/*
* OpenSimplex (Simplectic) Noise in C++
* by Arthur Tombs
*
* Modified 2015-01-08
*
* This is a derivative work based on OpenSimplex by Kurt Spencer:
* https://gist.github.com/KdotJPG/b1270127455a94ac5d19
*
* Anyone is free to make use of this software in whatever way they want.
* Attribution is appreciated, but not required.
*
* 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.
*/
#ifndef OPENSIMPLEXNOISE_HH
#define OPENSIMPLEXNOISE_HH
#include <cmath>
#if __cplusplus < 201103L
#pragma message("Info: Your compiler does not claim C++11 support. Some features may be unavailable.")
#else
#define OSN_USE_CSTDINT
#define OSN_USE_STATIC_ASSERT
#endif
#ifdef OSN_USE_CSTDINT
// cstdint is required for the int64_t type
#include <cstdint>
#else
#pragma message("Info: Not using <cstdint> for fixed-width integral types. To enable this feature, define OSN_USE_CSTDINT before including this header.")
// cstdlib is required for the srand and rand functions
#include <cstdlib>
#endif
#ifdef OSN_USE_STATIC_ASSERT
// type_traits is required for the is_floating_point function
#include <type_traits>
#endif
namespace OSN {
#ifdef OSN_USE_CSTDINT
typedef uint_fast8_t OSN_BYTE;
#ifndef OSN_INT_TYPE
#define OSN_INT_TYPE int64_t
#endif
#else
typedef unsigned char OSN_BYTE;
#ifndef OSN_INT_TYPE
#define OSN_INT_TYPE long
#endif
#endif
typedef OSN_INT_TYPE inttype;
namespace {
// This function seems to be faster than std::pow(x, 4) in all cases
template <typename T>
inline T pow4(T x) {
x *= x;
return x * x;
}
template <typename T>
inline T pow2(T x) {
return x * x;
}
template <typename T>
inline inttype fastFloori(T x) {
inttype ip = (inttype)x;
#ifndef OSN_ALWAYS_POSITIVE
if (x < 0.0) --ip;
#endif
return ip;
}
}
class NoiseBase {
protected:
int perm[256];
// Empty constructor to allow child classes to set up perm themselves.
NoiseBase(void) {}
#ifdef OSN_USE_CSTDINT
// Perform one step of the Linear Congruential Generator algorithm.
inline static void LCG_STEP(int64_t& x) {
// Magic constants are attributed to Donald Knuth's MMIX implementation.
static const int64_t MULTIPLIER = 6364136223846793005LL;
static const int64_t INCREMENT = 1442695040888963407LL;
x = ((x * MULTIPLIER) + INCREMENT);
}
// Initializes the class 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.
NoiseBase(int64_t seed) {
int source[256];
for (int i = 0; i < 256; ++i) { source[i] = i; }
LCG_STEP(seed);
LCG_STEP(seed);
LCG_STEP(seed);
for (int i = 255; i >= 0; --i) {
LCG_STEP(seed);
int r = (int)((seed + 31) % (i + 1));
if (r < 0) { r += (i + 1); }
perm[i] = source[r];
source[r] = source[i];
}
}
#else
// Initializes the class using a permutation array generated from a 32-bit seed.
// Generates a proper permutation (i.e. doesn't merely perform N successive
// pair swaps on a base array).
NoiseBase(long seed) {
int source[256];
for (int i = 0; i < 256; ++i) { source[i] = i; }
srand(seed);
for (int i = 255; i >= 0; --i) {
int r = (int)(rand() % (i + 1));
perm[i] = source[r];
source[r] = source[i];
}
}
#endif
NoiseBase(const int* p) {
// Copy the supplied permutation array into this instance
for (int i = 0; i < 256; ++i) { perm[i] = p[i]; }
}
};
template <int N>
class Noise : public NoiseBase {
};
// 2D Implementation of the OpenSimplexNoise generator.
template <>
class Noise <2> : public NoiseBase {
private:
static const int gradients[16];
template <typename T>
inline T extrapolate(inttype xsb, inttype ysb, T dx, T dy) const {
unsigned int index = perm[(perm[xsb & 0xFF] + ysb) & 0xFF] & 0x0E;
return gradients[index] * dx +
gradients[index + 1] * dy;
}
template <typename T>
inline T extrapolate(inttype xsb, inttype ysb, T dx, T dy, T(&v)[2]) const {
unsigned int index = perm[(perm[xsb & 0xFF] + ysb) & 0xFF] & 0x0E;
return (v[0] = gradients[index]) * dx +
(v[1] = gradients[index + 1]) * dy;
}
public:
#ifdef OSN_USE_CSTDINT
Noise(int64_t seed = 0LL) : NoiseBase(seed) {}
#else
Noise(long seed = 0L) : NoiseBase(seed) {}
#endif
Noise(const int* p) : NoiseBase(p) {}
template <typename T>
T eval(T x, T y) const {
#ifdef OSN_USE_STATIC_ASSERT
static_assert(std::is_floating_point<T>::value, "OpenSimplexNoise can only be used with floating-point types");
#endif
static const T STRETCH_CONSTANT = (T)((1.0 / std::sqrt(2.0 + 1.0) - 1.0) * 0.5);
static const T SQUISH_CONSTANT = (T)((std::sqrt(2.0 + 1.0) - 1.0) * 0.5);
static const T NORM_CONSTANT = (T)(1.0 / 47.0);
inttype xsb, ysb, xsv_ext, ysv_ext;
T dx0, dy0, dx_ext, dy_ext;
T xins, yins;
// Parameters for the four contributions
T contr_m[4], contr_ext[4];
{
// Place input coordinates on a grid.
T stretchOffset = (x + y) * STRETCH_CONSTANT;
T xs = x + stretchOffset;
T ys = y + stretchOffset;
// Floor to get grid coordinates of rhombus super-cell origin.
#ifdef __FAST_MATH__
T xsbd = std::floor(xs);
T ysbd = std::floor(ys);
xsb = (inttype)xsbd;
ysb = (inttype)ysbd;
#else
xsb = fastFloori(xs);
ysb = fastFloori(ys);
T xsbd = (T)xsb;
T ysbd = (T)ysb;
#endif
// Skew out to get actual coordinates of rhombohedron origin.
T squishOffset = (xsbd + ysbd) * SQUISH_CONSTANT;
T xb = xsbd + squishOffset;
T yb = ysbd + squishOffset;
// Positions relative to origin point.
dx0 = x - xb;
dy0 = y - yb;
// Compute grid coordinates relative to rhomboidal origin.
xins = xs - xsbd;
yins = ys - ysbd;
}
// Contribution (1,0).
{
T dx1 = dx0 - (T)1.0 - SQUISH_CONSTANT;
T dy1 = dy0 - SQUISH_CONSTANT;
contr_m[0] = pow2(dx1) + pow2(dy1);
contr_ext[0] = extrapolate(xsb + 1, ysb, dx1, dy1);
}
// Contribution (0,1).
{
T dx2 = dx0 - SQUISH_CONSTANT;
T dy2 = dy0 - (T)1.0 - SQUISH_CONSTANT;
contr_m[1] = pow2(dx2) + pow2(dy2);
contr_ext[1] = extrapolate(xsb, ysb + 1, dx2, dy2);
}
if ((xins + yins) <= (T)1.0) {
// Inside the triangle (2-Simplex) at (0,0).
T zins = (T)1.0 - (xins + yins);
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 - (T)1.0;
dy_ext = dy0 + (T)1.0;
}
else {
xsv_ext = xsb - 1;
ysv_ext = ysb + 1;
dx_ext = dx0 + (T)1.0;
dy_ext = dy0 - (T)1.0;
}
}
else {
// (1,0) and (0,1) are the closest two vertices.
xsv_ext = xsb + 1;
ysv_ext = ysb + 1;
dx_ext = dx0 - (T)1.0 - (SQUISH_CONSTANT * (T)2.0);
dy_ext = dy0 - (T)1.0 - (SQUISH_CONSTANT * (T)2.0);
}
}
else {
// Inside the triangle (2-Simplex) at (1,1).
T zins = (T)2.0 - (xins + yins);
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;
dx_ext = dx0 - (T)2.0 - (SQUISH_CONSTANT * (T)2.0);
dy_ext = dy0 - (SQUISH_CONSTANT * (T)2.0);
}
else {
xsv_ext = xsb;
ysv_ext = ysb + 2;
dx_ext = dx0 - (SQUISH_CONSTANT * (T)2.0);
dy_ext = dy0 - (T)2.0 - (SQUISH_CONSTANT * (T)2.0);
}
}
else {
// (1,0) and (0,1) are the closest two vertices.
xsv_ext = xsb;
ysv_ext = ysb;
dx_ext = dx0;
dy_ext = dy0;
}
xsb += 1;
ysb += 1;
dx0 = dx0 - (T)1.0 - (SQUISH_CONSTANT * (T)2.0);
dy0 = dy0 - (T)1.0 - (SQUISH_CONSTANT * (T)2.0);
}
// Contribution (0,0) or (1,1).
{
contr_m[2] = pow2(dx0) + pow2(dy0);
contr_ext[2] = extrapolate(xsb, ysb, dx0, dy0);
}
// Extra vertex.
{
contr_m[3] = pow2(dx_ext) + pow2(dy_ext);
contr_ext[3] = extrapolate(xsv_ext, ysv_ext, dx_ext, dy_ext);
}
T value = 0.0;
for (int i = 0; i < 4; ++i) {
value += pow4(std::max((T)2.0 - contr_m[i], (T)0.0)) * contr_ext[i];
}
return (value * NORM_CONSTANT);
}
template <typename T>
void deval(T x, T y, T(&v)[2]) const {
#ifdef OSN_USE_STATIC_ASSERT
static_assert(std::is_floating_point<T>::value, "OpenSimplexNoise can only be used with floating-point types");
#endif
static const T STRETCH_CONSTANT = (T)((1.0 / std::sqrt(2.0 + 1.0) - 1.0) * 0.5);
static const T SQUISH_CONSTANT = (T)((std::sqrt(2.0 + 1.0) - 1.0) * 0.5);
static const T NORM_CONSTANT = (T)(1.0 / 47.0);
inttype xsb, ysb, xsv_ext, ysv_ext;
T dx0, dy0, dx_ext, dy_ext;
T xins, yins;
{
// Place input coordinates on a grid.
T stretchOffset = (x + y) * STRETCH_CONSTANT;
T xs = x + stretchOffset;
T ys = y + stretchOffset;
// Floor to get grid coordinates of rhombus super-cell origin.
#ifdef __FAST_MATH__
T xsbd = std::floor(xs);
T ysbd = std::floor(ys);
xsb = (inttype)xsbd;
ysb = (inttype)ysbd;
#else
xsb = fastFloori(xs);
ysb = fastFloori(ys);
T xsbd = (T)xsb;
T ysbd = (T)ysb;
#endif
// Skew out to get actual coordinates of rhombohedron origin.
T squishOffset = (xsbd + ysbd) * SQUISH_CONSTANT;
T xb = xsbd + squishOffset;
T yb = ysbd + squishOffset;
// Positions relative to origin point.
dx0 = x - xb;
dy0 = y - yb;
// Compute grid coordinates relative to rhomboidal origin.
xins = xs - xsbd;
yins = ys - ysbd;
}
T dv[2] = { 0.0, 0.0 };
// Contribution (1,0).
{
T dx1 = dx0 - (T)1.0 - SQUISH_CONSTANT;
T dy1 = dy0 - SQUISH_CONSTANT;
T attn1 = std::max((T)2.0 - ((dx1 * dx1) + (dy1 * dy1)), (T)0.0);
T de[2];
T ext = extrapolate(xsb + 1, ysb, dx1, dy1, de);
dv[0] += pow2(attn1) * (pow2(attn1) * de[0] - ((T)8.0) * attn1 * dx1 * ext);
dv[1] += pow2(attn1) * (pow2(attn1) * de[1] - ((T)8.0) * attn1 * dy1 * ext);
}
// Contribution (0,1).
{
T dx2 = dx0 - SQUISH_CONSTANT;
T dy2 = dy0 - (T)1.0 - SQUISH_CONSTANT;
T attn2 = std::max((T)2.0 - ((dx2 * dx2) + (dy2 * dy2)), (T)0.0);
T de[2];
T ext = extrapolate(xsb, ysb + 1, dx2, dy2, de);
dv[0] += pow2(attn2) * (pow2(attn2) * de[0] - ((T)8.0) * attn2 * dx2 * ext);
dv[1] += pow2(attn2) * (pow2(attn2) * de[1] - ((T)8.0) * attn2 * dy2 * ext);
}
if ((xins + yins) <= (T)1.0) {
// Inside the triangle (2-Simplex) at (0,0).
