Created
March 3, 2018 21:09
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using System; | |
public abstract class FractalNoise | |
{ | |
public abstract long GetSeed(); | |
public abstract double Eval(double x); | |
public abstract double Eval(double x, double y); | |
public abstract double Eval(double x, double y, double z); | |
public abstract double Eval(double x, double y, double z, double w); | |
public double Eval(double x, int octNum, double frq, double amp) | |
{ | |
var gain = 1.0; | |
var sum = 0.0; | |
for (int i = 0; i < octNum; i++) | |
{ | |
sum += Eval(x * gain / frq) * amp / gain; | |
gain *= 2.0; | |
} | |
return sum; | |
} | |
public double Eval(double x, double y, int octNum, double frq, double amp) | |
{ | |
var gain = 1.0; | |
var sum = 0.0; | |
for (int i = 0; i < octNum; i++) | |
{ | |
sum += Eval(x * gain / frq, y * gain / frq) * amp / gain; | |
gain *= 2.0; | |
} | |
return sum; | |
} | |
public double Eval(double x, double y, double z, int octNum, double frq, double amp) | |
{ | |
var gain = 1.0; | |
var sum = 0.0; | |
for (int i = 0; i < octNum; i++) | |
{ | |
sum += Eval(x * gain / frq, y * gain / frq, z * gain / frq) * amp / gain; | |
gain *= 2.0; | |
} | |
return sum; | |
} | |
public double Eval(double x, double y, double z, double w, int octNum, double frq, double amp) | |
{ | |
var gain = 1.0; | |
var sum = 0.0; | |
for (int i = 0; i < octNum; i++) | |
{ | |
sum += Eval(x * gain / frq, y * gain / frq, z * gain / frq, w * gain / frq) * amp / gain; | |
gain *= 2.0; | |
} | |
return sum; | |
} | |
} | |
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using System; | |
/* | |
* OpenSimplex Noise in Java. | |
* by Kurt Spencer | |
* | |
* Ported to C# By Simon Waite 2016/04/01 | |
* | |
* 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. | |
*/ | |
public class OpenSimplexNoise : FractalNoise | |
{ | |
#region constants | |
private static readonly double STRETCH_CONSTANT_2D = -0.211324865405187; | |
//(1/Math.sqrt(2+1)-1)/2; | |
private static readonly double SQUISH_CONSTANT_2D = 0.366025403784439; | |
//(Math.sqrt(2+1)-1)/2; | |
private static readonly double STRETCH_CONSTANT_3D = -1.0 / 6; | |
//(1/Math.sqrt(3+1)-1)/3; | |
private static readonly double SQUISH_CONSTANT_3D = 1.0 / 3; | |
//(Math.sqrt(3+1)-1)/3; | |
private static readonly double STRETCH_CONSTANT_4D = -0.138196601125011; | |
//(1/Math.sqrt(4+1)-1)/4; | |
private static readonly double SQUISH_CONSTANT_4D = 0.309016994374947; | |
//(Math.sqrt(4+1)-1)/4; | |
private static readonly double NORM_CONSTANT_2D = 47; | |
private static readonly double NORM_CONSTANT_3D = 103; | |
private static readonly double NORM_CONSTANT_4D = 30; | |
private static readonly long DEFAULT_SEED = 0; | |
#endregion | |
#region vars | |
private short[] perm; | |
private short[] permGradIndex3D; | |
#endregion | |
#region ctors | |
public OpenSimplexNoise() | |
{ | |
Init(DEFAULT_SEED); | |
} | |
public OpenSimplexNoise(short[] perm) | |
{ | |
this.perm = perm; | |
permGradIndex3D = new short[256]; | |
for (int i = 0; i < 256; i++) | |
