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open-simplex-noise.c
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open-simplex-noise.c
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/*
* 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.
*/
#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)
struct osn_context {
int16_t *perm;
int16_t *permGradIndex3D;
};
#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;
}
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;
}
/*
* 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)
{
int rc;
int16_t source[256];
int i;
int16_t *perm;
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;
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;
}
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);
}
/* 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;