T zins = (T)1.0 - (xins + yins);
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 - (T)1.0;
dy_ext = dy0 + (T)1.0;
}
else {
xsv_ext = xsb - 1;
ysv_ext = ysb + 1;
dx_ext = dx0 + (T)1.0;
dy_ext = dy0 - (T)1.0;
}
}
else {
// (1,0) and (0,1) are the closest two vertices.
xsv_ext = xsb + 1;
ysv_ext = ysb + 1;
dx_ext = dx0 - (T)1.0 - (SQUISH_CONSTANT * (T)2.0);
dy_ext = dy0 - (T)1.0 - (SQUISH_CONSTANT * (T)2.0);
}
}
else {
// Inside the triangle (2-Simplex) at (1,1).
T zins = (T)2.0 - (xins + yins);
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;
dx_ext = dx0 - (T)2.0 - (SQUISH_CONSTANT * (T)2.0);
dy_ext = dy0 - (SQUISH_CONSTANT * (T)2.0);
}
else {
xsv_ext = xsb;
ysv_ext = ysb + 2;
dx_ext = dx0 - (SQUISH_CONSTANT * (T)2.0);
dy_ext = dy0 - (T)2.0 - (SQUISH_CONSTANT * (T)2.0);
}
}
else {
// (1,0) and (0,1) are the closest two vertices.
xsv_ext = xsb;
ysv_ext = ysb;
dx_ext = dx0;
dy_ext = dy0;
}
xsb += 1;
ysb += 1;
dx0 = dx0 - (T)1.0 - (SQUISH_CONSTANT * (T)2.0);
dy0 = dy0 - (T)1.0 - (SQUISH_CONSTANT * (T)2.0);
}
// Contribution (0,0) or (1,1).
{
T attn = std::max((T)2.0 - ((dx0 * dx0) + (dy0 * dy0)), (T)0.0);
T de[2];
T ext = extrapolate(xsb, ysb, dx0, dy0, de);
dv[0] += pow2(attn) * (pow2(attn) * de[0] - ((T)8.0) * attn * dx0 * ext);
dv[1] += pow2(attn) * (pow2(attn) * de[1] - ((T)8.0) * attn * dy0 * ext);
}
// Extra vertex.
{
T attn = std::max((T)2.0 - ((dx_ext * dx_ext) + (dy_ext * dy_ext)), (T)0.0);
T de[2];
T ext = extrapolate(xsv_ext, ysv_ext, dx_ext, dy_ext, de);
dv[0] += pow2(attn) * (pow2(attn) * de[0] - ((T)8.0) * attn * dx_ext * ext);
dv[1] += pow2(attn) * (pow2(attn) * de[1] - ((T)8.0) * attn * dy_ext * ext);
}
v[0] = dv[0] * NORM_CONSTANT;
v[1] = dv[1] * NORM_CONSTANT;
}
};
// Array of gradient values for 2D. They approximate the directions to the
// vertices of a octagon from its center.
// Gradient set 2014-10-06.
const int Noise<2>::gradients[] = {
5, 2, 2, 5, -5, 2, -2, 5,
5,-2, 2,-5, -5,-2, -2,-5
};
// 3D Implementation of the OpenSimplexNoise generator.
template <>
class Noise <3> : public NoiseBase {
private:
// Array of gradient values for 3D. Values are defined below the class definition.
static const int gradients[72];
// Because 72 is not a power of two, extrapolate cannot use a bitmask to index
// into the perm array. Pre-calculate and store the indices instead.
int permGradIndex[256];
template <typename T>
inline T extrapolate(inttype xsb, inttype ysb, inttype zsb, T dx, T dy, T dz) const {
unsigned int index = permGradIndex[(perm[(perm[xsb & 0xFF] + ysb) & 0xFF] + zsb) & 0xFF];
return gradients[index] * dx +
gradients[index + 1] * dy +
gradients[index + 2] * dz;
}
template <typename T>
inline T extrapolate(inttype xsb, inttype ysb, inttype zsb, T dx, T dy, T dz, T(&de)[3]) const {
unsigned int index = permGradIndex[(perm[(perm[xsb & 0xFF] + ysb) & 0xFF] + zsb) & 0xFF];
return (de[0] = gradients[index]) * dx +
(de[1] = gradients[index + 1]) * dy +
(de[2] = gradients[index + 2]) * dz;
}
public:
#ifdef OSN_USE_CSTDINT
// Initializes the class 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.
Noise(int64_t seed = 0LL) : NoiseBase() {
int source[256];
for (int i = 0; i < 256; ++i) { source[i] = i; }
LCG_STEP(seed);
LCG_STEP(seed);
LCG_STEP(seed);
for (int i = 255; i >= 0; --i) {
LCG_STEP(seed);
int r = (int)((seed + 31) % (i + 1));
if (r < 0) { r += (i + 1); }
perm[i] = source[r];
permGradIndex[i] = (int)((perm[i] % (72 / 3)) * 3);
source[r] = source[i];
}
}
#else
// Initializes the class using a permutation array generated from a 32-bit seed.
// Generates a proper permutation (i.e. doesn't merely perform N successive
// pair swaps on a base array).
Noise(long seed = 0L) : NoiseBase() {
int source[256];
for (int i = 0; i < 256; ++i) { source[i] = i; }
srand(seed);
for (int i = 255; i >= 0; --i) {
int r = (int)(rand() % (i + 1));
perm[i] = source[r];
// NB: 72 is the number of elements of the gradients3D array
permGradIndex[i] = (int)((perm[i] % (72 / 3)) * 3);
source[r] = source[i];
}
}
#endif
Noise(const int* p) : NoiseBase() {
// Copy the supplied permutation array into this instance.
for (int i = 0; i < 256; ++i) {
perm[i] = p[i];
permGradIndex[i] = (int)((perm[i] % (72 / 3)) * 3);
}
}
template <typename T>
T eval(T x, T y, T z) const {
#ifdef OSN_USE_STATIC_ASSERT
static_assert(std::is_floating_point<T>::value, "OpenSimplexNoise can only be used with floating-point types");
#endif
static const T STRETCH_CONSTANT = (T)(-1.0 / 6.0); // (1 / sqrt(3 + 1) - 1) / 3
static const T SQUISH_CONSTANT = (T)(1.0 / 3.0); // (sqrt(3 + 1) - 1) / 3
static const T NORM_CONSTANT = (T)(1.0 / 103.0);
inttype xsb, ysb, zsb;
T dx0, dy0, dz0;
T xins, yins, zins;
// Parameters for the individual contributions
T contr_m[9], contr_ext[9];
{
// Place input coordinates on simplectic lattice.
T stretchOffset = (x + y + z) * STRETCH_CONSTANT;
T xs = x + stretchOffset;
T ys = y + stretchOffset;
T zs = z + stretchOffset;
// Floor to get simplectic lattice coordinates of rhombohedron
// (stretched cube) super-cell.
#ifdef __FAST_MATH__
T xsbd = std::floor(xs);
T ysbd = std::floor(ys);
T zsbd = std::floor(zs);
xsb = (inttype)xsbd;
ysb = (inttype)ysbd;
zsb = (inttype)zsbd;
#else
xsb = fastFloori(xs);
ysb = fastFloori(ys);
zsb = fastFloori(zs);
T xsbd = (T)xsb;
T ysbd = (T)ysb;
T zsbd = (T)zsb;
#endif
// Skew out to get actual coordinates of rhombohedron origin.
T squishOffset = (xsbd + ysbd + zsbd) * SQUISH_CONSTANT;
T xb = xsbd + squishOffset;
T yb = ysbd + squishOffset;
T zb = zsbd + squishOffset;
// Positions relative to origin point.
dx0 = x - xb;
dy0 = y - yb;
dz0 = z - zb;
// Compute simplectic lattice coordinates relative to rhombohedral origin.
xins = xs - xsbd;
yins = ys - ysbd;
zins = zs - zsbd;
}
// These are given values inside the next block, and used afterwards.
inttype xsv_ext0, ysv_ext0, zsv_ext0;
inttype xsv_ext1, ysv_ext1, zsv_ext1;
T dx_ext0, dy_ext0, dz_ext0;
T dx_ext1, dy_ext1, dz_ext1;
// Sum together to get a value that determines which cell we are in.
T inSum = xins + yins + zins;
if (inSum > (T)1.0 && inSum < (T)2.0) {
// The point is inside the octahedron (rectified 3-Simplex) inbetween.
T aScore;
OSN_BYTE aPoint;
bool aIsFurtherSide;
T bScore;
OSN_BYTE bPoint;
bool bIsFurtherSide;
// Decide between point (1,0,0) and (0,1,1) as closest.
T p1 = xins + yins;
if (p1 <= (T)1.0) {
aScore = (T)1.0 - p1;
aPoint = 4;
aIsFurtherSide = false;
}
else {
aScore = p1 - (T)1.0;
aPoint = 3;
aIsFurtherSide = true;
}
// Decide between point (0,1,0) and (1,0,1) as closest.
T p2 = xins + zins;
if (p2 <= (T)1.0) {
bScore = (T)1.0 - p2;
bPoint = 2;
bIsFurtherSide = false;
}
else {
bScore = p2 - (T)1.0;
bPoint = 5;
bIsFurtherSide = true;
}
// The closest out of the two (0,0,1) and (1,1,0) will replace the
// furthest out of the two decided above if closer.
T p3 = yins + zins;
if (p3 > (T)1.0) {
T score = p3 - (T)1.0;
if (aScore > bScore && bScore < score) {
bScore = score;
bPoint = 6;
bIsFurtherSide = true;
}
else if (aScore <= bScore && aScore < score) {
aScore = score;
aPoint = 6;
aIsFurtherSide = true;
}
}
else {
T score = (T)1.0 - p3;
if (aScore > bScore && bScore < score) {
bScore = score;
bPoint = 1;
bIsFurtherSide = false;
}
else if (aScore <= bScore && aScore < score) {
aScore = score;
aPoint = 1;
aIsFurtherSide = false;
}
}
// Where each of the two closest points are determines how the
// extra two vertices are calculated.
if (aIsFurtherSide == bIsFurtherSide) {
if (aIsFurtherSide) {
// Both closest points on (1,1,1) side.
// One of the two extra points is (1,1,1)
xsv_ext0 = xsb + 1;
ysv_ext0 = ysb + 1;
zsv_ext0 = zsb + 1;
dx_ext0 = dx0 - (T)1.0 - (SQUISH_CONSTANT * (T)3.0);
dy_ext0 = dy0 - (T)1.0 - (SQUISH_CONSTANT * (T)3.0);
dz_ext0 = dz0 - (T)1.0 - (SQUISH_CONSTANT * (T)3.0);
// Other extra point is based on the shared axis.
OSN_BYTE c = aPoint & bPoint;
if (c & 0x01) {
xsv_ext1 = xsb + 2;
ysv_ext1 = ysb;
zsv_ext1 = zsb;
dx_ext1 = dx0 - (T)2.0 - (SQUISH_CONSTANT * (T)2.0);
dy_ext1 = dy0 - (SQUISH_CONSTANT * (T)2.0);
dz_ext1 = dz0 - (SQUISH_CONSTANT * (T)2.0);
}
else if (c & 0x02) {
xsv_ext1 = xsb;
ysv_ext1 = ysb + 2;
zsv_ext1 = zsb;
dx_ext1 = dx0 - (SQUISH_CONSTANT * (T)2.0);
dy_ext1 = dy0 - (T)2.0 - (SQUISH_CONSTANT * (T)2.0);
dz_ext1 = dz0 - (SQUISH_CONSTANT * (T)2.0);
}
else {
xsv_ext1 = xsb;
ysv_ext1 = ysb;
zsv_ext1 = zsb + 2;
dx_ext1 = dx0 - (SQUISH_CONSTANT * (T)2.0);
dy_ext1 = dy0 - (SQUISH_CONSTANT * (T)2.0);
dz_ext1 = dz0 - (T)2.0 - (SQUISH_CONSTANT * (T)2.0);
}
}
else {
// Both closest points are on the (0,0,0) side.
// One of the two extra points is (0,0,0).
xsv_ext0 = xsb;
ysv_ext0 = ysb;
zsv_ext0 = zsb;
dx_ext0 = dx0;
dy_ext0 = dy0;
dz_ext0 = dz0;
// The other extra point is based on the omitted axis.
OSN_BYTE c = aPoint | bPoint;
if (!(c & 0x01)) {
xsv_ext1 = xsb - 1;
ysv_ext1 = ysb + 1;
zsv_ext1 = zsb + 1;
dx_ext1 = dx0 + (T)1.0 - SQUISH_CONSTANT;
dy_ext1 = dy0 - (T)1.0 - SQUISH_CONSTANT;
dz_ext1 = dz0 - (T)1.0 - SQUISH_CONSTANT;
}
else if (!(c & 0x02)) {
xsv_ext1 = xsb + 1;
ysv_ext1 = ysb - 1;
zsv_ext1 = zsb + 1;
dx_ext1 = dx0 - (T)1.0 - SQUISH_CONSTANT;
dy_ext1 = dy0 + (T)1.0 - SQUISH_CONSTANT;
dz_ext1 = dz0 - (T)1.0 - SQUISH_CONSTANT;
}
else {
xsv_ext1 = xsb + 1;
ysv_ext1 = ysb + 1;
zsv_ext1 = zsb - 1;
dx_ext1 = dx0 - (T)1.0 - SQUISH_CONSTANT;
dy_ext1 = dy0 - (T)1.0 - SQUISH_CONSTANT;
dz_ext1 = dz0 + (T)1.0 - SQUISH_CONSTANT;
}
}
}
else {
// One point is on the (0,0,0) side, one point is on the (1,1,1) side.