{ | |
//Since 3D has 24 gradients, simple bitmask won't work, so precompute modulo array. | |
permGradIndex3D [i] = (short)((perm [i] % (gradients3D.Length / 3)) * 3); | |
} | |
} | |
//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. | |
public OpenSimplexNoise(long seed) | |
{ | |
Init(seed); | |
savedSeed = seed; | |
} | |
long savedSeed = 0; | |
public override long GetSeed() | |
{ | |
return savedSeed; | |
} | |
private void Init(long seed) | |
{ | |
perm = new short[256]; | |
permGradIndex3D = new short[256]; | |
short[] source = new short[256]; | |
for (short i = 0; i < 256; i++) | |
source [i] = i; | |
seed = seed * 6364136223846793005L + 1442695040888963407L; | |
seed = seed * 6364136223846793005L + 1442695040888963407L; | |
seed = seed * 6364136223846793005L + 1442695040888963407L; | |
for (int i = 255; i >= 0; i--) | |
{ | |
seed = seed * 6364136223846793005L + 1442695040888963407L; | |
int r = (int)((seed + 31) % (i + 1)); | |
if (r < 0) | |
r += (i + 1); | |
perm [i] = source [r]; | |
permGradIndex3D [i] = (short)((perm [i] % (gradients3D.Length / 3)) * 3); | |
source [r] = source [i]; | |
} | |
} | |
#endregion | |
#region public | |
public override double Eval(double x) | |
{ | |
return Eval(x, 0.5); | |
} | |
//2D OpenSimplex Noise. | |
public override double Eval(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 value = 0; | |
//Contribution (1,0) | |
double dx1 = dx0 - 1 - SQUISH_CONSTANT_2D; | |
double dy1 = dy0 - 0 - SQUISH_CONSTANT_2D; | |
double attn1 = 2 - dx1 * dx1 - dy1 * dy1; | |
if (attn1 > 0) | |
{ | |
attn1 *= attn1; | |
value += attn1 * attn1 * extrapolate(xsb + 1, ysb + 0, dx1, dy1); | |
} | |
//Contribution (0,1) | |
double dx2 = dx0 - 0 - SQUISH_CONSTANT_2D; | |
double dy2 = dy0 - 1 - SQUISH_CONSTANT_2D; | |
double attn2 = 2 - dx2 * dx2 - dy2 * dy2; | |
if (attn2 > 0) | |
{ | |
attn2 *= attn2; | |
value += attn2 * attn2 * extrapolate(xsb + 0, ysb + 1, dx2, dy2); | |
} | |
if (inSum <= 1) | |
{ //We're inside the triangle (2-Simplex) at (0,0) | |
double zins = 1 - inSum; | |
if (zins > xins || zins > yins) | |
{ //(0,0) is one of the closest two triangular vertices | |
if (xins > yins) | |
{ | |
xsv_ext = xsb + 1; | |
ysv_ext = ysb - 1; | |
dx_ext = dx0 - 1; | |
dy_ext = dy0 + 1; | |
} else | |
{ | |
xsv_ext = xsb - 1; | |
ysv_ext = ysb + 1; | |
dx_ext = dx0 + 1; | |
dy_ext = dy0 - 1; | |
} | |
} else | |
{ //(1,0) and (0,1) are the closest two vertices. | |
xsv_ext = xsb + 1; | |
ysv_ext = ysb + 1; | |
dx_ext = dx0 - 1 - 2 * SQUISH_CONSTANT_2D; | |
dy_ext = dy0 - 1 - 2 * SQUISH_CONSTANT_2D; | |
} | |
} else | |
{ //We're inside the triangle (2-Simplex) at (1,1) | |
double zins = 2 - inSum; | |
if (zins < xins || zins < yins) | |
{ //(0,0) is one of the closest two triangular vertices | |
if (xins > yins) | |
{ | |
xsv_ext = xsb + 2; | |
ysv_ext = ysb + 0; | |
dx_ext = dx0 - 2 - 2 * 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) | |
double attn0 = 2 - dx0 * dx0 - dy0 * dy0; | |
if (attn0 > 0) | |
{ | |
attn0 *= attn0; | |
