/* * 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; }