OSN_BYTE c1, c2;
if (aIsFurtherSide) {
c1 = aPoint;
c2 = bPoint;
}
else {
c1 = bPoint;
c2 = aPoint;
}
// One contribution is a permutation of (1,1,-1).
if (!(c1 & 0x01)) {
xsv_ext0 = xsb - 1;
ysv_ext0 = ysb + 1;
zsv_ext0 = zsb + 1;
dx_ext0 = dx0 + (T)1.0 - SQUISH_CONSTANT;
dy_ext0 = dy0 - (T)1.0 - SQUISH_CONSTANT;
dz_ext0 = dz0 - (T)1.0 - SQUISH_CONSTANT;
}
else if (!(c1 & 0x02)) {
xsv_ext0 = xsb + 1;
ysv_ext0 = ysb - 1;
zsv_ext0 = zsb + 1;
dx_ext0 = dx0 - (T)1.0 - SQUISH_CONSTANT;
dy_ext0 = dy0 + (T)1.0 - SQUISH_CONSTANT;
dz_ext0 = dz0 - (T)1.0 - SQUISH_CONSTANT;
}
else {
xsv_ext0 = xsb + 1;
ysv_ext0 = ysb + 1;
zsv_ext0 = zsb - 1;
dx_ext0 = dx0 - (T)1.0 - SQUISH_CONSTANT;
dy_ext0 = dy0 - (T)1.0 - SQUISH_CONSTANT;
dz_ext0 = dz0 + (T)1.0 - SQUISH_CONSTANT;
}
// One contribution is a permutation of (0,0,2).
if (c2 & 0x01) {
xsv_ext1 = xsb + 2;
ysv_ext1 = ysb;
zsv_ext1 = zsb;
dx_ext1 = dx0 - (T)2.0 - (SQUISH_CONSTANT * (T)2.0);
dy_ext1 = dy0 - (SQUISH_CONSTANT * (T)2.0);
dz_ext1 = dz0 - (SQUISH_CONSTANT * (T)2.0);
}
else if (c2 & 0x02) {
xsv_ext1 = xsb;
ysv_ext1 = ysb + 2;
zsv_ext1 = zsb;
dx_ext1 = dx0 - (SQUISH_CONSTANT * (T)2.0);
dy_ext1 = dy0 - (T)2.0 - (SQUISH_CONSTANT * (T)2.0);
dz_ext1 = dz0 - (SQUISH_CONSTANT * (T)2.0);
}
else {
xsv_ext1 = xsb;
ysv_ext1 = ysb;
zsv_ext1 = zsb + 2;
dx_ext1 = dx0 - (SQUISH_CONSTANT * (T)2.0);
dy_ext1 = dy0 - (SQUISH_CONSTANT * (T)2.0);
dz_ext1 = dz0 - (T)2.0 - (SQUISH_CONSTANT * (T)2.0);
}
}
contr_m[0] = contr_ext[0] = 0.0;
// Contribution (0,0,1).
T dx1 = dx0 - (T)1.0 - SQUISH_CONSTANT;
T dy1 = dy0 - SQUISH_CONSTANT;
T dz1 = dz0 - SQUISH_CONSTANT;
contr_m[1] = pow2(dx1) + pow2(dy1) + pow2(dz1);
contr_ext[1] = extrapolate(xsb + 1, ysb, zsb, dx1, dy1, dz1);
// Contribution (0,1,0).
T dx2 = dx0 - SQUISH_CONSTANT;
T dy2 = dy0 - (T)1.0 - SQUISH_CONSTANT;
T dz2 = dz1;
contr_m[2] = pow2(dx2) + pow2(dy2) + pow2(dz2);
contr_ext[2] = extrapolate(xsb, ysb + 1, zsb, dx2, dy2, dz2);
// Contribution (1,0,0).
T dx3 = dx2;
T dy3 = dy1;
T dz3 = dz0 - (T)1.0 - SQUISH_CONSTANT;
contr_m[3] = pow2(dx3) + pow2(dy3) + pow2(dz3);
contr_ext[3] = extrapolate(xsb, ysb, zsb + 1, dx3, dy3, dz3);
// Contribution (1,1,0).
T dx4 = dx0 - (T)1.0 - (SQUISH_CONSTANT * (T)2.0);
T dy4 = dy0 - (T)1.0 - (SQUISH_CONSTANT * (T)2.0);
T dz4 = dz0 - (SQUISH_CONSTANT * (T)2.0);
contr_m[4] = pow2(dx4) + pow2(dy4) + pow2(dz4);
contr_ext[4] = extrapolate(xsb + 1, ysb + 1, zsb, dx4, dy4, dz4);
// Contribution (1,0,1).
T dx5 = dx4;
T dy5 = dy0 - (SQUISH_CONSTANT * (T)2.0);
T dz5 = dz0 - (T)1.0 - (SQUISH_CONSTANT * (T)2.0);
contr_m[5] = pow2(dx5) + pow2(dy5) + pow2(dz5);
contr_ext[5] = extrapolate(xsb + 1, ysb, zsb + 1, dx5, dy5, dz5);
// Contribution (0,1,1).
T dx6 = dx0 - (SQUISH_CONSTANT * (T)2.0);
T dy6 = dy4;
T dz6 = dz5;
contr_m[6] = pow2(dx6) + pow2(dy6) + pow2(dz6);
contr_ext[6] = extrapolate(xsb, ysb + 1, zsb + 1, dx6, dy6, dz6);
}
else if (inSum <= (T)1.0) {
// The point is inside the tetrahedron (3-Simplex) at (0,0,0)
// Determine which of (0,0,1), (0,1,0), (1,0,0) are closest.
OSN_BYTE aPoint = 1;
T aScore = xins;
OSN_BYTE bPoint = 2;
T bScore = yins;
if (aScore < bScore && zins > aScore) {
aScore = zins;
aPoint = 4;
}
else if (aScore >= bScore && zins > bScore) {
bScore = zins;
bPoint = 4;
}
// 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).
T wins = (T)1.0 - inSum;
if (wins > aScore || wins > bScore) {
// (0,0,0) is one of the closest two tetrahedral vertices.
// The other closest vertex is the closer of a and b.
OSN_BYTE c = ((bScore > aScore) ? bPoint : aPoint);
if (c != 1) {
xsv_ext0 = xsb - 1;
xsv_ext1 = xsb;
dx_ext0 = dx0 + (T)1.0;
dx_ext1 = dx0;
}
else {
xsv_ext0 = xsv_ext1 = xsb + 1;
dx_ext0 = dx_ext1 = dx0 - (T)1.0;
}
if (c != 2) {
ysv_ext0 = ysv_ext1 = ysb;
dy_ext0 = dy_ext1 = dy0;
if (c == 1) {
ysv_ext0 -= 1;
dy_ext0 += (T)1.0;
}
else {
ysv_ext1 -= 1;
dy_ext1 += (T)1.0;
}
}
else {
ysv_ext0 = ysv_ext1 = ysb + 1;
dy_ext0 = dy_ext1 = dy0 - (T)1.0;
}
if (c != 4) {
zsv_ext0 = zsb;
zsv_ext1 = zsb - 1;
dz_ext0 = dz0;
dz_ext1 = dz0 + (T)1.0;
}
else {
zsv_ext0 = zsv_ext1 = zsb + 1;
dz_ext0 = dz_ext1 = dz0 - (T)1.0;
}
}
else {
// (0,0,0) is not one of the closest two tetrahedral vertices.
// The two extra vertices are determined by the closest two.
OSN_BYTE c = (aPoint | bPoint);
if (c & 0x01) {
xsv_ext0 = xsv_ext1 = xsb + 1;
dx_ext0 = dx0 - (T)1.0 - (SQUISH_CONSTANT * (T)2.0);
dx_ext1 = dx0 - (T)1.0 - SQUISH_CONSTANT;
}
else {
xsv_ext0 = xsb;
xsv_ext1 = xsb - 1;
dx_ext0 = dx0 - (SQUISH_CONSTANT * (T)2.0);
dx_ext1 = dx0 + (T)1.0 - SQUISH_CONSTANT;
}
if (c & 0x02) {
ysv_ext0 = ysv_ext1 = ysb + 1;
dy_ext0 = dy0 - (T)1.0 - (SQUISH_CONSTANT * (T)2.0);
dy_ext1 = dy0 - (T)1.0 - SQUISH_CONSTANT;
}
else {
ysv_ext0 = ysb;
ysv_ext1 = ysb - 1;
dy_ext0 = dy0 - (SQUISH_CONSTANT * (T)2.0);
dy_ext1 = dy0 + (T)1.0 - SQUISH_CONSTANT;
}
if (c & 0x04) {
zsv_ext0 = zsv_ext1 = zsb + 1;
dz_ext0 = dz0 - (T)1.0 - (SQUISH_CONSTANT * (T)2.0);
dz_ext1 = dz0 - (T)1.0 - SQUISH_CONSTANT;
}
else {
zsv_ext0 = zsb;
zsv_ext1 = zsb - 1;
dz_ext0 = dz0 - (SQUISH_CONSTANT * (T)2.0);
dz_ext1 = dz0 + (T)1.0 - SQUISH_CONSTANT;
}
}
// Contribution (0,0,0)
{
contr_m[0] = pow2(dx0) + pow2(dy0) + pow2(dz0);
contr_ext[0] = extrapolate(xsb, ysb, zsb, dx0, dy0, dz0);
}
// Contribution (0,0,1)
T dx1 = dx0 - (T)1.0 - SQUISH_CONSTANT;
T dy1 = dy0 - SQUISH_CONSTANT;
T dz1 = dz0 - SQUISH_CONSTANT;
contr_m[1] = pow2(dx1) + pow2(dy1) + pow2(dz1);
contr_ext[1] = extrapolate(xsb + 1, ysb, zsb, dx1, dy1, dz1);
// Contribution (0,1,0)
T dx2 = dx0 - SQUISH_CONSTANT;
T dy2 = dy0 - (T)1.0 - SQUISH_CONSTANT;
T dz2 = dz1;
contr_m[2] = pow2(dx2) + pow2(dy2) + pow2(dz2);
contr_ext[2] = extrapolate(xsb, ysb + 1, zsb, dx2, dy2, dz2);
// Contribution (1,0,0)
T dx3 = dx2;
T dy3 = dy1;
T dz3 = dz0 - (T)1.0 - SQUISH_CONSTANT;
contr_m[3] = pow2(dx3) + pow2(dy3) + pow2(dz3);
contr_ext[3] = extrapolate(xsb, ysb, zsb + 1, dx3, dy3, dz3);
contr_m[4] = contr_m[5] = contr_m[6] = 0.0;
contr_ext[4] = contr_ext[5] = contr_ext[6] = 0.0;
}
else {
// The point is 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), and (0,1,1), but not (1,1,1).
OSN_BYTE aPoint = 6;
T aScore = xins;
OSN_BYTE bPoint = 5;
T bScore = yins;
if (aScore <= bScore && zins < bScore) {
bScore = zins;
bPoint = 3;
}
else if (aScore > bScore && zins < aScore) {
aScore = zins;
aPoint = 3;
}
// 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).
T wins = 3.0 - inSum;
if (wins < aScore || wins < bScore) {
// (1,1,1) is one of the closest two tetrahedral vertices.
// The other closest vertex is the closest of a and b.
OSN_BYTE c = ((bScore < aScore) ? bPoint : aPoint);
if (c & 0x01) {
xsv_ext0 = xsb + 2;
xsv_ext1 = xsb + 1;
dx_ext0 = dx0 - (T)2.0 - (SQUISH_CONSTANT * (T)3.0);
dx_ext1 = dx0 - (T)1.0 - (SQUISH_CONSTANT * (T)3.0);
}
else {
xsv_ext0 = xsv_ext1 = xsb;
dx_ext0 = dx_ext1 = dx0 - (SQUISH_CONSTANT * (T)3.0);
}
if (c & 0x02) {
ysv_ext0 = ysv_ext1 = ysb + 1;
dy_ext0 = dy_ext1 = dy0 - (T)1.0 - (SQUISH_CONSTANT * (T)3.0);
if (c & 0x01) {
ysv_ext1 += 1;
dy_ext1 -= (T)1.0;
}
else {
ysv_ext0 += 1;
dy_ext0 -= (T)1.0;
}
}
else {
ysv_ext0 = ysv_ext1 = ysb;
dy_ext0 = dy_ext1 = dy0 - (SQUISH_CONSTANT * (T)3.0);
}
if (c & 0x04) {
zsv_ext0 = zsb + 1;
zsv_ext1 = zsb + 2;
dz_ext0 = dz0 - (T)1.0 - (SQUISH_CONSTANT * (T)3.0);
dz_ext1 = dz0 - (T)2.0 - (SQUISH_CONSTANT * (T)3.0);
}
else {
zsv_ext0 = zsv_ext1 = zsb;
dz_ext0 = dz_ext1 = dz0 - (SQUISH_CONSTANT * (T)3.0);
}
}
else {
// (1,1,1) is not one of the closest two tetrahedral vertices.
