2(ctx, xsb + 1, ysb + 0, dx1, dy1); + } + + /* Contribution (0,1) */ + dx2 = dx0 - 0 - SQUISH_CONSTANT_2D; + dy2 = dy0 - 1 - SQUISH_CONSTANT_2D; + attn2 = 2 - dx2 * dx2 - dy2 * dy2; + if (attn2 > 0) { + attn2 *= attn2; + value += attn2 * attn2 * extrapolate2(ctx, xsb + 0, ysb + 1, dx2, dy2); + } + + if (inSum <= 1) { /* We're inside the triangle (2-Simplex) at (0,0) */ + 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 * SQUISH_CONSTANT_2D; + dy_ext = dy0 - 1 - 2 * SQUISH_CONSTANT_2D; + } + } else { /* We're inside the triangle (2-Simplex) at (1,1) */ + 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 * SQUISH_CONSTANT_2D; + dy_ext = dy0 + 0 - 2 * SQUISH_CONSTANT_2D; + } else { + xsv_ext = xsb + 0; + ysv_ext = ysb + 2; + dx_ext = dx0 + 0 - 2 * SQUISH_CONSTANT_2D; + dy_ext = dy0 - 2 - 2 * SQUISH_CONSTANT_2D; + } + } 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 * SQUISH_CONSTANT_2D; + dy0 = dy0 - 1 - 2 * SQUISH_CONSTANT_2D; + } + + /* Contribution (0,0) or (1,1) */ + attn0 = 2 - dx0 * dx0 - dy0 * dy0; + if (attn0 > 0) { + attn0 *= attn0; + value += attn0 * attn0 * extrapolate2(ctx, xsb, ysb, dx0, dy0); + } + + /* Extra Vertex */ + attn_ext = 2 - dx_ext * dx_ext - dy_ext * dy_ext; + if (attn_ext > 0) { + attn_ext *= attn_ext; + value += attn_ext * attn_ext * extrapolate2(ctx, xsv_ext, ysv_ext, dx_ext, dy_ext); + } + + return value / NORM_CONSTANT_2D; +} + +/* + * 3D OpenSimplex (Simplectic) Noise + */ +double open_simplex_noise3(struct osn_context *ctx, double x, double y, double z) +{ + + /* Place input coordinates on simplectic honeycomb. */ + double stretchOffset = (x + y + z) * STRETCH_CONSTANT_3D; + double xs = x + stretchOffset; + double ys = y + stretchOffset; + double zs = z + stretchOffset; + + /* Floor to get simplectic honeycomb coordinates of rhombohedron (stretched cube) super-cell origin. */ + int xsb = fastFloor(xs); + int ysb = fastFloor(ys); + int zsb = fastFloor(zs); + + /* Skew out to get actual coordinates of rhombohedron origin. We'll need these later. */ + double squishOffset = (xsb + ysb + zsb) * SQUISH_CONSTANT_3D; + 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 wins; + int8_t c, c1, c2; + int8_t aPoint, bPoint; + double aScore, bScore; + int aIsFurtherSide; + int bIsFurtherSide; + double p1, p2, p3; + double score; + double attn0, attn1, attn2, attn3, attn4, attn5, attn6; + double dx1, dy1, dz1; + double dx2, dy2, dz2; + double dx3, dy3, dz3; + double dx4, dy4, dz4; + double dx5, dy5, dz5; + double dx6, dy6, dz6; + double attn_ext0, attn_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. */ + aPoint = 0x01; + aScore = xins; + bPoint = 0x02; + 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) */ + wins = 1 - inSum; + if (wins > aScore || wins > bScore) { /* (0,0,0) is one of the closest two tetrahedral vertices. */ + 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. */ + c = (int8_t)(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 * SQUISH_CONSTANT_3D; + dx_ext1 = dx0 + 1 - SQUISH_CONSTANT_3D; + } else { + xsv_ext0 = xsv_ext1 = xsb + 1; + dx_ext0 = dx0 - 1 - 2 * SQUISH_CONSTANT_3D; + dx_ext1 = dx0 - 1 - SQUISH_CONSTANT_3D; + } + + if ((c & 0x02) == 0) { + ysv_ext0 = ysb; + ysv_ext1 = ysb - 1; + dy_ext0 = dy0 - 2 * SQUISH_CONSTANT_3D; + dy_ext1 = dy0 + 1 - SQUISH_CONSTANT_3D; + } else { + ysv_ext0 = ysv_ext1 = ysb + 1; + dy_ext0 = dy0 - 1 - 2 * SQUISH_CONSTANT_3D; + dy_ext1 = dy0 - 1 - SQUISH_CONSTANT_3D; + } + + if ((c & 0x04) == 0) { + zsv_ext0 = zsb; + zsv_ext1 = zsb - 1; + dz_ext0 = dz0 - 2 * SQUISH_CONSTANT_3D; + dz_ext1 = dz0 + 1 - SQUISH_CONSTANT_3D; + } else { + zsv_ext0 = zsv_ext1 = zsb + 1; + dz_ext0 = dz0 - 1 - 2 * SQUISH_CONSTANT_3D; + dz_ext1 = dz0 - 1 - SQUISH_CONSTANT_3D; + } + } + + /* Contribution (0,0,0) */ + attn0 = 2 - dx0 * dx0 - dy0 * dy0 - dz0 * dz0; + if (attn0 > 0) { + attn0 *= attn0; + value += attn0 * attn0 * extrapolate3(ctx, xsb + 0, ysb + 0, zsb + 0, dx0, dy0, dz0); + } + + /* Contribution (1,0,0) */ + dx1 = dx0 - 1 - SQUISH_CONSTANT_3D; + dy1 = dy0 - 0 - SQUISH_CONSTANT_3D; + dz1 = dz0 - 0 - SQUISH_CONSTANT_3D; + attn1 = 2 - dx1 * dx1 - dy1 * dy1 - dz1 * dz1; + if (attn1 > 0) { + attn1 *= attn1; + value += attn1 * attn1 * extrapolate3(ctx, xsb + 1, ysb + 0, zsb + 0, dx1, dy1, dz1); + } + + /* Contribution (0,1,0) */ + dx2 = dx0 - 0 - SQUISH_CONSTANT_3D; + dy2 = dy0 - 1 - SQUISH_CONSTANT_3D; + dz2 = dz1; + attn2 = 2 - dx2 * dx2 - dy2 * dy2 - dz2 * dz2; + if (attn2 > 0) { + attn2 *= attn2; + value += attn2 * attn2 * extrapolate3(ctx, xsb + 0, ysb + 1, zsb + 0, dx2, dy2, dz2); + } + + /* Contribution (0,0,1) */ + dx3 = dx2; + dy3 = dy1; + dz3 = dz0 - 1 - SQUISH_CONSTANT_3D; + attn3 = 2 - dx3 * dx3 - dy3 * dy3 - dz3 * dz3; + if (attn3 > 0) { + attn3 *= attn3; + value += attn3 * attn3 * extrapolate3(ctx, 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). */ + aPoint = 0x06; + aScore = xins; + bPoint = 0x05; + 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) */ + wins = 3 - inSum; + if (wins < aScore || wins < bScore) { /* (1,1,1) is one of the closest two tetrahedral vertices. */ + 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 * SQUISH_CONSTANT_3D; + dx_ext1 = dx0 - 1 - 3 * SQUISH_CONSTANT_3D; + } else { + xsv_ext0 = xsv_ext1 = xsb; + dx_ext0 = dx_ext1 = dx0 - 3 * SQUISH_CONSTANT_3D; + } + + if ((c & 0x02) != 0) { + ysv_ext0 = ysv_ext1 = ysb + 1; + dy_ext0 = dy_ext1 = dy0 - 1 - 3 * SQUISH_CONSTANT_3D; + 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 * SQUISH_CONSTANT_3D; + } + + if ((c & 0x04) != 0) { + zsv_ext0 = zsb + 1; + zsv_ext1 = zsb + 2; + dz_ext0 = dz0 - 1 - 3 * SQUISH_CONSTANT_3D; + dz_ext1 = dz0 - 2 - 3 * SQUISH_CONSTANT_3D; + } else { + zsv_ext0 = zsv_ext1 = zsb; + dz_ext0 = dz_ext1 = dz0 - 3 * SQUISH_CONSTANT_3D; + } + } else { /* (1,1,1) is not one of the closest two tetrahedral vertices. */ + c = (int8_t)(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 - SQUISH_CONSTANT_3D; + dx_ext1 = dx0 - 2 - 2 * SQUISH_CONSTANT_3D; + } else { + xsv_ext0 = xsv_ext1 = xsb; + dx_ext0 = dx0 - SQUISH_CONSTANT_3D; + dx_ext1 = dx0 - 2 * SQUISH_CONSTANT_3D; + } + + if ((c & 0x02) != 0) { + ysv_ext0 = ysb + 1; + ysv_ext1 = ysb + 2; + dy_ext0 = dy0 - 1 - SQUISH_CONSTANT_3D; + dy_ext1 = dy0 - 2 - 2 * SQUISH_CONSTANT_3D; + } else { + ysv_ext0 = ysv_ext1 = ysb; + dy_ext0 = dy0 - SQUISH_CONSTANT_3D; + dy_ext1 = dy0 - 2 * SQUISH_CONSTANT_3D; + } + + if ((c & 0x04) != 0) { + zsv_ext0 = zsb + 1; + zsv_ext1 = zsb + 2; + dz_ext0 = dz0 - 1 - SQUISH_CONSTANT_3D; + dz_ext1 = dz0 - 2 - 2 * SQUISH_CONSTANT_3D; + } else { + zsv_ext0 = zsv_ext1 = zsb; + dz_ext0 = dz0 - SQUISH_CONSTANT_3D; + dz_ext1 = dz0 - 2 * SQUISH_CONSTANT_3D; + } + } + + /* Contribution (1,1,0) */ + dx3 = dx0 - 1 - 2 * SQUISH_CONSTANT_3D; + dy3 = dy0 - 1 - 2 * SQUISH_CONSTANT_3D; + dz3 = dz0 - 0 - 2 * SQUISH_CONSTANT_3D; + attn3 = 2 - dx3 * dx3 - dy3 * dy3 - dz3 * dz3; + if (attn3 > 0) { + attn3 *= attn3; + value += attn3 * attn3 * extrapolate3(ctx, xsb + 1, ysb + 1, zsb + 0, dx3, dy3, dz3); + } + + /* Contribution (1,0,1) */ + dx2 = dx3; + dy2 = dy0 - 0 - 2 * SQUISH_CONSTANT_3D; + dz2 = dz0 - 1 - 2 * SQUISH_CONSTANT_3D; + attn2 = 2 - dx2 * dx2 - dy2 * dy2 - dz2 * dz2; + if (attn2 > 0) { + attn2 *= attn2; + value += attn2 * attn2 * extrapolate3(ctx, xsb + 1, ysb + 0, zsb + 1, dx2, dy2, dz2); + } + + /* Contribution (0,1,1) */ + dx1 = dx0 - 0 - 2 * SQUISH_CONSTANT_3D; + dy1 = dy3; + dz1 = dz2; + attn1 = 2 - dx1 * dx1 - dy1 * dy1 - dz1 * dz1; + if (attn1 > 0) { + attn1 *= attn1; + value += attn1 * attn1 * extrapolate3(ctx, xsb + 0, ysb + 1, zsb + 1, dx1, dy1, dz1); + } + + /* Contribution (1,1,1) */ + dx0 = dx0 - 1 - 3 * SQUISH_CONSTANT_3D; + dy0 = dy0 - 1 - 3 * SQUISH_CONSTANT_3D; + dz0 = dz0 - 1 - 3 * SQUISH_CONSTANT_3D; + attn0 = 2 - dx0 * dx0 - dy0 * dy0 - dz0 * dz0; + if (attn0 > 0) { + attn0 *= attn0; + value += attn0 * attn0 * extrapolate3(ctx, xsb + 1, ysb + 1, zsb + 1, dx0, dy0, dz0); + } + } else { /* We're inside the octahedron (Rectified 3-Simplex) in between. + Decide between point (0,0,1) and (1,1,0) as closest */ + p1 = xins + yins; + if (p1 > 1) { + aScore = p1 - 1; + aPoint = 0x03; + aIsFurtherSide = 1; + } else { + aScore = 1 - p1; + aPoint = 0x04; + aIsFurtherSide = 0; + } + + /* Decide between point (0,1,0) and (1,0,1) as closest */ + p2 = xins + zins; + if (p2 > 1) { + bScore = p2 - 1; + bPoint = 0x05; + bIsFurtherSide = 1; + } else { + bScore = 1 - p2; + bPoint = 0x02; + bIsFurtherSide = 0; + } + + /* 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. */ + p3 = yins + zins; + if (p3 > 1) { + score = p3 - 1; + if (aScore <= bScore && aScore < score) { + aScore = score; + aPoint = 0x06; + aIsFurtherSide = 1; + } else if (aScore > bScore && bScore < score) { + bScore = score; + bPoint = 0x06; + bIsFurtherSide = 1; + } + } else { + score = 1 - p3; + if (aScore <= bScore && aScore < score) { + aScore = score; + aPoint = 0x01; + aIsFurtherSide = 0; + } else if (aScore > bScore && bScore < score) { + bScore = score; + bPoint = 0x01; + bIsFurtherSide = 0; + } + } + + /* 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 * SQUISH_CONSTANT_3D; + dy_ext0 = dy0 - 1 - 3 * SQUISH_CONSTANT_3D; + dz_ext0 = dz0 - 1 - 3 * SQUISH_CONSTANT_3D; + xsv_ext0 = xsb + 1; + ysv_ext0 = ysb + 1; + zsv_ext0 = zsb + 1; + + /* Other extra point is based on the shared axis. */ + c = (int8_t)(aPoint & bPoint); + if ((c & 0x01) != 0) { + dx_ext1 = dx0 - 2 - 2 * SQUISH_CONSTANT_3D; + dy_ext1 = dy0 - 2 * SQUISH_CONSTANT_3D; + dz_ext1 = dz0 - 2 * SQUISH_CONSTANT_3D; + xsv_ext1 = xsb + 2; + ysv_ext1 = ysb; + zsv_ext1 = zsb; + } else if ((c & 0x02) != 0) { + dx_ext1 = dx0 - 2 * SQUISH_CONSTANT_3D; + dy_ext1 = dy0 - 2 - 2 * SQUISH_CONSTANT_3D; + dz_ext1 = dz0 - 2 * SQUISH_CONSTANT_3D; + xsv_ext1 = xsb; + ysv_ext1 = ysb + 2; + zsv_ext1 = zsb; + } else { + dx_ext1 = dx0 - 2 * SQUISH_CONSTANT_3D; + dy_ext1 = dy0 - 2 * SQUISH_CONSTANT_3D; + dz_ext1 = dz0 - 2 - 2 * SQUISH_CONSTANT_3D; + 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. */ + c = (int8_t)(aPoint | bPoint); + if ((c & 0x01) == 0) { + dx_ext1 = dx0 + 1 - SQUISH_CONSTANT_3D; + dy_ext1 = dy0 - 1 - SQUISH_CONSTANT_3D; + dz_ext1 = dz0 - 1 - SQUISH_CONSTANT_3D; + xsv_ext1 = xsb - 1; + ysv_ext1 = ysb + 1; + zsv_ext1 = zsb + 1; + } else if ((c & 0x02) == 0) { + dx_ext1 = dx0 - 1 - SQUISH_CONSTANT_3D; + dy_ext1 = dy0 + 1 - SQUISH_CONSTANT_3D; + dz_ext1 = dz0 - 1 - SQUISH_CONSTANT_3D; + xsv_ext1 = xsb + 1; + ysv_ext1 = ysb - 1; + zsv_ext1 = zsb + 1; + } else { + dx_ext1 = dx0 - 1 - SQUISH_CONSTANT_3D; + dy_ext1 = dy0 - 1 - SQUISH_CONSTANT_3D; + dz_ext1 = dz0 + 1 - SQUISH_CONSTANT_3D; + 