value += attn0 * attn0 * extrapolate(xsb, ysb, dx0, dy0); | |
} | |
//Extra Vertex | |
double attn_ext = 2 - dx_ext * dx_ext - dy_ext * dy_ext; | |
if (attn_ext > 0) | |
{ | |
attn_ext *= attn_ext; | |
value += attn_ext * attn_ext * extrapolate(xsv_ext, ysv_ext, dx_ext, dy_ext); | |
} | |
return value / NORM_CONSTANT_2D; | |
} | |
//3D OpenSimplex Noise. | |
public override double Eval(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 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. | |
sbyte aPoint = 0x01; | |
double aScore = xins; | |
sbyte bPoint = 0x02; | |
double bScore = yins; | |
if (aScore >= bScore && zins > bScore) | |
{ | |
bScore = zins; | |
bPoint = 0x04; | |
} else if (aScore < bScore && zins > aScore) | |
{ | |
aScore = zins; | |
aPoint = 0x04; | |
} | |
//Now we determine the two lattice points not part of the tetrahedron that may contribute. | |
//This depends on the closest two tetrahedral vertices, including (0,0,0) | |
double wins = 1 - inSum; | |
if (wins > aScore || wins > bScore) | |
{ //(0,0,0) is one of the closest two tetrahedral vertices. | |
sbyte 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. | |
sbyte c = (sbyte)(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) | |
double attn0 = 2 - dx0 * dx0 - dy0 * dy0 - dz0 * dz0; | |
if (attn0 > 0) | |
{ | |
attn0 *= attn0; | |
value += attn0 * attn0 * extrapolate(xsb + 0, ysb + 0, zsb + 0, dx0, dy0, dz0); | |
} | |
//Contribution (1,0,0) | |
double dx1 = dx0 - 1 - SQUISH_CONSTANT_3D; | |
double dy1 = dy0 - 0 - SQUISH_CONSTANT_3D; | |
double dz1 = dz0 - 0 - SQUISH_CONSTANT_3D; | |
double attn1 = 2 - dx1 * dx1 - dy1 * dy1 - dz1 * dz1; | |
if (attn1 > 0) | |
{ | |
attn1 *= attn1; | |
value += attn1 * attn1 * extrapolate(xsb + 1, ysb + 0, zsb + 0, dx1, dy1, dz1); | |
} | |
//Contribution (0,1,0) | |
double dx2 = dx0 - 0 - SQUISH_CONSTANT_3D; | |
double dy2 = dy0 - 1 - SQUISH_CONSTANT_3D; | |
double dz2 = dz1; | |
double attn2 = 2 - dx2 * dx2 - dy2 * dy2 - dz2 * dz2; | |
if (attn2 > 0) | |
{ | |
attn2 *= attn2; | |
value += attn2 * attn2 * extrapolate(xsb + 0, ysb + 1, zsb + 0, dx2, dy2, dz2); | |
} | |
//Contribution (0,0,1) | |
double dx3 = dx2; | |
double dy3 = dy1; | |
double dz3 = dz0 - 1 - SQUISH_CONSTANT_3D; | |
double attn3 = 2 - dx3 * dx3 - dy3 * dy3 - dz3 * dz3; | |
if (attn3 > 0) | |
{ | |
attn3 *= attn3; | |
value += attn3 * attn3 * extrapolate(xsb + 0, ysb + 0, zsb + 1, dx3, dy3, dz3); | |
} | |
} else if (inSum >= 2) | |
{ //We're inside the tetrahedron (3-Simplex) at (1,1,1) | |
//Determine which two tetrahedral vertices are the closest, out of (1,1,0), (1,0,1), (0,1,1) but not (1,1,1). | |
sbyte aPoint = 0x06; | |
double aScore = xins; | |
sbyte bPoint = 0x05; | |
double bScore = yins; | |
if (aScore <= bScore && zins < bScore) | |
{ | |
bScore = zins; | |
bPoint = 0x03; | |
} else if (aScore > bScore && zins < aScore) | |
{ | |
aScore = zins; | |
aPoint = 0x03; | |
} | |
//Now we determine the two lattice points not part of the tetrahedron that may contribute. | |
//This depends on the closest two tetrahedral vertices, including (1,1,1) | |