// The two extra vertices are determined by the closest two.
OSN_BYTE c = aPoint & bPoint;
if (c & 0x01) {
xsv_ext0 = xsb + 1;
xsv_ext1 = xsb + 2;
dx_ext0 = dx0 - (T)1.0 - SQUISH_CONSTANT;
dx_ext1 = dx0 - (T)2.0 - (SQUISH_CONSTANT * (T)2.0);
}
else {
xsv_ext0 = xsv_ext1 = xsb;
dx_ext0 = dx0 - SQUISH_CONSTANT;
dx_ext1 = dx0 - (SQUISH_CONSTANT * (T)2.0);
}
if (c & 0x02) {
ysv_ext0 = ysb + 1;
ysv_ext1 = ysb + 2;
dy_ext0 = dy0 - (T)1.0 - SQUISH_CONSTANT;
dy_ext1 = dy0 - (T)2.0 - (SQUISH_CONSTANT * (T)2.0);
}
else {
ysv_ext0 = ysv_ext1 = ysb;
dy_ext0 = dy0 - SQUISH_CONSTANT;
dy_ext1 = dy0 - (SQUISH_CONSTANT * (T)2.0);
}
if (c & 0x04) {
zsv_ext0 = zsb + 1;
zsv_ext1 = zsb + 2;
dz_ext0 = dz0 - (T)1.0 - SQUISH_CONSTANT;
dz_ext1 = dz0 - (T)2.0 - (SQUISH_CONSTANT * (T)2.0);
}
else {
zsv_ext0 = zsv_ext1 = zsb;
dz_ext0 = dz0 - SQUISH_CONSTANT;
dz_ext1 = dz0 - (SQUISH_CONSTANT * (T)2.0);
}
}
// Contribution (1,1,0)
T dx3 = dx0 - (T)1.0 - (SQUISH_CONSTANT * (T)2.0);
T dy3 = dy0 - (T)1.0 - (SQUISH_CONSTANT * (T)2.0);
T dz3 = dz0 - (SQUISH_CONSTANT * (T)2.0);
contr_m[3] = pow2(dx3) + pow2(dy3) + pow2(dz3);
contr_ext[3] = extrapolate(xsb + 1, ysb + 1, zsb, dx3, dy3, dz3);
// Contribution (1,0,1)
T dx2 = dx3;
T dy2 = dy0 - (SQUISH_CONSTANT * (T)2.0);
T dz2 = dz0 - (T)1.0 - (SQUISH_CONSTANT * (T)2.0);
contr_m[2] = pow2(dx2) + pow2(dy2) + pow2(dz2);
contr_ext[2] = extrapolate(xsb + 1, ysb, zsb + 1, dx2, dy2, dz2);
// Contribution (0,1,1)
{
T dx1 = dx0 - (SQUISH_CONSTANT * (T)2.0);
T dy1 = dy3;
T dz1 = dz2;
contr_m[1] = pow2(dx1) + pow2(dy1) + pow2(dz1);
contr_ext[1] = extrapolate(xsb, ysb + 1, zsb + 1, dx1, dy1, dz1);
}
// Contribution (1,1,1)
{
dx0 = dx0 - (T)1.0 - (SQUISH_CONSTANT * (T)3.0);
dy0 = dy0 - (T)1.0 - (SQUISH_CONSTANT * (T)3.0);
dz0 = dz0 - (T)1.0 - (SQUISH_CONSTANT * (T)3.0);
contr_m[0] = pow2(dx0) + pow2(dy0) + pow2(dz0);
contr_ext[0] = extrapolate(xsb + 1, ysb + 1, zsb + 1, dx0, dy0, dz0);
}
contr_m[4] = contr_m[5] = contr_m[6] = 0.0;
contr_ext[4] = contr_ext[5] = contr_ext[6] = 0.0;
}
// First extra vertex.
contr_m[7] = pow2(dx_ext0) + pow2(dy_ext0) + pow2(dz_ext0);
contr_ext[7] = extrapolate(xsv_ext0, ysv_ext0, zsv_ext0, dx_ext0, dy_ext0, dz_ext0);
// Second extra vertex.
contr_m[8] = pow2(dx_ext1) + pow2(dy_ext1) + pow2(dz_ext1);
contr_ext[8] = extrapolate(xsv_ext1, ysv_ext1, zsv_ext1, dx_ext1, dy_ext1, dz_ext1);
T value = 0.0;
for (int i = 0; i < 9; ++i) {
value += pow4(std::max((T)2.0 - contr_m[i], (T)0.0)) * contr_ext[i];
}
return (value * NORM_CONSTANT);
}
};
// Array of gradient values for 3D. They approximate the directions to the
// vertices of a rhombicuboctahedron from its center, skewed so that the
// triangular and square facets can be inscribed in circles of the same radius.
// New gradient set 2014-10-06.
const int Noise<3>::gradients[] = {
-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
};
// 4D Implementation of the OpenSimplexNoise generator.
template <>
class Noise <4> : public NoiseBase {
private:
// Array of gradient values for 4D. Values are defined below the class definition.
static const int gradients[256];
template <typename T>
inline T extrapolate(inttype xsb, inttype ysb, inttype zsb, inttype wsb, T dx, T dy, T dz, T dw) const {
unsigned int index = perm[(perm[(perm[(perm[xsb & 0xFF] + ysb) & 0xFF] + zsb) & 0xFF] + wsb) & 0xFF] & 0xFC;
return gradients[index] * dx +
gradients[index + 1] * dy +
gradients[index + 2] * dz +
gradients[index + 3] * dw;
}
public:
#ifdef OSN_USE_CSTDINT
Noise(int64_t seed = 0LL) : NoiseBase(seed) {}
#else
Noise(long seed = 0L) : NoiseBase(seed) {}
#endif
Noise(const int* p) : NoiseBase(p) {}
template <typename T>
T eval(T x, T y, T z, T w) const {
#ifdef OSN_USE_STATIC_ASSERT
static_assert(std::is_floating_point<T>::value, "OpenSimplexNoise can only be used with floating-point types");
#endif
static const T STRETCH_CONSTANT = (T)((1.0 / std::sqrt(4.0 + 1.0) - 1.0) * 0.25);
static const T SQUISH_CONSTANT = (T)((std::sqrt(4.0 + 1.0) - 1.0) * 0.25);
static const T NORM_CONSTANT = (T)(1.0 / 30.0);
T dx0, dy0, dz0, dw0;
inttype xsb, ysb, zsb, wsb;
T xins, yins, zins, wins;
{
// Place input coordinates on simplectic honeycomb.
T stretchOffset = (x + y + z + w) * STRETCH_CONSTANT;
T xs = x + stretchOffset;
T ys = y + stretchOffset;
T zs = z + stretchOffset;
T ws = w + stretchOffset;
// Floor to get simplectic honeycomb coordinates of rhombo-hypercube origin.
#ifdef __FAST_MATH__
T xsbd = std::floor(xs);
T ysbd = std::floor(ys);
T zsbd = std::floor(zs);
T wsbd = std::floor(ws);
xsb = (inttype)xsbd;
ysb = (inttype)ysbd;
zsb = (inttype)zsbd;
wsb = (inttype)wsbd;
#else
xsb = fastFloori(xs);
ysb = fastFloori(ys);
zsb = fastFloori(zs);
wsb = fastFloori(ws);
T xsbd = (T)xsb;
T ysbd = (T)ysb;
T zsbd = (T)zsb;
T wsbd = (T)wsb;
#endif
// Skew out to get actual coordinates of stretched rhombo-hypercube origin.
T squishOffset = (xsbd + ysbd + zsbd + wsbd) * SQUISH_CONSTANT;
T xb = xsbd + squishOffset;
T yb = ysbd + squishOffset;
T zb = zsbd + squishOffset;
T wb = wsbd + squishOffset;
// Positions relative to origin point.
dx0 = x - xb;
dy0 = y - yb;
dz0 = z - zb;
dw0 = w - wb;
// Compute simplectic honeycomb coordinates relative to rhombo-hypercube origin.
xins = xs - xsbd;
yins = ys - ysbd;
zins = zs - zsbd;
wins = ws - wsbd;
}
// These are given values inside the next block, and used afterwards.
inttype xsv_ext0, ysv_ext0, zsv_ext0, wsv_ext0;
inttype xsv_ext1, ysv_ext1, zsv_ext1, wsv_ext1;
inttype xsv_ext2, ysv_ext2, zsv_ext2, wsv_ext2;
T dx_ext0, dy_ext0, dz_ext0, dw_ext0;
T dx_ext1, dy_ext1, dz_ext1, dw_ext1;
T dx_ext2, dy_ext2, dz_ext2, dw_ext2;
T value = 0.0;
// Sum together to get a value that determines which cell we are in.
T inSum = xins + yins + zins + wins;
if (inSum <= (T)1.0) {
// Inside a pentachoron (4-Simplex) at (0,0,0,0)
// Determine which two of (0,0,0,1), (0,0,1,0), (0,1,0,0) and (1,0,0,0) are closest.
OSN_BYTE aPoint = 0x01, bPoint = 0x02;
T aScore = xins, bScore = yins;
if (aScore >= bScore && zins > bScore) {
bPoint = 0x04;
bScore = zins;
}
else if (aScore < bScore && zins > aScore) {
aPoint = 0x04;
aScore = zins;
}
if (aScore >= bScore && wins > bScore) {
bPoint = 0x08;
bScore = wins;
}
else if (aScore < bScore && wins > aScore) {
aPoint = 0x08;
aScore = wins;
}
// 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).
T uins = (T)1.0 - inSum;
if (uins > aScore || uins > bScore) {
// (0,0,0,0) is one of the closest two pentachoron vertices.
// The other closest vertex is the closest out of A and B.
OSN_BYTE c = (bScore > aScore ? bPoint : aPoint);
if (c != 0x01) {
xsv_ext0 = xsb - 1;
xsv_ext1 = xsv_ext2 = xsb;
dx_ext0 = dx0 + (T)1.0;
dx_ext1 = dx_ext2 = dx0;
}
else {
xsv_ext0 = xsv_ext1 = xsv_ext2 = xsb + 1;
dx_ext0 = dx_ext1 = dx_ext2 = dx0 - (T)1.0;
}
if (c != 0x02) {
ysv_ext0 = ysv_ext1 = ysv_ext2 = ysb;
dy_ext0 = dy_ext1 = dy_ext2 = dy0;
if (c != 0x01) {
ysv_ext1 -= 1;
dy_ext1 += (T)1.0;
}
else {
ysv_ext0 -= 1;
dy_ext0 += (T)1.0;
}
}
else {
ysv_ext0 = ysv_ext1 = ysv_ext2 = ysb + 1;
dy_ext0 = dy_ext1 = dy_ext2 = dy0 - (T)1.0;
}
if (c != 0x04) {
zsv_ext0 = zsv_ext1 = zsv_ext2 = zsb;
dz_ext0 = dz_ext1 = dz_ext2 = dz0;
if (c & 0x03) {
zsv_ext1 -= 1;
dz_ext1 += (T)1.0;
}
else {
zsv_ext2 -= 1;
dz_ext2 += (T)1.0;
}
}
else {
zsv_ext0 = zsv_ext1 = zsv_ext2 = zsb + 1;
dz_ext0 = dz_ext1 = dz_ext2 = dz0 - (T)1.0;
}
if (c != 0x08) {
wsv_ext0 = wsv_ext1 = wsb;
wsv_ext2 = wsb - 1;
dw_ext0 = dw_ext1 = dw0;
dw_ext2 = dw0 + (T)1.0;
}
else {
wsv_ext0 = wsv_ext1 = wsv_ext2 = wsb + 1;
dw_ext0 = dw_ext1 = dw_ext2 = dw0 - (T)1.0;
}
}
else {
// (0,0,0,0) is not one of the closest two pentachoron vertices.
// The three extra vertices are determined by the closest two.