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 */ + 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 - SQUISH_CONSTANT_3D; + dy_ext0 = dy0 - 1 - SQUISH_CONSTANT_3D; + dz_ext0 = dz0 - 1 - SQUISH_CONSTANT_3D; + xsv_ext0 = xsb - 1; + ysv_ext0 = ysb + 1; + zsv_ext0 = zsb + 1; + } else if ((c1 & 0x02) == 0) { + dx_ext0 = dx0 - 1 - SQUISH_CONSTANT_3D; + dy_ext0 = dy0 + 1 - SQUISH_CONSTANT_3D; + dz_ext0 = dz0 - 1 - SQUISH_CONSTANT_3D; + xsv_ext0 = xsb + 1; + ysv_ext0 = ysb - 1; + zsv_ext0 = zsb + 1; + } else { + dx_ext0 = dx0 - 1 - SQUISH_CONSTANT_3D; + dy_ext0 = dy0 - 1 - SQUISH_CONSTANT_3D; + dz_ext0 = dz0 + 1 - SQUISH_CONSTANT_3D; + 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 * SQUISH_CONSTANT_3D; + dy_ext1 = dy0 - 2 * SQUISH_CONSTANT_3D; + dz_ext1 = dz0 - 2 * SQUISH_CONSTANT_3D; + 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) */ + dx1 = dx0 - 1 - SQUISH_CONSTANT_3D; + dy1 = dy0 - 0 - SQUISH_CONSTANT_3D; + dz1 = dz0 - 0 - SQUISH_CONSTANT_3D; + attn1 = 2 - dx1 * dx1 - dy1 * dy1 - dz1 * dz1; + if (attn1 > 0) { + attn1 *= attn1; + value += attn1 * attn1 * extrapolate3(ctx, xsb + 1, ysb + 0, zsb + 0, dx1, dy1, dz1); + } + + /* Contribution (0,1,0) */ + dx2 = dx0 - 0 - SQUISH_CONSTANT_3D; + dy2 = dy0 - 1 - SQUISH_CONSTANT_3D; + dz2 = dz1; + attn2 = 2 - dx2 * dx2 - dy2 * dy2 - dz2 * dz2; + if (attn2 > 0) { + attn2 *= attn2; + value += attn2 * attn2 * extrapolate3(ctx, xsb + 0, ysb + 1, zsb + 0, dx2, dy2, dz2); + } + + /* Contribution (0,0,1) */ + dx3 = dx2; + dy3 = dy1; + dz3 = dz0 - 1 - SQUISH_CONSTANT_3D; + attn3 = 2 - dx3 * dx3 - dy3 * dy3 - dz3 * dz3; + if (attn3 > 0) { + attn3 *= attn3; + value += attn3 * attn3 * extrapolate3(ctx, xsb + 0, ysb + 0, zsb + 1, dx3, dy3, dz3); + } + + /* Contribution (1,1,0) */ + dx4 = dx0 - 1 - 2 * SQUISH_CONSTANT_3D; + dy4 = dy0 - 1 - 2 * SQUISH_CONSTANT_3D; + dz4 = dz0 - 0 - 2 * SQUISH_CONSTANT_3D; + attn4 = 2 - dx4 * dx4 - dy4 * dy4 - dz4 * dz4; + if (attn4 > 0) { + attn4 *= attn4; + value += attn4 * attn4 * extrapolate3(ctx, xsb + 1, ysb + 1, zsb + 0, dx4, dy4, dz4); + } + + /* Contribution (1,0,1) */ + dx5 = dx4; + dy5 = dy0 - 0 - 2 * SQUISH_CONSTANT_3D; + dz5 = dz0 - 1 - 2 * SQUISH_CONSTANT_3D; + attn5 = 2 - dx5 * dx5 - dy5 * dy5 - dz5 * dz5; + if (attn5 > 0) { + attn5 *= attn5; + value += attn5 * attn5 * extrapolate3(ctx, xsb + 1, ysb + 0, zsb + 1, dx5, dy5, dz5); + } + + /* Contribution (0,1,1) */ + dx6 = dx0 - 0 - 2 * SQUISH_CONSTANT_3D; + dy6 = dy4; + dz6 = dz5; + attn6 = 2 - dx6 * dx6 - dy6 * dy6 - dz6 * dz6; + if (attn6 > 0) { + attn6 *= attn6; + value += attn6 * attn6 * extrapolate3(ctx, xsb + 0, ysb + 1, zsb + 1, dx6, dy6, dz6); + } + } + + /* First extra vertex */ + 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 * extrapolate3(ctx, xsv_ext0, ysv_ext0, zsv_ext0, dx_ext0, dy_ext0, dz_ext0); + } + + /* Second extra vertex */ + 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 * extrapolate3(ctx, xsv_ext1, ysv_ext1, zsv_ext1, dx_ext1, dy_ext1, dz_ext1); + } + + return value / NORM_CONSTANT_3D; +} + +/* + * 4D OpenSimplex (Simplectic) Noise. + */ +double open_simplex_noise4(struct osn_context *ctx, double x, double y, double z, double w) +{ + double uins; + double dx1, dy1, dz1, dw1; + double dx2, dy2, dz2, dw2; + double dx3, dy3, dz3, dw3; + double dx4, dy4, dz4, dw4; + double dx5, dy5, dz5, dw5; + double dx6, dy6, dz6, dw6; + double dx7, dy7, dz7, dw7; + double dx8, dy8, dz8, dw8; + double dx9, dy9, dz9, dw9; + double dx10, dy10, dz10, dw10; + double attn0, attn1, attn2, attn3, attn4; + double attn5, attn6, attn7, attn8, attn9, attn10; + double attn_ext0, attn_ext1, attn_ext2; + int8_t c, c1, c2; + int8_t aPoint, bPoint; + double aScore, bScore; + int aIsBiggerSide; + int bIsBiggerSide; + double p1, p2, p3, p4; + double score; + + /* Place input coordinates on simplectic honeycomb. */ + double stretchOffset = (x + y + z + w) * STRETCH_CONSTANT_4D; + double xs = x + stretchOffset; + double ys = y + stretchOffset; + double zs = z + stretchOffset; + double ws = w + stretchOffset; + + /* Floor to get simplectic honeycomb coordinates of rhombo-hypercube super-cell origin. */ + int xsb = fastFloor(xs); + int ysb = fastFloor(ys); + int zsb = fastFloor(zs); + int wsb = fastFloor(ws); + + /* Skew out to get actual coordinates of stretched rhombo-hypercube origin. We'll need these later. */ + double squishOffset = (xsb + ysb + zsb + wsb) * SQUISH_CONSTANT_4D; + 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. */ + aPoint = 0x01; + aScore = xins; + bPoint = 0x02; + 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) */ + uins = 1 - inSum; + if (uins > aScore || uins > bScore) { /* (0,0,0,0) is one of the closest two pentachoron vertices. */ + 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. */ + c = (int8_t)(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 * SQUISH_CONSTANT_4D; + dx_ext1 = dx0 + 1 - SQUISH_CONSTANT_4D; + dx_ext2 = dx0 - SQUISH_CONSTANT_4D; + } else { + xsv_ext0 = xsv_ext1 = xsv_ext2 = xsb + 1; + dx_ext0 = dx0 - 1 - 2 * SQUISH_CONSTANT_4D; + dx_ext1 = dx_ext2 = dx0 - 1 - SQUISH_CONSTANT_4D; + } + + if ((c & 0x02) == 0) { + ysv_ext0 = ysv_ext1 = ysv_ext2 = ysb; + dy_ext0 = dy0 - 2 * SQUISH_CONSTANT_4D; + dy_ext1 = dy_ext2 = dy0 - SQUISH_CONSTANT_4D; + 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 * SQUISH_CONSTANT_4D; + dy_ext1 = dy_ext2 = dy0 - 1 - SQUISH_CONSTANT_4D; + } + + if ((c & 0x04) == 0) { + zsv_ext0 = zsv_ext1 = zsv_ext2 = zsb; + dz_ext0 = dz0 - 2 * SQUISH_CONSTANT_4D; + dz_ext1 = dz_ext2 = dz0 - SQUISH_CONSTANT_4D; + 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 * SQUISH_CONSTANT_4D; + dz_ext1 = dz_ext2 = dz0 - 1 - SQUISH_CONSTANT_4D; + } + + if ((c & 0x08) == 0) { + wsv_ext0 = wsv_ext1 = wsb; + wsv_ext2 = wsb - 1; + dw_ext0 = dw0 - 2 * SQUISH_CONSTANT_4D; + dw_ext1 = dw0 - SQUISH_CONSTANT_4D; + dw_ext2 = dw0 + 1 - SQUISH_CONSTANT_4D; + } else { + wsv_ext0 = wsv_ext1 = wsv_ext2 = wsb + 1; + dw_ext0 = dw0 - 1 - 2 * SQUISH_CONSTANT_4D; + dw_ext1 = dw_ext2 = dw0 - 1 - SQUISH_CONSTANT_4D; + } + } + + /* Contribution (0,0,0,0) */ + attn0 = 2 - dx0 * dx0 - dy0 * dy0 - dz0 * dz0 - dw0 * dw0; + if (attn0 > 0) { + attn0 *= attn0; + value += attn0 * attn0 * extrapolate4(ctx, xsb + 0, ysb + 0, zsb + 0, wsb + 0, dx0, dy0, dz0, dw0); + } + + /* Contribution (1,0,0,0) */ + dx1 = dx0 - 1 - SQUISH_CONSTANT_4D; + dy1 = dy0 - 0 - SQUISH_CONSTANT_4D; + dz1 = dz0 - 0 - SQUISH_CONSTANT_4D; + dw1 = dw0 - 0 - SQUISH_CONSTANT_4D; + attn1 = 2 - dx1 * dx1 - dy1 * dy1 - dz1 * dz1 - dw1 * dw1; + if (attn1 > 0) { + attn1 *= attn1; + value += attn1 * attn1 * extrapolate4(ctx, xsb + 1, ysb + 0, zsb + 0, wsb + 0, dx1, dy1, dz1, dw1); + } + + /* Contribution (0,1,0,0) */ + dx2 = dx0 - 0 - SQUISH_CONSTANT_4D; + dy2 = dy0 - 1 - SQUISH_CONSTANT_4D; + dz2 = dz1; + dw2 = dw1; + attn2 = 2 - dx2 * dx2 - dy2 * dy2 - dz2 * dz2 - dw2 * dw2; + if (attn2 > 0) { + attn2 *= attn2; + value += attn2 * attn2 * extrapolate4(ctx, xsb + 0, ysb + 1, zsb + 0, wsb + 0, dx2, dy2, dz2, dw2); + } + + /* Contribution (0,0,1,0) */ + dx3 = dx2; + dy3 = dy1; + dz3 = dz0 - 1 - SQUISH_CONSTANT_4D; + dw3 = dw1; + attn3 = 2 - dx3 * dx3 - dy3 * dy3 - dz3 * dz3 - dw3 * dw3; + if (attn3 > 0) { + attn3 *= attn3; + value += attn3 * attn3 * extrapolate4(ctx, xsb + 0, ysb + 0, zsb + 1, wsb + 0, dx3, dy3, dz3, dw3); + } + + /* Contribution (0,0,0,1) */ + dx4 = dx2; + dy4 = dy1; + dz4 = dz1; + dw4 = dw0 - 1 - SQUISH_CONSTANT_4D; + attn4 = 2 - dx4 * dx4 - dy4 * dy4 - dz4 * dz4 - dw4 * dw4; + if (attn4 > 0) { + attn4 *= attn4; + value += attn4 * attn4 * extrapolate4(ctx, 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. */ + aPoint = 0x0E; + aScore = xins; + bPoint = 0x0D; + 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) */ + uins = 4 - inSum; + if (uins < aScore || uins < bScore) { /* (1,1,1,1) is one of the closest two pentachoron vertices. */ + 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 * SQUISH_CONSTANT_4D; + dx_ext1 = dx_ext2 = dx0 - 1 - 4 * SQUISH_CONSTANT_4D; + } else { + xsv_ext0 = xsv_ext1 = xsv_ext2 = xsb; + dx_ext0 = dx_ext1 = dx_ext2 = dx0 - 4 * SQUISH_CONSTANT_4D; + } + + if ((c & 0x02) != 0) { + ysv_ext0 = ysv_ext1 = ysv_ext2 = ysb + 1; + dy_ext0 = dy_ext1 = dy_ext2 = dy0 - 1 - 4 * SQUISH_CONSTANT_4D; + 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 * SQUISH_CONSTANT_4D; + } + + if ((c & 0x04) != 0) { + zsv_ext0 = zsv_ext1 = zsv_ext2 = zsb + 1; + dz_ext0 = dz_ext1 = dz_ext2 = dz0 - 1 - 4 * SQUISH_CONSTANT_4D; + 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 * SQUISH_CONSTANT_4D; + } + + if ((c & 0x08) != 0) { + wsv_ext0 = wsv_ext1 = wsb + 1; + wsv_ext2 = wsb + 2; + dw_ext0 = dw_ext1 = dw0 - 1 - 4 * SQUISH_CONSTANT_4D; + dw_ext2 = dw0 - 2 - 4 * SQUISH_CONSTANT_4D; + } else { + wsv_ext0 = wsv_ext1 = wsv_ext2 = wsb; + dw_ext0 = dw_ext1 = dw_ext2 = dw0 - 4 * SQUISH_CONSTANT_4D; + } + } else { /* (1,1,1,1) is not one of the closest two pentachoron vertices. */ + c = (int8_t)(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 * SQUISH_CONSTANT_4D; + dx_ext1 = dx0 - 2 - 3 * SQUISH_CONSTANT_4D; + dx_ext2 = dx0 - 1 - 3 * SQUISH_CONSTANT_4D; + } else { + xsv_ext0 = xsv_ext1 = xsv_ext2 = xsb; + dx_ext0 = dx0 - 2 * SQUISH_CONSTANT_4D; + dx_ext1 = dx_ext2 = dx0 - 3 * SQUISH_CONSTANT_4D; + } + + if ((c & 0x02) != 0) { + ysv_ext0 = ysv_ext1 = ysv_ext2 = ysb + 1; + dy_ext0 = dy0 - 1 - 2 * SQUISH_CONSTANT_4D; + dy_ext1 = dy_ext2 = dy0 - 1 - 3 * SQUISH_CONSTANT_4D; + 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 * SQUISH_CONSTANT_4D; + dy_ext1 = dy_ext2 = dy0 - 3 * SQUISH_CONSTANT_4D; + } + + if ((c & 0x04) != 0) { + zsv_ext0 = zsv_ext1 = zsv_ext2 = zsb + 1; + dz_ext0 = dz0 - 1 - 2 * SQUISH_CONSTANT_4D; + dz_ext1 = dz_ext2 = dz0 - 1 - 3 * SQUISH_CONSTANT_4D; + 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 * SQUISH_CONSTANT_4D; + dz_ext1 = dz_ext2 = dz0 - 3 * SQUISH_CONSTANT_4D; + } + + if ((c & 0x08) != 0) { + wsv_ext0 = wsv_ext1 = wsb + 1; + wsv_ext2 = wsb + 2; + dw_ext0 = dw0 - 1 - 2 * SQUISH_CONSTANT_4D; + dw_ext1 = dw0 - 1 - 3 * SQUISH_CONSTANT_4D; + dw_ext2 = dw0 - 2 - 3 * SQUISH_CONSTANT_4D; + } else { + wsv_ext0 = wsv_ext1 = wsv_ext2 = wsb; + dw_ext0 = dw0 - 2 * SQUISH_CONSTANT_4D; + dw_ext1 = dw_ext2 = dw0 - 3 * SQUISH_CONSTANT_4D; + } + } + + /* Contribution (1,1,1,0) */ + dx4 = dx0 - 1 - 3 * SQUISH_CONSTANT_4D; + dy4 = dy0 - 1 - 3 * SQUISH_CONSTANT_4D; + dz4 = dz0 - 1 - 3 * SQUISH_CONSTANT_4D; + dw4 = dw0 - 3 * SQUISH_CONSTANT_4D; + attn4 = 2 - dx4 * dx4 - dy4 * dy4 - dz4 * dz4 - dw4 * dw4; + if (attn4 > 0) { + attn4 *= attn4; + value += attn4 * attn4 * extrapolate4(ctx, xsb + 1, ysb + 1, zsb + 1, wsb + 0, dx4, dy4, dz4, dw4); + } + + /* Contribution (1,1,0,1) */ + dx3 = dx4; + dy3 = dy4; + dz3 = dz0 - 3 * SQUISH_CONSTANT_4D; + dw3 = dw0 - 1 - 3 * SQUISH_CONSTANT_4D; + attn3 = 2 - dx3 * dx3 - dy3 * dy3 - dz3 * dz3 - dw3 * dw3; + if (attn3 > 0) { + attn3 *= attn3; + value += attn3 * attn3 * extrapolate4(ctx, xsb + 1, ysb + 1, zsb + 0, wsb + 1, dx3, dy3, dz3, dw3); + } + + /* Contribution (1,0,1,1) */ + dx2 = dx4; + dy2 = dy0 - 3 * SQUISH_CONSTANT_4D; + dz2 = dz4; + dw2 = dw3; + attn2 = 2 - dx2 * dx2 - dy2 * dy2 - dz2 * dz2 - dw2 * dw2; + if (attn2 > 0) { + attn2 *= attn2; + value += attn2 * attn2 * extrapolate4(ctx, xsb + 1, ysb + 0, zsb + 1, wsb + 1, dx2, dy2, dz2, dw2); + } + + /* Contribution (0,1,1,1) */ + dx1 = dx0 - 3 * SQUISH_CONSTANT_4D; + dz1 = dz4; + dy1 = dy4; + dw1 = dw3; + attn1 = 2 - dx1 * dx1 - dy1 * dy1 - dz1 * dz1 - dw1 * dw1; + if (attn1 > 0) { + attn1 *= attn1; + value += attn1 * attn1 * extrapolate4(ctx, xsb + 0, ysb + 1, zsb + 1, wsb + 1, dx1, dy1, dz1, dw1); + } + + /* Contribution (1,1,1,1) */ + dx0 = dx0 - 1 - 4 * SQUISH_CONSTANT_4D; + dy0 = dy0 - 1 - 4 * SQUISH_CONSTANT_4D; + dz0 = dz0 - 1 - 4 * SQUISH_CONSTANT_4D; + dw0 = dw0 - 1 - 4 * SQUISH_CONSTANT_4D; + attn0 = 2 - dx0 * dx0 - dy0 * dy0 - dz0 * dz0 - dw0 * dw0; + if (attn0 > 0) { + attn0 *= attn0; + value += attn0 * attn0 * extrapolate4(ctx, 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) */ + aIsBiggerSide = 1; + bIsBiggerSide = 1; + + /* 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) { + score = xins + wins; + if (aScore >= bScore && score > bScore) { + bScore = score; + bPoint = 0x09; + } else if (aScore < bScore && score > aScore) { + aScore = score; + aPoint = 0x09; + } + } else { + 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. */ + p1 = 2 - inSum + xins; + if (aScore >= bScore && p1 > bScore) { + bScore = p1; + bPoint = 0x01; + bIsBiggerSide = 0; + } else if (aScore < bScore && p1 > aScore) { + aScore = p1; + aPoint = 0x01; + aIsBiggerSide = 0; + } + + /* Decide if (0,1,0,0) is closer. */ + p2 = 2 - inSum + yins; + if (aScore >= bScore && p2 > bScore) { + bScore = p2; + bPoint = 0x02; + bIsBiggerSide = 0; + } else if (aScore < bScore && p2 > aScore) { + aScore = p2; + aPoint = 0x02; + aIsBiggerSide = 0; + } + + /* Decide if (0,0,1,0) is closer. */ + p3 = 2 - inSum + zins; + if (aScore >= bScore && p3 > bScore) { + bScore = p3; + bPoint = 0x04; + bIsBiggerSide = 0; + } else if (aScore < bScore && p3 > aScore) { + aScore = p3; + aPoint = 0x04; + aIsBiggerSide = 0; + } + + /* Decide if (0,0,0,1) is closer. */ + p4 = 2 - inSum + wins; + if (aScore >= bScore && p4 > bScore) { + bScore = p4; + bPoint = 0x08; + bIsBiggerSide = 0; + } else if (aScore < bScore && p4 > aScore) { + aScore = p4; + aPoint = 0x08; + aIsBiggerSide = 0; + } + + /* 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 */ + c1 = (int8_t)(aPoint | bPoint); + c2 = (int8_t)(aPoint & bPoint); + if ((c1 & 0x01) == 0) { + xsv_ext0 = xsb; + xsv_ext1 = xsb - 1; + dx_ext0 = dx0 - 3 * SQUISH_CONSTANT_4D; + dx_ext1 = dx0 + 1 - 2 * SQUISH_CONSTANT_4D; + } else { + xsv_ext0 = xsv_ext1 = xsb + 1; + dx_ext0 = dx0 - 1 - 3 * SQUISH_CONSTANT_4D; + dx_ext1 = dx0 - 1 - 2 * SQUISH_CONSTANT_4D; + } + + if ((c1 & 0x02) == 0) { + ysv_ext0 = ysb; + ysv_ext1 = ysb - 1; + dy_ext0 = dy0 - 3 * SQUISH_CONSTANT_4D; + dy_ext1 = dy0 + 1 - 2 * SQUISH_CONSTANT_4D; + } else { + ysv_ext0 = ysv_ext1 = ysb + 1; + dy_ext0 = dy0 - 1 - 3 * SQUISH_CONSTANT_4D; + dy_ext1 = dy0 - 1 - 2 * SQUISH_CONSTANT_4D; + } + + if ((c1 & 0x04) == 0) { + zsv_ext0 = zsb; + zsv_ext1 = zsb - 1; + dz_ext0 = dz0 - 3 * SQUISH_CONSTANT_4D; + dz_ext1 = dz0 + 1 - 2 * SQUISH_CONSTANT_4D; + } else { + zsv_ext0 = zsv_ext1 = zsb + 1; + dz_ext0 = dz0 - 1 - 3 * SQUISH_CONSTANT_4D; + dz_ext1 = dz0 - 1 - 2 * SQUISH_CONSTANT_4D; + } + + if ((c1 & 0x08) == 0) { + wsv_ext0 = wsb; + wsv_ext1 = wsb - 1; + dw_ext0 = dw0 - 3 * SQUISH_CONSTANT_4D; + dw_ext1 = dw0 + 1 - 2 * SQUISH_CONSTANT_4D; + } else { + wsv_ext0 = wsv_ext1 = wsb + 1; + dw_ext0 = dw0 - 1 - 3 * SQUISH_CONSTANT_4D; + dw_ext1 = dw0 - 1 - 2 * SQUISH_CONSTANT_4D; + } + + /* 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 * SQUISH_CONSTANT_4D; + dy_ext2 = dy0 - 2 * SQUISH_CONSTANT_4D; + dz_ext2 = dz0 - 2 * SQUISH_CONSTANT_4D; + dw_ext2 = dw0 - 2 * SQUISH_CONSTANT_4D; + 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. */ + c = (int8_t)(aPoint | bPoint); + + if ((c & 0x01) == 0) { + xsv_ext0 = xsb - 1; + xsv_ext1 = xsb; + dx_ext0 = dx0 + 1 - SQUISH_CONSTANT_4D; + dx_ext1 = dx0 - SQUISH_CONSTANT_4D; + } else { + xsv_ext0 = xsv_ext1 = xsb + 1; + dx_ext0 = dx_ext1 = dx0 - 1 - SQUISH_CONSTANT_4D; + } + + if ((c & 0x02) == 0) { + ysv_ext0 = ysv_ext1 = ysb; + dy_ext0 = dy_ext1 = dy0 - SQUISH_CONSTANT_4D; + 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 - SQUISH_CONSTANT_4D; + } + + if ((c & 0x04) == 0) { + zsv_ext0 = zsv_ext1 = zsb; + dz_ext0 = dz_ext1 = dz0 - SQUISH_CONSTANT_4D; + 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 - SQUISH_CONSTANT_4D; + } + + if ((c & 0x08) == 0) + { + wsv_ext0 = wsb; + wsv_ext1 = wsb - 1; + dw_ext0 = dw0 - SQUISH_CONSTANT_4D; + dw_ext1 = dw0 + 1 - SQUISH_CONSTANT_4D; + } else { + wsv_ext0 = wsv_ext1 = wsb + 1; + dw_ext0 = dw_ext1 = dw0 - 1 - SQUISH_CONSTANT_4D; + } + + } + } else { /* One point on each "side" */ + 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 - SQUISH_CONSTANT_4D; + dx_ext1 = dx0 - SQUISH_CONSTANT_4D; + } else { + xsv_ext0 = xsv_ext1 = xsb + 1; + dx_ext0 = dx_ext1 = dx0 - 1 - SQUISH_CONSTANT_4D; + } + + if ((c1 & 0x02) == 0) { + ysv_ext0 = ysv_ext1 = ysb; + dy_ext0 = dy_ext1 = dy0 - SQUISH_CONSTANT_4D; + 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 - SQUISH_CONSTANT_4D; + } + + if ((c1 & 0x04) == 0) { + zsv_ext0 = zsv_ext1 = zsb; + dz_ext0 = dz_ext1 = dz0 - SQUISH_CONSTANT_4D; + 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 - SQUISH_CONSTANT_4D; + } + + if ((c1 & 0x08) == 0) { + wsv_ext0 = wsb; + wsv_ext1 = wsb - 1; + dw_ext0 = dw0 - SQUISH_CONSTANT_4D; + dw_ext1 = dw0 + 1 - SQUISH_CONSTANT_4D; + } else { + wsv_ext0 = wsv_ext1 = wsb + 1; + dw_ext0 = dw_ext1 = dw0 - 1 - SQUISH_CONSTANT_4D; + } + + /* 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 * SQUISH_CONSTANT_4D; + dy_ext2 = dy0 - 2 * SQUISH_CONSTANT_4D; + dz_ext2 = dz0 - 2 * SQUISH_CONSTANT_4D; + dw_ext2 = dw0 - 2 * SQUISH_CONSTANT_4D; + 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) */ + dx1 = dx0 - 1 - SQUISH_CONSTANT_4D; + dy1 = dy0 - 0 - SQUISH_CONSTANT_4D; + dz1 = dz0 - 0 - SQUISH_CONSTANT_4D; + dw1 = dw0 - 0 - SQUISH_CONSTANT_4D; + attn1 = 2 - dx1 * dx1 - dy1 * dy1 - dz1 * dz1 - dw1 * dw1; + if (attn1 > 0) { + attn1 *= attn1; + value += attn1 * attn1 * extrapolate4(ctx, xsb + 1, ysb + 0, zsb + 0, wsb + 0, dx1, dy1, dz1, dw1); + } + + /* Contribution (0,1,0,0) */ + dx2 = dx0 - 0 - SQUISH_CONSTANT_4D; + dy2 = dy0 - 1 - SQUISH_CONSTANT_4D; + dz2 = dz1; + dw2 = dw1; + attn2 = 2 - dx2 * dx2 - dy2 * dy2 - dz2 * dz2 - dw2 * dw2; + if (attn2 > 0) { + attn2 *= attn2; + value += attn2 * attn2 * extrapolate4(ctx, xsb + 0, ysb + 1, zsb + 0, wsb + 0, dx2, dy2, dz2, dw2); + } + + /* Contribution (0,0,1,0) */ + dx3 = dx2; + dy3 = dy1; + dz3 = dz0 - 1 - SQUISH_CONSTANT_4D; + dw3 = dw1; + attn3 = 2 - dx3 * dx3 - dy3 * dy3 - dz3 * dz3 - dw3 * dw3; + if (attn3 > 0) { + attn3 *= attn3; + value += attn3 * attn3 * extrapolate4(ctx, xsb + 0, ysb + 0, zsb + 1, wsb + 0, dx3, dy3, dz3, dw3); + } + + /* Contribution (0,0,0,1) */ + dx4 = dx2; + dy4 = dy1; + dz4 = dz1; + dw4 = dw0 - 1 - SQUISH_CONSTANT_4D; + attn4 = 2 - dx4 * dx4 - dy4 * dy4 - dz4 * dz4 - dw4 * dw4; + if (attn4 > 0) { + attn4 *= attn4; + value += attn4 * attn4 * extrapolate4(ctx, xsb + 0, ysb + 0, zsb + 0, wsb + 1, dx4, dy4, dz4, dw4); + } + + /* Contribution (1,1,0,0) */ + dx5 = dx0 - 1 - 2 * SQUISH_CONSTANT_4D; + dy5 = dy0 - 1 - 2 * SQUISH_CONSTANT_4D; + dz5 = dz0 - 0 - 2 * SQUISH_CONSTANT_4D; + dw5 = dw0 - 0 - 2 * SQUISH_CONSTANT_4D; + attn5 = 2 - dx5 * dx5 - dy5 * dy5 - dz5 * dz5 - dw5 * dw5; + if (attn5 > 0) { + attn5 *= attn5; + value += attn5 * attn5 * extrapolate4(ctx, xsb + 1, ysb + 1, zsb + 0, wsb + 0, dx5, dy5, dz5, dw5); + } + + /* Contribution (1,0,1,0) */ + dx6 = dx0 - 1 - 2 * SQUISH_CONSTANT_4D; + dy6 = dy0 - 0 - 2 * SQUISH_CONSTANT_4D; + dz6 = dz0 - 1 - 2 * SQUISH_CONSTANT_4D; + dw6 = dw0 - 0 - 2 * SQUISH_CONSTANT_4D; + attn6 = 2 - dx6 * dx6 - dy6 * dy6 - dz6 * dz6 - dw6 * dw6; + if (attn6 > 0) { + attn6 *= attn6; + value += attn6 * attn6 * extrapolate4(ctx, xsb + 1, ysb + 0, zsb + 1, wsb + 0, dx6, dy6, dz6, dw6); + } + + /* Contribution (1,0,0,1) */ + dx7 = dx0 - 1 - 2 * SQUISH_CONSTANT_4D; + dy7 = dy0 - 0 - 2 * SQUISH_CONSTANT_4D; + dz7 = dz0 - 0 - 2 * SQUISH_CONSTANT_4D; + dw7 = dw0 - 1 - 2 * SQUISH_CONSTANT_4D; + attn7 = 2 - dx7 * dx7 - dy7 * dy7 - dz7 * dz7 - dw7 * dw7; + if (attn7 > 0) { + attn7 *= attn7; + value += attn7 * attn7 * extrapolate4(ctx, xsb + 1, ysb + 0, zsb + 0, wsb + 1, dx7, dy7, dz7, dw7); + } + + /* Contribution (0,1,1,0) */ + dx8 = dx0 - 0 - 2 * SQUISH_CONSTANT_4D; + dy8 = dy0 - 1 - 2 * SQUISH_CONSTANT_4D; + dz8 = dz0 - 1 - 2 * SQUISH_CONSTANT_4D; + dw8 = dw0 - 0 - 2 * SQUISH_CONSTANT_4D; + attn8 = 2 - dx8 * dx8 - dy8 * dy8 - dz8 * dz8 - dw8 * dw8; + if (attn8 > 0) { + attn8 *= attn8; + value += attn8 * attn8 * extrapolate4(ctx, xsb + 0, ysb + 1, zsb + 1, wsb + 0, dx8, dy8, dz8, dw8); + } + + /* Contribution (0,1,0,1) */ + dx9 = dx0 - 0 - 2 * SQUISH_CONSTANT_4D; + dy9 = dy0 - 1 - 2 * SQUISH_CONSTANT_4D; + dz9 = dz0 - 0 - 2 * SQUISH_CONSTANT_4D; + dw9 = dw0 - 1 - 2 * SQUISH_CONSTANT_4D; + attn9 = 2 - dx9 * dx9 - dy9 * dy9 - dz9 * dz9 - dw9 * dw9; + if (attn9 > 0) { + attn9 *= attn9; + value += attn9 * attn9 * extrapolate4(ctx, xsb + 0, ysb + 1, zsb + 0, wsb + 1, dx9, dy9, dz9, dw9); + } + + /* Contribution (0,0,1,1) */ + dx10 = dx0 - 0 - 2 * SQUISH_CONSTANT_4D; + dy10 = dy0 - 0 - 2 * SQUISH_CONSTANT_4D; + dz10 = dz0 - 1 - 2 * SQUISH_CONSTANT_4D; + dw10 = dw0 - 1 - 2 * SQUISH_CONSTANT_4D; + attn10 = 2 - dx10 * dx10 - dy10 * dy10 - dz10 * dz10 - dw10 * dw10; + if (attn10 > 0) { + attn10 *= attn10; + value += attn10 * attn10 * extrapolate4(ctx, xsb + 0, ysb + 0, zsb + 1, wsb + 1, dx10, dy10, dz10, dw10); + } + } else { /* We're inside the second dispentachoron (Rectified 4-Simplex) */ + aIsBiggerSide = 1; + bIsBiggerSide = 1; + + /* 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) { + score = xins + wins; + if (aScore <= bScore && score < bScore) { + bScore = score; + bPoint = 0x06; + } else if (aScore > bScore && score < aScore) { + aScore = score; + aPoint = 0x06; + } + } else { + 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. */ + p1 = 3 - inSum + xins; + if (aScore <= bScore && p1 < bScore) { + bScore = p1; + bPoint = 0x0E; + bIsBiggerSide = 0; + } else if (aScore > bScore && p1 < aScore) { + aScore = p1; + aPoint = 0x0E; + aIsBiggerSide = 0; + } + + /* Decide if (1,0,1,1) is closer. */ + p2 = 3 - inSum + yins; + if (aScore <= bScore && p2 < bScore) { + bScore = p2; + bPoint = 0x0D; + bIsBiggerSide = 0; + } else if (aScore > bScore && p2 < aScore) { + aScore = p2; + aPoint = 0x0D; + aIsBiggerSide = 0; + } + + /* Decide if (1,1,0,1) is closer. */ + p3 = 3 - inSum + zins; + if (aScore <= bScore && p3 < bScore) { + bScore = p3; + bPoint = 0x0B; + bIsBiggerSide = 0; + } else if (aScore > bScore && p3 < aScore) { + aScore = p3; + aPoint = 0x0B; + aIsBiggerSide = 0; + } + + /* Decide if (1,1,1,0) is closer. */ + p4 = 3 - inSum + wins; + if (aScore <= bScore && p4 < bScore) { + bScore = p4; + bPoint = 0x07; + bIsBiggerSide = 0; + } else if (aScore > bScore && p4 < aScore) { + aScore = p4; + aPoint = 0x07; + aIsBiggerSide = 0; + } + + /* 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 */ + c1 = (int8_t)(aPoint & bPoint); + c2 = (int8_t)(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 - SQUISH_CONSTANT_4D; + dy_ext0 = dy0 - SQUISH_CONSTANT_4D; + dz_ext0 = dz0 - SQUISH_CONSTANT_4D; + dw_ext0 = dw0 - SQUISH_CONSTANT_4D; + dx_ext1 = dx0 - 2 * SQUISH_CONSTANT_4D; + dy_ext1 = dy0 - 2 * SQUISH_CONSTANT_4D; + dz_ext1 = dz0 - 2 * SQUISH_CONSTANT_4D; + dw_ext1 = dw0 - 2 * SQUISH_CONSTANT_4D; + 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 * SQUISH_CONSTANT_4D; + dy_ext2 = dy0 - 1 - 2 * SQUISH_CONSTANT_4D; + dz_ext2 = dz0 - 1 - 2 * SQUISH_CONSTANT_4D; + dw_ext2 = dw0 - 1 - 2 * SQUISH_CONSTANT_4D; + 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 * SQUISH_CONSTANT_4D; + dy_ext2 = dy0 - 1 - 4 * SQUISH_CONSTANT_4D; + dz_ext2 = dz0 - 1 - 4 * SQUISH_CONSTANT_4D; + dw_ext2 = dw0 - 1 - 4 * SQUISH_CONSTANT_4D; + + /* Other two points are based on the shared axes. */ + c = (int8_t)(aPoint & bPoint); + + if ((c & 0x01) != 0) { + xsv_ext0 = xsb + 2; + xsv_ext1 = xsb + 1; + dx_ext0 = dx0 - 2 - 3 * SQUISH_CONSTANT_4D; + dx_ext1 = dx0 - 1 - 3 * SQUISH_CONSTANT_4D; + } else { + xsv_ext0 = xsv_ext1 = xsb; + dx_ext0 = dx_ext1 = dx0 - 3 * SQUISH_CONSTANT_4D; + } + + if ((c & 0x02) != 0) { + ysv_ext0 = ysv_ext1 = ysb + 1; + dy_ext0 = dy_ext1 = dy0 - 1 - 3 * SQUISH_CONSTANT_4D; + 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 * SQUISH_CONSTANT_4D; + } + + if ((c & 0x04) != 0) { + zsv_ext0 = zsv_ext1 = zsb + 1; + dz_ext0 = dz_ext1 = dz0 - 1 - 3 * SQUISH_CONSTANT_4D; + 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 * SQUISH_CONSTANT_4D; + } + + if ((c & 0x08) != 0) + { + wsv_ext0 = wsb + 1; + wsv_ext1 = wsb + 2; + dw_ext0 = dw0 - 1 - 3 * SQUISH_CONSTANT_4D; + dw_ext1 = dw0 - 2 - 3 * SQUISH_CONSTANT_4D; + } else { + wsv_ext0 = wsv_ext1 = wsb; + dw_ext0 = dw_ext1 = dw0 - 3 * SQUISH_CONSTANT_4D; + } + } + } else { /* One point on each "side" */ + 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 * SQUISH_CONSTANT_4D; + dx_ext1 = dx0 - 1 - 3 * SQUISH_CONSTANT_4D; + } else { + xsv_ext0 = xsv_ext1 = xsb; + dx_ext0 = dx_ext1 = dx0 - 3 * SQUISH_CONSTANT_4D; + } + + if ((c1 & 0x02) != 0) { + ysv_ext0 = ysv_ext1 = ysb + 1; + dy_ext0 = dy_ext1 = dy0 - 1 - 3 * SQUISH_CONSTANT_4D; + 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 * SQUISH_CONSTANT_4D; + } + + if ((c1 & 0x04) != 0) { + zsv_ext0 = zsv_ext1 = zsb + 1; + dz_ext0 = dz_ext1 = dz0 - 1 - 3 * SQUISH_CONSTANT_4D; + 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 * SQUISH_CONSTANT_4D; + } + + if ((c1 & 0x08) != 0) { + wsv_ext0 = wsb + 1; + wsv_ext1 = wsb + 2; + dw_ext0 = dw0 - 1 - 3 * SQUISH_CONSTANT_4D; + dw_ext1 = dw0 - 2 - 3 * SQUISH_CONSTANT_4D; + } else { + wsv_ext0 = wsv_ext1 = wsb; + dw_ext0 = dw_ext1 = dw0 - 3 * SQUISH_CONSTANT_4D; + } + + /* 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 * SQUISH_CONSTANT_4D; + dy_ext2 = dy0 - 1 - 2 * SQUISH_CONSTANT_4D; + dz_ext2 = dz0 - 1 - 2 * SQUISH_CONSTANT_4D; + dw_ext2 = dw0 - 1 - 2 * SQUISH_CONSTANT_4D; + 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) */ + dx4 = dx0 - 1 - 3 * SQUISH_CONSTANT_4D; + dy4 = dy0 - 1 - 3 * SQUISH_CONSTANT_4D; + dz4 = dz0 - 1 - 3 * SQUISH_CONSTANT_4D; + dw4 = dw0 - 3 * SQUISH_CONSTANT_4D; + attn4 = 2 - dx4 * dx4 - dy4 * dy4 - dz4 * dz4 - dw4 * dw4; + if (attn4 > 0) { + attn4 *= attn4; + value += attn4 * attn4 * extrapolate4(ctx, xsb + 1, ysb + 1, zsb + 1, wsb + 0, dx4, dy4, dz4, dw4); + } + + /* Contribution (1,1,0,1) */ + dx3 = dx4; + dy3 = dy4; + dz3 = dz0 - 3 * SQUISH_CONSTANT_4D; + dw3 = dw0 - 1 - 3 * SQUISH_CONSTANT_4D; + attn3 = 2 - dx3 * dx3 - dy3 * dy3 - dz3 * dz3 - dw3 * dw3; + if (attn3 > 0) { + attn3 *= attn3; + value += attn3 * attn3 * extrapolate4(ctx, xsb + 1, ysb + 1, zsb + 0, wsb + 1, dx3, dy3, dz3, dw3); + } + + /* Contribution (1,0,1,1) */ + dx2 = dx4; + dy2 = dy0 - 3 * SQUISH_CONSTANT_4D; + dz2 = dz4; + dw2 = dw3; + attn2 = 2 - dx2 * dx2 - dy2 * dy2 - dz2 * dz2 - dw2 * dw2; + if (attn2 > 0) { + attn2 *= attn2; + value += attn2 * attn2 * extrapolate4(ctx, xsb + 1, ysb + 0, zsb + 1, wsb + 1, dx2, dy2, dz2, dw2); + } + + /* Contribution (0,1,1,1) */ + dx1 = dx0 - 3 * SQUISH_CONSTANT_4D; + dz1 = dz4; + dy1 = dy4; + dw1 = dw3; + attn1 = 2 - dx1 * dx1 - dy1 * dy1 - dz1 * dz1 - dw1 * dw1; + if (attn1 > 0) { + attn1 *= attn1; + value += attn1 * attn1 * extrapolate4(ctx, xsb + 0, ysb + 1, zsb + 1, wsb + 1, dx1, dy1, dz1, dw1); + } + + /* Contribution (1,1,0,0) */ + dx5 = dx0 - 1 - 2 * SQUISH_CONSTANT_4D; + dy5 = dy0 - 1 - 2 * SQUISH_CONSTANT_4D; + dz5 = dz0 - 0 - 2 * SQUISH_CONSTANT_4D; + dw5 = dw0 - 0 - 2 * SQUISH_CONSTANT_4D; + attn5 = 2 - dx5 * dx5 - dy5 * dy5 - dz5 * dz5 - dw5 * dw5; + if (attn5 > 0) { + attn5 *= attn5; + value += attn5 * attn5 * extrapolate4(ctx, xsb + 1, ysb + 1, zsb + 0, wsb + 0, dx5, dy5, dz5, dw5); + } + + /* Contribution (1,0,1,0) */ + dx6 = dx0 - 1 - 2 * SQUISH_CONSTANT_4D; + dy6 = dy0 - 0 - 2 * SQUISH_CONSTANT_4D; + dz6 = dz0 - 1 - 2 * SQUISH_CONSTANT_4D; + dw6 = dw0 - 0 - 2 * SQUISH_CONSTANT_4D; + attn6 = 2 - dx6 * dx6 - dy6 * dy6 - dz6 * dz6 - dw6 * dw6; + if (attn6 > 0) { + attn6 *= attn6; + value += attn6 * attn6 * extrapolate4(ctx, xsb + 1, ysb + 0, zsb + 1, wsb + 0, dx6, dy6, dz6, dw6); + } + + /* Contribution (1,0,0,1) */ + dx7 = dx0 - 1 - 2 * SQUISH_CONSTANT_4D; + dy7 = dy0 - 0 - 2 * SQUISH_CONSTANT_4D; + dz7 = dz0 - 0 - 2 * SQUISH_CONSTANT_4D; + dw7 = dw0 - 1 - 2 * SQUISH_CONSTANT_4D; + attn7 = 2 - dx7 * dx7 - dy7 * dy7 - dz7 * dz7 - dw7 * dw7; + if (attn7 > 0) { + attn7 *= attn7; + value += attn7 * attn7 * extrapolate4(ctx, xsb + 1, ysb + 0, zsb + 0, wsb + 1, dx7, dy7, dz7, dw7); + } + + /* Contribution (0,1,1,0) */ + dx8 = dx0 - 0 - 2 * SQUISH_CONSTANT_4D; + dy8 = dy0 - 1 - 2 * SQUISH_CONSTANT_4D; + dz8 = dz0 - 1 - 2 * SQUISH_CONSTANT_4D; + dw8 = dw0 - 0 - 2 * SQUISH_CONSTANT_4D; + attn8 = 2 - dx8 * dx8 - dy8 * dy8 - dz8 * dz8 - dw8 * dw8; + if (attn8 > 0) { + attn8 *= attn8; + value += attn8 * attn8 * extrapolate4(ctx, xsb + 0, ysb + 1, zsb + 1, wsb + 0, dx8, dy8, dz8, dw8); + } + + /* Contribution (0,1,0,1) */ + dx9 = dx0 - 0 - 2 * SQUISH_CONSTANT_4D; + dy9 = dy0 - 1 - 2 * SQUISH_CONSTANT_4D; + dz9 = dz0 - 0 - 2 * SQUISH_CONSTANT_4D; + dw9 = dw0 - 1 - 2 * SQUISH_CONSTANT_4D; + attn9 = 2 - dx9 * dx9 - dy9 * dy9 - dz9 * dz9 - dw9 * dw9; + if (attn9 > 0) { + attn9 *= attn9; + value += attn9 * attn9 * extrapolate4(ctx, xsb + 0, ysb + 1, zsb + 0, wsb + 1, dx9, dy9, dz9, dw9); + } + + /* Contribution (0,0,1,1) */ + dx10 = dx0 - 0 - 2 * SQUISH_CONSTANT_4D; + dy10 = dy0 - 0 - 2 * SQUISH_CONSTANT_4D; + dz10 = dz0 - 1 - 2 * SQUISH_CONSTANT_4D; + dw10 = dw0 - 1 - 2 * SQUISH_CONSTANT_4D; + attn10 = 2 - dx10 * dx10 - dy10 * dy10 - dz10 * dz10 - dw10 * dw10; + if (attn10 > 0) { + attn10 *= attn10; + value += attn10 * attn10 * extrapolate4(ctx, xsb + 0, ysb + 0, zsb + 1, wsb + 1, dx10, dy10, dz10, dw10); + } + } + + /* First extra vertex */ + 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 * extrapolate4(ctx, xsv_ext0, ysv_ext0, zsv_ext0, wsv_ext0, dx_ext0, dy_ext0, dz_ext0, dw_ext0); + } + + /* Second extra vertex */ + 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 * extrapolate4(ctx, xsv_ext1, ysv_ext1, zsv_ext1, wsv_ext1, dx_ext1, dy_ext1, dz_ext1, dw_ext1); + } + + /* Third extra vertex */ + 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 * extrapolate4(ctx, xsv_ext2, ysv_ext2, zsv_ext2, wsv_ext2, dx_ext2, dy_ext2, dz_ext2, dw_ext2); + } + + return value / NORM_CONSTANT_4D; +} + diff --git a/thirdparty/misc/open-simplex-noise.h b/thirdparty/misc/open-simplex-noise.h new file mode 100644 index 0000000000..89e0df8218 --- /dev/null +++ b/thirdparty/misc/open-simplex-noise.h @@ -0,0 +1,58 @@ +#ifndef OPEN_SIMPLEX_NOISE_H__ +#define OPEN_SIMPLEX_NOISE_H__ + +/* + * OpenSimplex (Simplectic) Noise in C. + * Ported to C from Kurt Spencer's java implementation by Stephen M. Cameron + * + * v1.1 (October 6, 2014) + * - Ported to C + * + * v1.1 (October 5, 2014) + * - Added 2D and 4D implementations. + * - Proper gradient sets for all dimensions, from a + * dimensionally-generalizable scheme with an actual + * rhyme and reason behind it. + * - Removed default permutation array in favor of + * default seed. + * - Changed seed-based constructor to be independent + * of any particular randomization library, so results + * will be the same when ported to other languages. + */ + +#if ((__GNUC_STDC_INLINE__) || (__STDC_VERSION__ >= 199901L)) + #include <stdint.h> + #define INLINE inline +#elif (defined (_MSC_VER) || defined (__GNUC_GNU_INLINE__)) + #include <stdint.h> + #define INLINE __inline +#else + /* ANSI C doesn't have inline or stdint.h. */ + #define INLINE +#endif + +#ifdef __cplusplus + extern "C" { +#endif + +// -- GODOT start -- +// Modified to work without allocating memory, also removed some unused function. + +struct osn_context { + int16_t perm[256]; + int16_t permGradIndex3D[256]; +}; + +int open_simplex_noise(int64_t seed, struct osn_context *ctx); +//int open_simplex_noise_init_perm(struct osn_context *ctx, int16_t p[], int nelements); +// -- GODOT end -- +void open_simplex_noise_free(struct osn_context *ctx); +double open_simplex_noise2(struct osn_context *ctx, double x, double y); +double open_simplex_noise3(struct osn_context *ctx, double x, double y, double z); +double open_simplex_noise4(struct osn_context *ctx, double x, double y, double z, double w); + +#ifdef __cplusplus + } +#endif + +#endif |