double wins = 3 - inSum; | |
if (wins < aScore || wins < bScore) | |
{ //(1,1,1) is one of the closest two tetrahedral vertices. | |
sbyte 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. | |
sbyte c = (sbyte)(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) | |
double dx3 = dx0 - 1 - 2 * SQUISH_CONSTANT_3D; | |
double dy3 = dy0 - 1 - 2 * SQUISH_CONSTANT_3D; | |
double dz3 = dz0 - 0 - 2 * SQUISH_CONSTANT_3D; | |
double attn3 = 2 - dx3 * dx3 - dy3 * dy3 - dz3 * dz3; | |
if (attn3 > 0) | |
{ | |
attn3 *= attn3; | |
value += attn3 * attn3 * extrapolate(xsb + 1, ysb + 1, zsb + 0, dx3, dy3, dz3); | |
} | |
//Contribution (1,0,1) | |
double dx2 = dx3; | |
double dy2 = dy0 - 0 - 2 * SQUISH_CONSTANT_3D; | |
double dz2 = dz0 - 1 - 2 * SQUISH_CONSTANT_3D; | |
double attn2 = 2 - dx2 * dx2 - dy2 * dy2 - dz2 * dz2; | |
if (attn2 > 0) | |
{ | |
attn2 *= attn2; | |
value += attn2 * attn2 * extrapolate(xsb + 1, ysb + 0, zsb + 1, dx2, dy2, dz2); | |
} | |
//Contribution (0,1,1) | |
double dx1 = dx0 - 0 - 2 * SQUISH_CONSTANT_3D; | |
double dy1 = dy3; | |
double dz1 = dz2; | |
double attn1 = 2 - dx1 * dx1 - dy1 * dy1 - dz1 * dz1; | |
if (attn1 > 0) | |
{ | |
attn1 *= attn1; | |
value += attn1 * attn1 * extrapolate(xsb + 0, ysb + 1, zsb + 1, dx1, dy1, dz1); | |
} | |
//Contribution (1,1,1) | |
dx0 = dx0 - 1 - 3 * SQUISH_CONSTANT_3D; | |
dy0 = dy0 - 1 - 3 * SQUISH_CONSTANT_3D; | |
dz0 = dz0 - 1 - 3 * SQUISH_CONSTANT_3D; | |
double attn0 = 2 - dx0 * dx0 - dy0 * dy0 - dz0 * dz0; | |
if (attn0 > 0) | |
{ | |
attn0 *= attn0; | |
value += attn0 * attn0 * extrapolate(xsb + 1, ysb + 1, zsb + 1, dx0, dy0, dz0); | |
} | |
} else | |
{ //We're inside the octahedron (Rectified 3-Simplex) in between. | |
double aScore; | |
sbyte aPoint; | |
bool aIsFurtherSide; | |
double bScore; | |
sbyte bPoint; | |
bool bIsFurtherSide; | |
//Decide between point (0,0,1) and (1,1,0) as closest | |
double p1 = xins + yins; | |
if (p1 > 1) | |
{ | |
aScore = p1 - 1; | |
aPoint = 0x03; | |
aIsFurtherSide = true; | |
} else | |
{ | |
aScore = 1 - p1; | |
aPoint = 0x04; | |
aIsFurtherSide = false; | |
} | |
//Decide between point (0,1,0) and (1,0,1) as closest | |
double p2 = xins + zins; | |
if (p2 > 1) | |
{ | |
bScore = p2 - 1; | |
bPoint = 0x05; | |
bIsFurtherSide = true; | |
} else | |
{ | |
bScore = 1 - p2; | |
bPoint = 0x02; | |
bIsFurtherSide = false; | |
} | |
//The closest out of the two (1,0,0) and (0,1,1) will replace the furthest out of the two decided above, if closer. | |
double p3 = yins + zins; | |
if (p3 > 1) | |
{ | |
double score = p3 - 1; | |
if (aScore <= bScore && aScore < score) | |
{ | |
aScore = score; | |
aPoint = 0x06; | |
aIsFurtherSide = true; | |
} else if (aScore > bScore && bScore < score) | |
{ | |
bScore = score; | |
bPoint = 0x06; | |
bIsFurtherSide = true; | |
} | |
} else | |
{ | |
double score = 1 - p3; | |
if (aScore <= bScore && aScore < score) | |
{ | |
aScore = score; | |
aPoint = 0x01; | |
aIsFurtherSide = false; | |
} else if (aScore > bScore && bScore < score) | |
{ | |
bScore = score; | |