OSN_BYTE c = (aPoint | bPoint);
if (!(c & 0x01)) {
xsv_ext0 = xsv_ext2 = xsb;
xsv_ext1 = xsb - 1;
dx_ext0 = dx0 - (SQUISH_CONSTANT * (T)2.0);
dx_ext1 = dx0 + (T)1.0 - SQUISH_CONSTANT;
dx_ext2 = dx0 - SQUISH_CONSTANT;
}
else {
xsv_ext0 = xsv_ext1 = xsv_ext2 = xsb + 1;
dx_ext0 = dx0 - (T)1.0 - (SQUISH_CONSTANT * (T)2.0);
dx_ext1 = dx_ext2 = dx0 - (T)1.0 - SQUISH_CONSTANT;
}
if (!(c & 0x02)) {
ysv_ext0 = ysv_ext1 = ysv_ext2 = ysb;
dy_ext0 = dy0 - (SQUISH_CONSTANT * (T)2.0);
dy_ext1 = dy_ext2 = dy0 - SQUISH_CONSTANT;
if (c & 0x01) {
ysv_ext1 -= 1;
dy_ext1 += (T)1.0;
}
else {
ysv_ext2 -= 1;
dy_ext2 += (T)1.0;
}
}
else {
ysv_ext0 = ysv_ext1 = ysv_ext2 = ysb + 1;
dy_ext0 = dy0 - (T)1.0 - (SQUISH_CONSTANT * (T)2.0);
dy_ext1 = dy_ext2 = dy0 - (T)1.0 - SQUISH_CONSTANT;
}
if (!(c & 0x04)) {
zsv_ext0 = zsv_ext1 = zsv_ext2 = zsb;
dz_ext0 = dz0 - (SQUISH_CONSTANT * (T)2.0);
dz_ext1 = dz_ext2 = dz0 - SQUISH_CONSTANT;
if (c & 0x03) {
zsv_ext1 -= 1;
dz_ext1 += (T)1.0;
}
else {
zsv_ext2 -= 1;
dz_ext2 += (T)1.0;
}
}
else {
zsv_ext0 = zsv_ext1 = zsv_ext2 = zsb + 1;
dz_ext0 = dz0 - (T)1.0 - (SQUISH_CONSTANT * (T)2.0);
dz_ext1 = dz_ext2 = dz0 - (T)1.0 - SQUISH_CONSTANT;
}
if (!(c & 0x08)) {
wsv_ext0 = wsv_ext1 = wsb;
wsv_ext2 = wsb - 1;
dw_ext0 = dw0 - (SQUISH_CONSTANT * (T)2.0);
dw_ext1 = dw0 - SQUISH_CONSTANT;
dw_ext2 = dw0 + (T)1.0 - SQUISH_CONSTANT;
}
else {
wsv_ext0 = wsv_ext1 = wsv_ext2 = wsb + 1;
dw_ext0 = dw0 - (T)1.0 - (SQUISH_CONSTANT * (T)2.0);
dw_ext1 = dw_ext2 = dw0 - (T)1.0 - SQUISH_CONSTANT;
}
}
// Contribution (0,0,0,0).
{
T attn = pow2(dx0) + pow2(dy0) + pow2(dz0) + pow2(dw0);
value = pow4(std::max((T)2.0 - attn, (T)0.0)) * extrapolate(xsb, ysb, zsb, wsb, dx0, dy0, dz0, dw0);
}
// Contribution (1,0,0,0).
T dx1 = dx0 - (T)1.0 - SQUISH_CONSTANT;
T dy1 = dy0 - SQUISH_CONSTANT;
T dz1 = dz0 - SQUISH_CONSTANT;
T dw1 = dw0 - SQUISH_CONSTANT;
{
T attn = pow2(dx1) + pow2(dy1) + pow2(dz1) + pow2(dw1);
value += pow4(std::max((T)2.0 - attn, (T)0.0)) * extrapolate(xsb + 1, ysb, zsb, wsb, dx1, dy1, dz1, dw1);
}
// Contribution (0,1,0,0).
T dx2 = dx0 - SQUISH_CONSTANT;
T dy2 = dy0 - (T)1.0 - SQUISH_CONSTANT;
T dz2 = dz1;
T dw2 = dw1;
{
T attn = pow2(dx2) + pow2(dy2) + pow2(dz2) + pow2(dw2);
value += pow4(std::max((T)2.0 - attn, (T)0.0)) * extrapolate(xsb, ysb + 1, zsb, wsb, dx2, dy2, dz2, dw2);
}
// Contribution (0,0,1,0).
{
T dx3 = dx2;
T dy3 = dy1;
T dz3 = dz0 - (T)1.0 - SQUISH_CONSTANT;
T dw3 = dw1;
T attn = pow2(dx3) + pow2(dy3) + pow2(dz3) + pow2(dw3);
value += pow4(std::max((T)2.0 - attn, (T)0.0)) * extrapolate(xsb, ysb, zsb + 1, wsb, dx3, dy3, dz3, dw3);
}
// Contribution (0,0,0,1).
{
T dx4 = dx2;
T dy4 = dy1;
T dz4 = dz1;
T dw4 = dw0 - (T)1.0 - SQUISH_CONSTANT;
T attn = pow2(dx4) + pow2(dy4) + pow2(dz4) + pow2(dw4);
value += pow4(std::max((T)2.0 - attn, (T)0.0)) * extrapolate(xsb, ysb, zsb, wsb + 1, dx4, dy4, dz4, dw4);
}
}
else if (inSum >= 3.0) {
// 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.
OSN_BYTE aPoint = 0x0E;
T aScore = xins;
OSN_BYTE bPoint = 0x0D;
T bScore = yins;
if (aScore <= bScore && zins < bScore) {
bPoint = 0x0B;
bScore = zins;
}
else if (aScore > bScore && zins < aScore) {
aPoint = 0x0B;
aScore = zins;
}
if (aScore <= bScore && wins < bScore) {
bPoint = 0x07;
bScore = wins;
}
else if (aScore > bScore && wins < aScore) {
aPoint = 0x07;
aScore = wins;
}
// 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).
T uins = 4.0 - inSum;
if (uins < aScore || uins < bScore) {
// (1,1,1,1) is one of the closest two pentachoron vertices.
// The other closest vertex is the closest out of A and B.
OSN_BYTE c = (bScore < aScore ? bPoint : aPoint);
if (c & 0x01) {
xsv_ext0 = xsb + 2;
xsv_ext1 = xsv_ext2 = xsb + 1;
dx_ext0 = dx0 - (T)2.0 - (SQUISH_CONSTANT * 4);
dx_ext1 = dx_ext2 = dx0 - (T)1.0 - (SQUISH_CONSTANT * 4);
}
else {
xsv_ext0 = xsv_ext1 = xsv_ext2 = xsb;
dx_ext0 = dx_ext1 = dx_ext2 = dx0 - (SQUISH_CONSTANT * 4);
}
if (c & 0x02) {
ysv_ext0 = ysv_ext1 = ysv_ext2 = ysb + 1;
dy_ext0 = dy_ext1 = dy_ext2 = dy0 - (T)1.0 - (SQUISH_CONSTANT * 4);
if (c & 0x01) {
ysv_ext1 += 1;
dy_ext1 -= (T)1.0;
}
else {
ysv_ext0 += 1;
dy_ext0 -= (T)1.0;
}
}
else {
ysv_ext0 = ysv_ext1 = ysv_ext2 = ysb;
dy_ext0 = dy_ext1 = dy_ext2 = dy0 - (SQUISH_CONSTANT * 4);
}
if (c & 0x04) {
zsv_ext0 = zsv_ext1 = zsv_ext2 = zsb + 1;
dz_ext0 = dz_ext1 = dz_ext2 = dz0 - (T)1.0 - (SQUISH_CONSTANT * 4);
if ((c & 0x03) != 0x03) {
if (!(c & 0x03)) {
zsv_ext0 += 1;
dz_ext0 -= (T)1.0;
}
else {
zsv_ext1 += 1;
dz_ext1 -= (T)1.0;
}
}
else {
zsv_ext2 += 1;
dz_ext2 -= (T)1.0;
}
}
else {
zsv_ext0 = zsv_ext1 = zsv_ext2 = zsb;
dz_ext0 = dz_ext1 = dz_ext2 = dz0 - (SQUISH_CONSTANT * 4);
}
if (c & 0x08) {
wsv_ext0 = wsv_ext1 = wsb + 1;
wsv_ext2 = wsb + 2;
dw_ext0 = dw_ext1 = dw0 - (T)1.0 - (SQUISH_CONSTANT * 4);
dw_ext2 = dw0 - (T)2.0 - (SQUISH_CONSTANT * 4);
}
else {
wsv_ext0 = wsv_ext1 = wsv_ext2 = wsb;
dw_ext0 = dw_ext1 = dw_ext2 = dw0 - (SQUISH_CONSTANT * 4);
}
}
else {
// (1,1,1,1) is not one of the closest two pentachoron vertices.
OSN_BYTE c = aPoint & bPoint;
if (c & 0x01) {
xsv_ext0 = xsv_ext2 = xsb + 1;
xsv_ext1 = xsb + 2;
dx_ext0 = dx0 - (T)1.0 - (SQUISH_CONSTANT * (T)2.0);
dx_ext1 = dx0 - (T)2.0 - (SQUISH_CONSTANT * (T)3.0);
dx_ext2 = dx0 - (T)1.0 - (SQUISH_CONSTANT * (T)3.0);
}
else {
xsv_ext0 = xsv_ext1 = xsv_ext2 = xsb;
dx_ext0 = dx0 - (SQUISH_CONSTANT * (T)2.0);
dx_ext1 = dx_ext2 = dx0 - (SQUISH_CONSTANT * (T)3.0);
}
if (c & 0x02) {
ysv_ext0 = ysv_ext1 = ysv_ext2 = ysb + 1;
dy_ext0 = dy0 - (T)1.0 - (SQUISH_CONSTANT * (T)2.0);
dy_ext1 = dy_ext2 = dy0 - (T)1.0 - (SQUISH_CONSTANT * (T)3.0);
if (c & 0x01) {
ysv_ext2 += 1;
dy_ext2 -= (T)1.0;
}
else {
ysv_ext1 += 1;
dy_ext1 -= (T)1.0;
}
}
else {
ysv_ext0 = ysv_ext1 = ysv_ext2 = ysb;
dy_ext0 = dy0 - (SQUISH_CONSTANT * (T)2.0);
dy_ext1 = dy_ext2 = dy0 - (SQUISH_CONSTANT * (T)3.0);
}
if (c & 0x04) {
zsv_ext0 = zsv_ext1 = zsv_ext2 = zsb + 1;
dz_ext0 = dz0 - (T)1.0 - (SQUISH_CONSTANT * (T)2.0);
dz_ext1 = dz_ext2 = dz0 - (T)1.0 - (SQUISH_CONSTANT * (T)3.0);
if (c & 0x03) {
zsv_ext2 += 1;
dz_ext2 -= (T)1.0;
}
else {
zsv_ext1 += 1;
dz_ext1 -= (T)1.0;
}
}
else {
zsv_ext0 = zsv_ext1 = zsv_ext2 = zsb;
dz_ext0 = dz0 - (SQUISH_CONSTANT * (T)2.0);
dz_ext1 = dz_ext2 = dz0 - (SQUISH_CONSTANT * (T)3.0);
}
if (c & 0x08) {
wsv_ext0 = wsv_ext1 = wsb + 1;
wsv_ext2 = wsb + 2;
dw_ext0 = dw0 - (T)1.0 - (SQUISH_CONSTANT * (T)2.0);
dw_ext1 = dw0 - (T)1.0 - (SQUISH_CONSTANT * (T)3.0);
dw_ext2 = dw0 - (T)2.0 - (SQUISH_CONSTANT * (T)3.0);
}
else {
wsv_ext0 = wsv_ext1 = wsv_ext2 = wsb;
dw_ext0 = dw0 - (SQUISH_CONSTANT * (T)2.0);
dw_ext1 = dw_ext2 = dw0 - (SQUISH_CONSTANT * (T)3.0);
}
}
// Contribution (1,1,1,0).
T dx4 = dx0 - (T)1.0 - (SQUISH_CONSTANT * (T)3.0);
T dy4 = dy0 - (T)1.0 - (SQUISH_CONSTANT * (T)3.0);
T dz4 = dz0 - (T)1.0 - (SQUISH_CONSTANT * (T)3.0);
T dw4 = dw0 - (SQUISH_CONSTANT * (T)3.0);
{
T attn = pow2(dx4) + pow2(dy4) + pow2(dz4) + pow2(dw4);
value = pow4(std::max((T)2.0 - attn, (T)0.0)) * extrapolate(xsb + 1, ysb + 1, zsb + 1, wsb, dx4, dy4, dz4, dw4);
}
// Contribution (1,1,0,1).
T dx3 = dx4;
T dy3 = dy4;
T dz3 = dz0 - (SQUISH_CONSTANT * (T)3.0);
T dw3 = dw0 - (T)1.0 - (SQUISH_CONSTANT * (T)3.0);
{
T attn = pow2(dx3) + pow2(dy3) + pow2(dz3) + pow2(dw3);
value += pow4(std::max((T)2.0 - attn, (T)0.0)) * extrapolate(xsb + 1, ysb + 1, zsb, wsb + 1, dx3, dy3, dz3, dw3);
}
// Contribution (1,0,1,1).
T dx2 = dx4;
T dy2 = dy0 - (SQUISH_CONSTANT * (T)3.0);
T dz2 = dz4;
T dw2 = dw3;
{
T attn = pow2(dx2) + pow2(dy2) + pow2(dz2) + pow2(dw2);
value += pow4(std::max((T)2.0 - attn, (T)0.0)) * extrapolate(xsb + 1, ysb, zsb + 1, wsb + 1, dx2, dy2, dz2, dw2);
}
// Contribution (0,1,1,1).
{
T dx1 = dx0 - (SQUISH_CONSTANT * (T)3.0);
T dy1 = dy4;
T dz1 = dz4;
T dw1 = dw3;
T attn = pow2(dx1) + pow2(dy1) + pow2(dz1) + pow2(dw1);
value += pow4(std::max((T)2.0 - attn, (T)0.0)) * extrapolate(xsb, ysb + 1, zsb + 1, wsb + 1, dx1, dy1, dz1, dw1);
}
// Contribution (1,1,1,1).
{
dx0 = dx0 - (T)1.0 - (SQUISH_CONSTANT * 4);
dy0 = dy0 - (T)1.0 - (SQUISH_CONSTANT * 4);
dz0 = dz0 - (T)1.0 - (SQUISH_CONSTANT * 4);
dw0 = dw0 - (T)1.0 - (SQUISH_CONSTANT * 4);
T attn = pow2(dx0) + pow2(dy0) + pow2(dz0) + pow2(dw0);
value += pow4(std::max((T)2.0 - attn, (T)0.0)) * extrapolate(xsb + 1, ysb + 1, zsb + 1, wsb + 1, dx0, dy0, dz0, dw0);
}
}
else if (inSum <= (T)2.0) {
// Inside the first dispentachoron (rectified 4-simplex).
T aScore;
OSN_BYTE aPoint;
bool aIsBiggerSide = true;
T bScore;
OSN_BYTE bPoint;
bool bIsBiggerSide = true;
// Decide between (1,1,0,0) and (0,0,1,1).
if (xins + yins > zins + wins) {
aPoint = 0x03;
aScore = xins + yins;
}
else {
aPoint = 0x0C;
aScore = zins + wins;
}
// Decide between (1,0,1,0) and (0,1,0,1).
if (xins + zins > yins + wins) {
bPoint = 0x05;
bScore = xins + zins;
}
else {
bPoint = 0x0A;
bScore = yins + wins;
}
// Closer of (1,0,0,1) and (0,1,1,0) will replace the further of A and B, if closer.
if (xins + wins > yins + zins) {
T score = xins + wins;
if (aScore >= bScore && score > bScore) {
bPoint = 0x09;
bScore = score;
}
else if (aScore < bScore && score > aScore) {
aPoint = 0x09;
aScore = score;
}
}
else {
T score = yins + zins;
if (aScore >= bScore && score > bScore) {
bPoint = 0x06;
bScore = score;
}
else if (aScore < bScore && score > aScore) {
aPoint = 0x06;
aScore = score;
}
}
// Decide if (1,0,0,0) is closer.
T p1 = (T)2.0 - inSum + xins;
if (aScore >= bScore && p1 > bScore) {
bPoint = 0x01;
bScore = p1;
bIsBiggerSide = false;
}
else if (aScore < bScore && p1 > aScore) {
aPoint = 0x01;
aScore = p1;
aIsBiggerSide = false;
}
// Decide if (0,1,0,0) is closer.
T p2 = (T)2.0 - inSum + yins;
if (aScore >= bScore && p2 > bScore) {
bPoint = 0x02;
bScore = p2;
bIsBiggerSide = false;
}
else if (aScore < bScore && p2 > aScore) {
aPoint = 0x02;
aScore = p2;
aIsBiggerSide = false;
}
// Decide if (0,0,1,0) is closer.
T p3 = (T)2.0 - inSum + zins;
if (aScore >= bScore && p3 > bScore) {
bPoint = 0x04;
bScore = p3;
bIsBiggerSide = false;
}
else if (aScore < bScore && p3 > aScore) {
aPoint = 0x04;
aScore = p3;
aIsBiggerSide = false;
}
// Decide if (0,0,0,1) is closer.
T p4 = (T)2.0 - inSum + wins;
if (aScore >= bScore && p4 > bScore) {
bPoint = 0x08;
bScore = p4;
bIsBiggerSide = false;
}
else if (aScore < bScore && p4 > aScore) {
aPoint = 0x08;
aScore = p4;
aIsBiggerSide = false;
}
// Where each of the two closest points are determines how the extra three vertices are calculated.
if (aIsBiggerSide == bIsBiggerSide) {
if (aIsBiggerSide) {
// Both closest points are on the bigger side.
OSN_BYTE c1 = aPoint | bPoint;
OSN_BYTE c2 = aPoint & bPoint;
if (!(c1 & 0x01)) {
xsv_ext0 = xsb;
xsv_ext1 = xsb - 1;
dx_ext0 = dx0 - (SQUISH_CONSTANT * (T)3.0);
dx_ext1 = dx0 + (T)1.0 - (SQUISH_CONSTANT * (T)2.0);
}
else {
xsv_ext0 = xsv_ext1 = xsb + 1;
dx_ext0 = dx0 - (T)1.0 - (SQUISH_CONSTANT * (T)3.0);
dx_ext1 = dx0 - (T)1.0 - (SQUISH_CONSTANT * (T)2.0);
}
if (!(c1 & 0x02)) {
ysv_ext0 = ysb;
ysv_ext1 = ysb - 1;
dy_ext0 = dy0 - (SQUISH_CONSTANT * (T)3.0);
dy_ext1 = dy0 + (T)1.0 - (SQUISH_CONSTANT * (T)2.0);
}
else {
ysv_ext0 = ysv_ext1 = ysb + 1;
dy_ext0 = dy0 - (T)1.0 - (SQUISH_CONSTANT * (T)3.0);
dy_ext1 = dy0 - (T)1.0 - (SQUISH_CONSTANT * (T)2.0);
}
if (!(c1 & 0x04)) {
zsv_ext0 = zsb;
zsv_ext1 = zsb - 1;
dz_ext0 = dz0 - (SQUISH_CONSTANT * (T)3.0);
dz_ext1 = dz0 + (T)1.0 - (SQUISH_CONSTANT * (T)2.0);
}
else {
zsv_ext0 = zsv_ext1 = zsb + 1;
dz_ext0 = dz0 - (T)1.0 - (SQUISH_CONSTANT * (T)3.0);
dz_ext1 = dz0 - (T)1.0 - (SQUISH_CONSTANT * (T)2.0);
}
if (!(c1 & 0x08)) {
wsv_ext0 = wsb;
wsv_ext1 = wsb - 1;
dw_ext0 = dw0 - (SQUISH_CONSTANT * (T)3.0);
dw_ext1 = dw0 + (T)1.0 - (SQUISH_CONSTANT * (T)2.0);
}
else {
wsv_ext0 = wsv_ext1 = wsb + 1;
dw_ext0 = dw0 - (T)1.0 - (SQUISH_CONSTANT * (T)3.0);
dw_ext1 = dw0 - (T)1.0 - (SQUISH_CONSTANT * (T)2.0);
}
// 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 - (SQUISH_CONSTANT * (T)2.0);
dy_ext2 = dy0 - (SQUISH_CONSTANT * (T)2.0);
dz_ext2 = dz0 - (SQUISH_CONSTANT * (T)2.0);
dw_ext2 = dw0 - (SQUISH_CONSTANT * (T)2.0);
if (c2 & 0x01) {
xsv_ext2 += 2;
dx_ext2 -= (T)2.0;
}
else if (c2 & 0x02) {
ysv_ext2 += 2;
dy_ext2 -= (T)2.0;
}
else if (c2 & 0x04) {
zsv_ext2 += 2;
dz_ext2 -= (T)2.0;
}
else {
wsv_ext2 += 2;
dw_ext2 -= (T)2.0;
}
}
else {
// Both closest points are 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;
// The other two points are based on the omitted axes.
OSN_BYTE c = aPoint | bPoint;
if (!(c & 0x01)) {
xsv_ext0 = xsb - 1;
xsv_ext1 = xsb;
dx_ext0 = dx0 + (T)1.0 - SQUISH_CONSTANT;
dx_ext1 = dx0 - SQUISH_CONSTANT;
}
else {
xsv_ext0 = xsv_ext1 = xsb + 1;
dx_ext0 = dx_ext1 = dx0 - (T)1.0 - SQUISH_CONSTANT;
}
if (!(c & 0x02)) {
ysv_ext0 = ysv_ext1 = ysb;
dy_ext0 = dy_ext1 = dy0 - SQUISH_CONSTANT;
if (c & 0x01) {
ysv_ext0 -= 1;
dy_ext0 += (T)1.0;
}
else {
ysv_ext1 -= 1;
dy_ext1 += (T)1.0;
}
}
else {
ysv_ext0 = ysv_ext1 = ysb + 1;
dy_ext0 = dy_ext1 = dy0 - (T)1.0 - SQUISH_CONSTANT;
}
if (!(c & 0x04)) {
zsv_ext0 = zsv_ext1 = zsb;
dz_ext0 = dz_ext1 = dz0 - SQUISH_CONSTANT;
if ((c & 0x03) == 0x03)
{
zsv_ext0 -= 1;
dz_ext0 += (T)1.0;
}
else {
zsv_ext1 -= 1;
dz_ext1 += (T)1.0;
}
}
else {
zsv_ext0 = zsv_ext1 = zsb + 1;
dz_ext0 = dz_ext1 = dz0 - (T)1.0 - SQUISH_CONSTANT;
}
if (!(c & 0x08)) {
wsv_ext0 = wsb;
wsv_ext1 = wsb - 1;
dw_ext0 = dw0 - SQUISH_CONSTANT;
dw_ext1 = dw0 + (T)1.0 - SQUISH_CONSTANT;
}
else {
wsv_ext0 = wsv_ext1 = wsb + 1;
dw_ext0 = dw_ext1 = dw0 - (T)1.0 - SQUISH_CONSTANT;
}
}
}
else {
// One point on each side.
OSN_BYTE c1, c2;
if (aIsBiggerSide) {
c1 = aPoint;
c2 = bPoint;
}
else {
c1 = bPoint;
c2 = aPoint;
}
// Two contributions are the bigger-sided point with each 0 replaced with -1.
if (!(c1 & 0x01)) {
xsv_ext0 = xsb - 1;
xsv_ext1 = xsb;
dx_ext0 = dx0 + (T)1.0 - SQUISH_CONSTANT;
dx_ext1 = dx0 - SQUISH_CONSTANT;
}
else {
xsv_ext0 = xsv_ext1 = xsb + 1;
dx_ext0 = dx_ext1 = dx0 - (T)1.0 - SQUISH_CONSTANT;
}
if (!(c1 & 0x02)) {
ysv_ext0 = ysv_ext1 = ysb;
dy_ext0 = dy_ext1 = dy0 - SQUISH_CONSTANT;
if ((c1 & 0x01) == 0x01) {
ysv_ext0 -= 1;
dy_ext0 += (T)1.0;
}
else {
ysv_ext1 -= 1;
dy_ext1 += (T)1.0;
}
}
else {
ysv_ext0 = ysv_ext1 = ysb + 1;
dy_ext0 = dy_ext1 = dy0 - (T)1.0 - SQUISH_CONSTANT;
}
if (!(c1 & 0x04)) {
zsv_ext0 = zsv_ext1 = zsb;
dz_ext0 = dz_ext1 = dz0 - SQUISH_CONSTANT;
if ((c1 & 0x03) == 0x03) {
zsv_ext0 -= 1;
dz_ext0 += (T)1.0;
}
else {
zsv_ext1 -= 1;
dz_ext1 += (T)1.0;
}
}
else {
zsv_ext0 = zsv_ext1 = zsb + 1;
dz_ext0 = dz_ext1 = dz0 - (T)1.0 - SQUISH_CONSTANT;
}
if (!(c1 & 0x08)) {
wsv_ext0 = wsb;
wsv_ext1 = wsb - 1;
dw_ext0 = dw0 - SQUISH_CONSTANT;
dw_ext1 = dw0 + (T)1.0 - SQUISH_CONSTANT;
}
else {
wsv_ext0 = wsv_ext1 = wsb + 1;
dw_ext0 = dw_ext1 = dw0 - (T)1.0 - SQUISH_CONSTANT;
}
// 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 - (SQUISH_CONSTANT * (T)2.0);
dy_ext2 = dy0 - (SQUISH_CONSTANT * (T)2.0);
dz_ext2 = dz0 - (SQUISH_CONSTANT * (T)2.0);
dw_ext2 = dw0 - (SQUISH_CONSTANT * (T)2.0);
if ((c2 & 0x01) != 0) {
xsv_ext2 += 2;
dx_ext2 -= (T)2.0;
}
else if ((c2 & 0x02) != 0) {
ysv_ext2 += 2;
dy_ext2 -= (T)2.0;
}
else if ((c2 & 0x04) != 0) {
zsv_ext2 += 2;
dz_ext2 -= (T)2.0;
}
else {
wsv_ext2 += 2;
dw_ext2 -= (T)2.0;
}
}
//Contribution (1,0,0,0).