bPoint = 0x01; | |
bIsFurtherSide = false; | |
} | |
} | |
//Where each of the two closest points are determines how the extra two vertices are calculated. | |
if (aIsFurtherSide == bIsFurtherSide) | |
{ | |
if (aIsFurtherSide) | |
{ //Both closest points on (1,1,1) side | |
//One of the two extra points is (1,1,1) | |
dx_ext0 = dx0 - 1 - 3 * 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. | |
sbyte c = (sbyte)(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. | |
sbyte c = (sbyte)(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 | |
sbyte c1, c2; | |
if (aIsFurtherSide) | |
{ | |
c1 = aPoint; | |
c2 = bPoint; | |
} else | |
{ | |
c1 = bPoint; | |
c2 = aPoint; | |
} | |
//One contribution is a permutation of (1,1,-1) | |
if ((c1 & 0x01) == 0) | |
{ | |
dx_ext0 = dx0 + 1 - 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) | |
double dx1 = dx0 - 1 - SQUISH_CONSTANT_3D; | |
double dy1 = dy0 - 0 - SQUISH_CONSTANT_3D; | |
double dz1 = dz0 - 0 - SQUISH_CONSTANT_3D; | |
double attn1 = 2 - dx1 * dx1 - dy1 * dy1 - dz1 * dz1; | |
if (attn1 > 0) | |
{ | |
attn1 *= attn1; | |
value += attn1 * attn1 * extrapolate(xsb + 1, ysb + 0, zsb + 0, dx1, dy1, dz1); | |
} | |
//Contribution (0,1,0) | |
double dx2 = dx0 - 0 - SQUISH_CONSTANT_3D; | |
double dy2 = dy0 - 1 - SQUISH_CONSTANT_3D; | |
double dz2 = dz1; | |
double attn2 = 2 - dx2 * dx2 - dy2 * dy2 - dz2 * dz2; | |
if (attn2 > 0) | |
{ | |
attn2 *= attn2; | |
value += attn2 * attn2 * extrapolate(xsb + 0, ysb + 1, zsb + 0, dx2, dy2, dz2); | |
} | |
//Contribution (0,0,1) | |
double dx3 = dx2; | |
double dy3 = dy1; | |
double dz3 = dz0 - 1 - SQUISH_CONSTANT_3D; | |
double attn3 = 2 - dx3 * dx3 - dy3 * dy3 - dz3 * dz3; | |
if (attn3 > 0) | |
{ | |
attn3 *= attn3; | |
value += attn3 * attn3 * extrapolate(xsb + 0, ysb + 0, zsb + 1, dx3, dy3, dz3); | |
} | |
//Contribution (1,1,0) | |
double dx4 = dx0 - 1 - 2 * SQUISH_CONSTANT_3D; | |
double dy4 = dy0 - 1 - 2 * SQUISH_CONSTANT_3D; | |
double dz4 = dz0 - 0 - 2 * SQUISH_CONSTANT_3D; | |
double attn4 = 2 - dx4 * dx4 - dy4 * dy4 - dz4 * dz4; | |
if (attn4 > 0) | |
{ | |
attn4 *= attn4; | |
value += attn4 * attn4 * extrapolate(xsb + 1, ysb + 1, zsb + 0, dx4, dy4, dz4); | |
} | |
//Contribution (1,0,1) | |
double dx5 = dx4; | |
double dy5 = dy0 - 0 - 2 * SQUISH_CONSTANT_3D; | |
double dz5 = dz0 - 1 - 2 * SQUISH_CONSTANT_3D; | |
double attn5 = 2 - dx5 * dx5 - dy5 * dy5 - dz5 * dz5; | |
if (attn5 > 0) | |
{ | |
attn5 *= attn5; | |
value += attn5 * attn5 * extrapolate(xsb + 1, ysb + 0, zsb + 1, dx5, dy5, dz5); | |
} | |
//Contribution (0,1,1) | |
double dx6 = dx0 - 0 - 2 * SQUISH_CONSTANT_3D; | |
double dy6 = dy4; | |
double dz6 = dz5; | |
double attn6 = 2 - dx6 * dx6 - dy6 * dy6 - dz6 * dz6; | |
if (attn6 > 0) | |
{ | |
attn6 *= attn6; | |
value += attn6 * attn6 * extrapolate(xsb + 0, ysb + 1, zsb + 1, dx6, dy6, dz6); | |
} | |
} | |
//First extra vertex | |
double attn_ext0 = 2 - dx_ext0 * dx_ext0 - dy_ext0 * dy_ext0 - dz_ext0 * dz_ext0; | |
if (attn_ext0 > 0) | |
{ | |
attn_ext0 *= attn_ext0; | |