T dx1 = dx0 - (T)1.0 - SQUISH_CONSTANT;
T dy1 = dy0 - SQUISH_CONSTANT;
T dz1 = dz0 - SQUISH_CONSTANT;
T dw1 = dw0 - SQUISH_CONSTANT;
{
T attn = pow2(dx1) + pow2(dy1) + pow2(dz1) + pow2(dw1);
value += pow4(std::max((T)2.0 - attn, (T)0.0)) * extrapolate(xsb + 1, ysb, zsb, wsb, dx1, dy1, dz1, dw1);
}
//Contribution (0,1,0,0).
T dx2 = dx0 - SQUISH_CONSTANT;
T dy2 = dy0 - (T)1.0 - SQUISH_CONSTANT;
T dz2 = dz1;
T dw2 = dw1;
{
T attn = pow2(dx2) + pow2(dy2) + pow2(dz2) + pow2(dw2);
value += pow4(std::max((T)2.0 - attn, (T)0.0)) * extrapolate(xsb, ysb + 1, zsb, wsb, dx2, dy2, dz2, dw2);
}
//Contribution (0,0,1,0).
{
T dx3 = dx2;
T dy3 = dy1;
T dz3 = dz0 - (T)1.0 - SQUISH_CONSTANT;
T dw3 = dw1;
T attn = pow2(dx3) + pow2(dy3) + pow2(dz3) + pow2(dw3);
value += pow4(std::max((T)2.0 - attn, (T)0.0)) * extrapolate(xsb, ysb, zsb + 1, wsb, dx3, dy3, dz3, dw3);
}
//Contribution (0,0,0,1).
{
T dx4 = dx2;
T dy4 = dy1;
T dz4 = dz1;
T dw4 = dw0 - (T)1.0 - SQUISH_CONSTANT;
T attn = pow2(dx4) + pow2(dy4) + pow2(dz4) + pow2(dw4);
value += pow4(std::max((T)2.0 - attn, (T)0.0)) * extrapolate(xsb, ysb, zsb, wsb + 1, dx4, dy4, dz4, dw4);
}
//Contribution (1,1,0,0).
{
T dx5 = dx0 - (T)1.0 - (SQUISH_CONSTANT * (T)2.0);
T dy5 = dy0 - (T)1.0 - (SQUISH_CONSTANT * (T)2.0);
T dz5 = dz0 - (SQUISH_CONSTANT * (T)2.0);
T dw5 = dw0 - (SQUISH_CONSTANT * (T)2.0);
T attn = pow2(dx5) + pow2(dy5) + pow2(dz5) + pow2(dw5);
value += pow4(std::max((T)2.0 - attn, (T)0.0)) * extrapolate(xsb + 1, ysb + 1, zsb, wsb, dx5, dy5, dz5, dw5);
}
//Contribution (1,0,1,0).
{
T dx6 = dx0 - (T)1.0 - (SQUISH_CONSTANT * (T)2.0);
T dy6 = dy0 - (SQUISH_CONSTANT * (T)2.0);
T dz6 = dz0 - (T)1.0 - (SQUISH_CONSTANT * (T)2.0);
T dw6 = dw0 - (SQUISH_CONSTANT * (T)2.0);
T attn = pow2(dx6) + pow2(dy6) + pow2(dz6) + pow2(dw6);
value += pow4(std::max((T)2.0 - attn, (T)0.0)) * extrapolate(xsb + 1, ysb, zsb + 1, wsb, dx6, dy6, dz6, dw6);
}
//Contribution (1,0,0,1).
{
T dx7 = dx0 - (T)1.0 - (SQUISH_CONSTANT * (T)2.0);
T dy7 = dy0 - (SQUISH_CONSTANT * (T)2.0);
T dz7 = dz0 - (SQUISH_CONSTANT * (T)2.0);
T dw7 = dw0 - (T)1.0 - (SQUISH_CONSTANT * (T)2.0);
T attn = pow2(dx7) + pow2(dy7) + pow2(dz7) + pow2(dw7);
value += pow4(std::max((T)2.0 - attn, (T)0.0)) * extrapolate(xsb + 1, ysb, zsb, wsb + 1, dx7, dy7, dz7, dw7);
}
// Contribution (0,1,1,0).
{
T dx8 = dx0 - (SQUISH_CONSTANT * (T)2.0);
T dy8 = dy0 - (T)1.0 - (SQUISH_CONSTANT * (T)2.0);
T dz8 = dz0 - (T)1.0 - (SQUISH_CONSTANT * (T)2.0);
T dw8 = dw0 - (SQUISH_CONSTANT * (T)2.0);
T attn = pow2(dx8) + pow2(dy8) + pow2(dz8) + pow2(dw8);
value += pow4(std::max((T)2.0 - attn, (T)0.0)) * extrapolate(xsb, ysb + 1, zsb + 1, wsb, dx8, dy8, dz8, dw8);
}
// Contribution (0,1,0,1).
{
T dx9 = dx0 - (SQUISH_CONSTANT * (T)2.0);
T dy9 = dy0 - (T)1.0 - (SQUISH_CONSTANT * (T)2.0);
T dz9 = dz0 - (SQUISH_CONSTANT * (T)2.0);
T dw9 = dw0 - (T)1.0 - (SQUISH_CONSTANT * (T)2.0);
T attn = pow2(dx9) + pow2(dy9) + pow2(dz9) + pow2(dw9);
value += pow4(std::max((T)2.0 - attn, (T)0.0)) * extrapolate(xsb, ysb + 1, zsb, wsb + 1, dx9, dy9, dz9, dw9);
}
// Contribution (0,0,1,1).
{
T dx10 = dx0 - 2 * SQUISH_CONSTANT;
T dy10 = dy0 - 2 * SQUISH_CONSTANT;
T dz10 = dz0 - (T)1.0 - (SQUISH_CONSTANT * (T)2.0);
T dw10 = dw0 - (T)1.0 - (SQUISH_CONSTANT * (T)2.0);
T attn = pow2(dx10) + pow2(dy10) + pow2(dz10) + pow2(dw10);
value += pow4(std::max((T)2.0 - attn, (T)0.0)) * extrapolate(xsb, ysb, zsb + 1, wsb + 1, dx10, dy10, dz10, dw10);
}
}
else {
// Inside the second dispentachoron (rectified 4-simplex).
OSN_BYTE aPoint, bPoint;
T aScore, bScore;
bool aIsBiggerSide(true), bIsBiggerSide(true);
// Decide between (0,0,1,1) and (1,1,0,0).
if (xins + yins < zins + wins) {
aPoint = 0x0C;
aScore = xins + yins;
}
else {
aPoint = 0x03;
aScore = zins + wins;
}
//Decide between (0,1,0,1) and (1,0,1,0).
if (xins + zins < yins + wins) {
bPoint = 0x0A;
bScore = xins + zins;
}
else {
bPoint = 0x05;
bScore = yins + wins;
}
// The closer of (0,1,1,0) and (1,0,0,1) will replace the further of a and b, if closer.
if (xins + wins < yins + zins) {
T score(xins + wins);
if (aScore <= bScore && score < bScore) {
bPoint = 0x06;
bScore = score;
}
else if (aScore > bScore && score < aScore) {
aPoint = 0x06;
aScore = score;
}
}
else {
T score(yins + zins);
if (aScore <= bScore && score < bScore) {
bPoint = 0x09;
bScore = score;
}
else if (aScore > bScore && score < aScore) {
aPoint = 0x09;
aScore = score;
}
}
// Decide if (0,1,1,1) is closer.
{
T p1 = 3.0 - inSum + xins;
if (aScore <= bScore && p1 < bScore) {
bPoint = 0x0E;
bScore = p1;
bIsBiggerSide = false;
}
else if (aScore > bScore && p1 < aScore) {
aPoint = 0x0E;
aScore = p1;
aIsBiggerSide = false;
}
}
// Decide if (1,0,1,1) is closer.
{
T p2 = 3.0 - inSum + yins;
if (aScore <= bScore && p2 < bScore) {
bPoint = 0x0D;
bScore = p2;
bIsBiggerSide = false;
}
else if (aScore > bScore && p2 < aScore) {
aPoint = 0x0D;
aScore = p2;
aIsBiggerSide = false;
}
}
// Decide if (1,1,0,1) is closer.
{
T p3 = 3.0 - inSum + zins;
if (aScore <= bScore && p3 < bScore) {
bPoint = 0x0B;
bScore = p3;
bIsBiggerSide = false;
}
else if (aScore > bScore && p3 < aScore) {
aPoint = 0x0B;
aScore = p3;
aIsBiggerSide = false;
}
}
// Decide if (1,1,1,0) is closer.
{
T p4 = 3.0 - inSum + wins;
if (aScore <= bScore && p4 < bScore) {
bPoint = 0x07;
bScore = p4;
bIsBiggerSide = false;
}
else if (aScore > bScore && p4 < aScore) {
aPoint = 0x07;
aScore = p4;
aIsBiggerSide = false;
}
}
// Where each of the two closest points are determines how the extra three vertices are calculated.
if (aIsBiggerSide == bIsBiggerSide) {
if (aIsBiggerSide) {
// Both closest points are on the bigger side.
OSN_BYTE c1 = aPoint & bPoint;
OSN_BYTE c2 = 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;
dy_ext0 = dy0 - SQUISH_CONSTANT;
dz_ext0 = dz0 - SQUISH_CONSTANT;
dw_ext0 = dw0 - SQUISH_CONSTANT;
dx_ext1 = dx0 - (SQUISH_CONSTANT * (T)2.0);
dy_ext1 = dy0 - (SQUISH_CONSTANT * (T)2.0);
dz_ext1 = dz0 - (SQUISH_CONSTANT * (T)2.0);
dw_ext1 = dw0 - (SQUISH_CONSTANT * (T)2.0);
if (c1 & 0x01) {
xsv_ext0 += 1;
dx_ext0 -= (T)1.0;
xsv_ext1 += 2;
dx_ext1 -= (T)2.0;
}
else if (c1 & 0x02) {
ysv_ext0 += 1;
dy_ext0 -= (T)1.0;
ysv_ext1 += 2;
dy_ext1 -= (T)2.0;
}
else if (c1 & 0x04) {
zsv_ext0 += 1;
dz_ext0 -= (T)1.0;
zsv_ext1 += 2;
dz_ext1 -= (T)2.0;
}
else {
wsv_ext0 += 1;
dw_ext0 -= (T)1.0;
wsv_ext1 += 2;
dw_ext1 -= (T)2.0;
}
// 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 - (T)1.0 - (SQUISH_CONSTANT * (T)2.0);
dy_ext2 = dy0 - (T)1.0 - (SQUISH_CONSTANT * (T)2.0);
dz_ext2 = dz0 - (T)1.0 - (SQUISH_CONSTANT * (T)2.0);
dw_ext2 = dw0 - (T)1.0 - (SQUISH_CONSTANT * (T)2.0);
if (!(c2 & 0x01)) {
xsv_ext2 -= 2;
dx_ext2 += (T)2.0;
}
else if (!(c2 & 0x02)) {
ysv_ext2 -= 2;
dy_ext2 += (T)2.0;
}
else if (!(c2 & 0x04)) {
zsv_ext2 -= 2;
dz_ext2 += (T)2.0;
}
else {
wsv_ext2 -= 2;
dw_ext2 += (T)2.0;
}
}
else {
// Both closest points are 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 - (T)1.0 - (SQUISH_CONSTANT * 4);
dy_ext2 = dy0 - (T)1.0 - (SQUISH_CONSTANT * 4);
dz_ext2 = dz0 - (T)1.0 - (SQUISH_CONSTANT * 4);
dw_ext2 = dw0 - (T)1.0 - (SQUISH_CONSTANT * 4);
// The other two points are based on the shared axes.
OSN_BYTE c = aPoint & bPoint;
if (c & 0x01) {
xsv_ext0 = xsb + 2;
xsv_ext1 = xsb + 1;
dx_ext0 = dx0 - (T)2.0 - (SQUISH_CONSTANT * (T)3.0);
dx_ext1 = dx0 - (T)1.0 - (SQUISH_CONSTANT * (T)3.0);
}
else {
xsv_ext0 = xsv_ext1 = xsb;
dx_ext0 = dx_ext1 = dx0 - (SQUISH_CONSTANT * (T)3.0);
}
if (c & 0x02) {
ysv_ext0 = ysv_ext1 = ysb + 1;
dy_ext0 = dy_ext1 = dy0 - (T)1.0 - (SQUISH_CONSTANT * (T)3.0);
if (!(c & 0x01)) {
ysv_ext0 += 1;
dy_ext0 -= (T)1.0;
}
else {
ysv_ext1 += 1;
dy_ext1 -= (T)1.0;
}
}
else {
ysv_ext0 = ysv_ext1 = ysb;
dy_ext0 = dy_ext1 = dy0 - (SQUISH_CONSTANT * (T)3.0);
}
if (c & 0x04) {
zsv_ext0 = zsv_ext1 = zsb + 1;
dz_ext0 = dz_ext1 = dz0 - (T)1.0 - (SQUISH_CONSTANT * (T)3.0);
if (!(c & 0x03)) {
zsv_ext0 += 1;
dz_ext0 -= (T)1.0;
}
else {
zsv_ext1 += 1;
dz_ext1 -= (T)1.0;
}
}
else {
zsv_ext0 = zsv_ext1 = zsb;
dz_ext0 = dz_ext1 = dz0 - (SQUISH_CONSTANT * (T)3.0);
}
if (c & 0x08) {
wsv_ext0 = wsb + 1;
wsv_ext1 = wsb + 2;
dw_ext0 = dw0 - (T)1.0 - (SQUISH_CONSTANT * (T)3.0);
dw_ext1 = dw0 - (T)2.0 - (SQUISH_CONSTANT * (T)3.0);
}
else {
wsv_ext0 = wsv_ext1 = wsb;
dw_ext0 = dw_ext1 = dw0 - (SQUISH_CONSTANT * (T)3.0);
}
}
}
else {
// One point on each "side".
OSN_BYTE c1, c2;
if (aIsBiggerSide) {
c1 = aPoint;
c2 = bPoint;
}
else {
c1 = bPoint;
c2 = aPoint;
}
// Two contributions are the bigger-sided point with each 1 replaced with 2.
if (c1 & 0x01) {
xsv_ext0 = xsb + 2;
xsv_ext1 = xsb + 1;
dx_ext0 = dx0 - (T)2.0 - (SQUISH_CONSTANT * (T)3.0);
dx_ext1 = dx0 - (T)1.0 - (SQUISH_CONSTANT * (T)3.0);
}
else {
xsv_ext0 = xsv_ext1 = xsb;
dx_ext0 = dx_ext1 = dx0 - (SQUISH_CONSTANT * (T)3.0);
}
if (c1 & 0x02) {
ysv_ext0 = ysv_ext1 = ysb + 1;
dy_ext0 = dy_ext1 = dy0 - (T)1.0 - (SQUISH_CONSTANT * (T)3.0);
if (!(c1 & 0x01)) {
ysv_ext0 += 1;
dy_ext0 -= (T)1.0;
}
else {
ysv_ext1 += 1;
dy_ext1 -= (T)1.0;
}
}
else {
ysv_ext0 = ysv_ext1 = ysb;
dy_ext0 = dy_ext1 = dy0 - (SQUISH_CONSTANT * (T)3.0);
}
if (c1 & 0x04) {
zsv_ext0 = zsv_ext1 = zsb + 1;
dz_ext0 = dz_ext1 = dz0 - (T)1.0 - (SQUISH_CONSTANT * (T)3.0);
if (!(c1 & 0x03)) {
zsv_ext0 += 1;
dz_ext0 -= (T)1.0;
}
else {
zsv_ext1 += 1;
dz_ext1 -= (T)1.0;
}
}
else {
zsv_ext0 = zsv_ext1 = zsb;
dz_ext0 = dz_ext1 = dz0 - 3 * (SQUISH_CONSTANT * (T)3.0);
}
if (c1 & 0x08) {
wsv_ext0 = wsb + 1;
wsv_ext1 = wsb + 2;
dw_ext0 = dw0 - (T)1.0 - (SQUISH_CONSTANT * (T)3.0);
dw_ext1 = dw0 - (T)2.0 - (SQUISH_CONSTANT * (T)3.0);
}
else {
wsv_ext0 = wsv_ext1 = wsb;
dw_ext0 = dw_ext1 = dw0 - (SQUISH_CONSTANT * (T)3.0);
}
// 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 - (T)1.0 - (SQUISH_CONSTANT * (T)2.0);
dy_ext2 = dy0 - (T)1.0 - (SQUISH_CONSTANT * (T)2.0);
dz_ext2 = dz0 - (T)1.0 - (SQUISH_CONSTANT * (T)2.0);
dw_ext2 = dw0 - (T)1.0 - (SQUISH_CONSTANT * (T)2.0);
if (!(c2 & 0x01)) {
xsv_ext2 -= 2;
dx_ext2 += (T)2.0;
}
else if (!(c2 & 0x02)) {
ysv_ext2 -= 2;
dy_ext2 += (T)2.0;
}
else if (!(c2 & 0x04)) {
zsv_ext2 -= 2;
dz_ext2 += (T)2.0;
}
else {
wsv_ext2 -= 2;
dw_ext2 += (T)2.0;
}
}
// Contribution (1,1,1,0).
T dx4 = dx0 - (T)1.0 - (SQUISH_CONSTANT * (T)3.0);
T dy4 = dy0 - (T)1.0 - (SQUISH_CONSTANT * (T)3.0);
T dz4 = dz0 - (T)1.0 - (SQUISH_CONSTANT * (T)3.0);
T dw4 = dw0 - (SQUISH_CONSTANT * (T)3.0);
{
T attn = pow2(dx4) + pow2(dy4) + pow2(dz4) + pow2(dw4);
value += pow4(std::max((T)2.0 - attn, (T)0.0)) * extrapolate(xsb + 1, ysb + 1, zsb + 1, wsb, dx4, dy4, dz4, dw4);
}
//Contribution (1,1,0,1).
T dx3 = dx4;
T dy3 = dy4;
T dz3 = dz0 - (SQUISH_CONSTANT * (T)3.0);
T dw3 = dw0 - (T)1.0 - (SQUISH_CONSTANT * (T)3.0);
{
T attn = pow2(dx3) + pow2(dy3) + pow2(dz3) + pow2(dw3);
value += pow4(std::max((T)2.0 - attn, (T)0.0)) * extrapolate(xsb + 1, ysb + 1, zsb, wsb + 1, dx3, dy3, dz3, dw3);
}
// Contribution (1,0,1,1).
{
T dx2 = dx4;
T dy2 = dy0 - (SQUISH_CONSTANT * (T)3.0);
T dz2 = dz4;
T dw2 = dw3;
T attn = pow2(dx2) + pow2(dy2) + pow2(dz2) + pow2(dw2);
value += pow4(std::max((T)2.0 - attn, (T)0.0)) * extrapolate(xsb + 1, ysb, zsb + 1, wsb + 1, dx2, dy2, dz2, dw2);
}
// Contribution (0,1,1,1).
{
T dx1 = dx0 - (SQUISH_CONSTANT * (T)3.0);
T dz1 = dz4;
T dy1 = dy4;
T dw1 = dw3;
T attn = pow2(dx1) + pow2(dy1) + pow2(dz1) + pow2(dw1);
value += pow4(std::max((T)2.0 - attn, (T)0.0)) * extrapolate(xsb, ysb + 1, zsb + 1, wsb + 1, dx1, dy1, dz1, dw1);
}
// Contribution (1,1,0,0).
{
T dx5 = dx0 - (T)1.0 - (SQUISH_CONSTANT * (T)2.0);
T dy5 = dy0 - (T)1.0 - (SQUISH_CONSTANT * (T)2.0);
T dz5 = dz0 - (SQUISH_CONSTANT * (T)2.0);
T dw5 = dw0 - (SQUISH_CONSTANT * (T)2.0);
T attn = pow2(dx5) + pow2(dy5) + pow2(dz5) + pow2(dw5);
value += pow4(std::max((T)2.0 - attn, (T)0.0)) * extrapolate(xsb + 1, ysb + 1, zsb, wsb, dx5, dy5, dz5, dw5);
}
// Contribution (1,0,1,0).
{
T dx6 = dx0 - (T)1.0 - (SQUISH_CONSTANT * (T)2.0);
T dy6 = dy0 - (SQUISH_CONSTANT * (T)2.0);
T dz6 = dz0 - (T)1.0 - (SQUISH_CONSTANT * (T)2.0);
T dw6 = dw0 - (SQUISH_CONSTANT * (T)2.0);
T attn = pow2(dx6) + pow2(dy6) + pow2(dz6) + pow2(dw6);
value += pow4(std::max((T)2.0 - attn, (T)0.0)) * extrapolate(xsb + 1, ysb, zsb + 1, wsb, dx6, dy6, dz6, dw6);
}
// Contribution (1,0,0,1).
{
T dx7 = dx0 - (T)1.0 - (SQUISH_CONSTANT * (T)2.0);
T dy7 = dy0 - (SQUISH_CONSTANT * (T)2.0);
T dz7 = dz0 - (SQUISH_CONSTANT * (T)2.0);
T dw7 = dw0 - (T)1.0 - (SQUISH_CONSTANT * (T)2.0);
T attn = pow2(dx7) + pow2(dy7) + pow2(dz7) + pow2(dw7);
value += pow4(std::max((T)2.0 - attn, (T)0.0)) * extrapolate(xsb + 1, ysb, zsb, wsb + 1, dx7, dy7, dz7, dw7);
}
// Contribution (0,1,1,0).
{
T dx8 = dx0 - (SQUISH_CONSTANT * (T)2.0);
T dy8 = dy0 - (T)1.0 - (SQUISH_CONSTANT * (T)2.0);
T dz8 = dz0 - (T)1.0 - (SQUISH_CONSTANT * (T)2.0);
T dw8 = dw0 - (SQUISH_CONSTANT * (T)2.0);
T attn = pow2(dx8) + pow2(dy8) + pow2(dz8) + pow2(dw8);
value += pow4(std::max((T)2.0 - attn, (T)0.0)) * extrapolate(xsb, ysb + 1, zsb + 1, wsb, dx8, dy8, dz8, dw8);
}
// Contribution (0,1,0,1).
{
T dx9 = dx0 - (SQUISH_CONSTANT * (T)2.0);
T dy9 = dy0 - (T)1.0 - (SQUISH_CONSTANT * (T)2.0);
T dz9 = dz0 - (SQUISH_CONSTANT * (T)2.0);
T dw9 = dw0 - (T)1.0 - (SQUISH_CONSTANT * (T)2.0);
T attn = pow2(dx9) + pow2(dy9) + pow2(dz9) + pow2(dw9);
value += pow4(std::max((T)2.0 - attn, (T)0.0)) * extrapolate(xsb, ysb + 1, zsb, wsb + 1, dx9, dy9, dz9, dw9);
}
// Contribution (0,0,1,1).
{
T dx10 = dx0 - (SQUISH_CONSTANT * (T)2.0);
T dy10 = dy0 - (SQUISH_CONSTANT * (T)2.0);
T dz10 = dz0 - (T)1.0 - (SQUISH_CONSTANT * (T)2.0);
T dw10 = dw0 - (T)1.0 - (SQUISH_CONSTANT * (T)2.0);
T attn = pow2(dx10) + pow2(dy10) + pow2(dz10) + pow2(dw10);
value += pow4(std::max((T)2.0 - attn, (T)0.0)) * extrapolate(xsb, ysb, zsb + 1, wsb + 1, dx10, dy10, dz10, dw10);
}
}
// First extra vertex.
{
T attn = pow2(dx_ext0) + pow2(dy_ext0) + pow2(dz_ext0) + pow2(dw_ext0);
value += pow4(std::max((T)2.0 - attn, (T)0.0)) * extrapolate(xsv_ext0, ysv_ext0, zsv_ext0, wsv_ext0, dx_ext0, dy_ext0, dz_ext0, dw_ext0);
}
// Second extra vertex.
{
T attn = pow2(dx_ext1) + pow2(dy_ext1) + pow2(dz_ext1) + pow2(dw_ext1);
value += pow4(std::max((T)2.0 - attn, (T)0.0)) * extrapolate(xsv_ext1, ysv_ext1, zsv_ext1, wsv_ext1, dx_ext1, dy_ext1, dz_ext1, dw_ext1);
}
// Third extra vertex.
{
T attn = pow2(dx_ext2) + pow2(dy_ext2) + pow2(dz_ext2) + pow2(dw_ext2);
value += pow4(std::max((T)2.0 - attn, (T)0.0)) * extrapolate(xsv_ext2, ysv_ext2, zsv_ext2, wsv_ext2, dx_ext2, dy_ext2, dz_ext2, dw_ext2);
}
return (value * NORM_CONSTANT);
}
};
// Array of gradient values for 4D. They approximate the directions to the
// vertices of a disprismatotesseractihexadecachoron from its center, skewed so that the
// tetrahedral and cubic facets can be inscribed in spheres of the same radius.
// Gradient set 2014-10-06.
const int Noise<4>::gradients[] = {
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
};
}
#else
#pragma message("OpenSimplexNoise.hh included multiple times")
#endif