value += attn_ext0 * attn_ext0 * extrapolate(xsv_ext0, ysv_ext0, zsv_ext0, dx_ext0, dy_ext0, dz_ext0); | |
} | |
//Second extra vertex | |
double attn_ext1 = 2 - dx_ext1 * dx_ext1 - dy_ext1 * dy_ext1 - dz_ext1 * dz_ext1; | |
if (attn_ext1 > 0) | |
{ | |
attn_ext1 *= attn_ext1; | |
value += attn_ext1 * attn_ext1 * extrapolate(xsv_ext1, ysv_ext1, zsv_ext1, dx_ext1, dy_ext1, dz_ext1); | |
} | |
return value / NORM_CONSTANT_3D; | |
} | |
//4D OpenSimplex Noise. | |
public override double Eval(double x, double y, double z, double w) | |
{ | |
//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. | |
sbyte aPoint = 0x01; | |
double aScore = xins; | |
sbyte bPoint = 0x02; | |
double bScore = yins; | |
if (aScore >= bScore && zins > bScore) | |
{ | |
bScore = zins; | |
bPoint = 0x04; | |
} else if (aScore < bScore && zins > aScore) | |
{ | |
aScore = zins; | |
aPoint = 0x04; | |
} | |
if (aScore >= bScore && wins > bScore) | |
{ | |
bScore = wins; | |
bPoint = 0x08; | |
} else if (aScore < bScore && wins > aScore) | |
{ | |
aScore = wins; | |
aPoint = 0x08; | |
} | |
//Now we determine the three lattice points not part of the pentachoron that may contribute. | |
//This depends on the closest two pentachoron vertices, including (0,0,0,0) | |
double uins = 1 - inSum; | |
if (uins > aScore || uins > bScore) | |
{ //(0,0,0,0) is one of the closest two pentachoron vertices. | |
sbyte c = (bScore > aScore ? bPoint : aPoint); //Our other closest vertex is the closest out of a and b. | |
if ((c & 0x01) == 0) | |
{ | |
xsv_ext0 = xsb - 1; | |
xsv_ext1 = xsv_ext2 = xsb; | |
dx_ext0 = dx0 + 1; | |
dx_ext1 = dx_ext2 = dx0; | |
} else | |
{ | |
xsv_ext0 = xsv_ext1 = xsv_ext2 = xsb + 1; | |
dx_ext0 = dx_ext1 = dx_ext2 = dx0 - 1; | |
} | |
if ((c & 0x02) == 0) | |
{ | |
ysv_ext0 = ysv_ext1 = ysv_ext2 = ysb; | |
dy_ext0 = dy_ext1 = dy_ext2 = dy0; | |
if ((c & 0x01) == 0x01) | |
{ | |
ysv_ext0 -= 1; | |
dy_ext0 += 1; | |
} else | |
{ | |
ysv_ext1 -= 1; | |
dy_ext1 += 1; | |
} | |
} else | |
{ | |
ysv_ext0 = ysv_ext1 = ysv_ext2 = ysb + 1; | |
dy_ext0 = dy_ext1 = dy_ext2 = dy0 - 1; | |
} | |
if ((c & 0x04) == 0) | |
{ | |
zsv_ext0 = zsv_ext1 = zsv_ext2 = zsb; | |
dz_ext0 = dz_ext1 = dz_ext2 = dz0; | |
if ((c & 0x03) != 0) | |
{ | |
if ((c & 0x03) == 0x03) | |
{ | |
zsv_ext0 -= 1; | |
dz_ext0 += 1; | |
} else | |
{ | |
zsv_ext1 -= 1; | |
dz_ext1 += 1; | |
} | |
} else | |
{ | |
zsv_ext2 -= 1; | |
dz_ext2 += 1; | |
} | |
} else | |
{ | |
zsv_ext0 = zsv_ext1 = zsv_ext2 = zsb + 1; | |
dz_ext0 = dz_ext1 = dz_ext2 = dz0 - 1; | |
} | |
if ((c & 0x08) == 0) | |
{ | |
wsv_ext0 = wsv_ext1 = wsb; | |
wsv_ext2 = wsb - 1; | |
dw_ext0 = dw_ext1 = dw0; | |
dw_ext2 = dw0 + 1; | |
} else | |
{ | |
wsv_ext0 = wsv_ext1 = wsv_ext2 = wsb + 1; | |
dw_ext0 = dw_ext1 = dw_ext2 = dw0 - 1; | |
} | |
} else | |
{ //(0,0,0,0) is not one of the closest two pentachoron vertices. | |
sbyte c = (sbyte)(aPoint | bPoint); //Our three extra vertices are determined by the closest two. | |
if ((c & 0x01) == 0) | |
{ | |
xsv_ext0 = xsv_ext2 = xsb; | |
xsv_ext1 = xsb - 1; | |
dx_ext0 = dx0 - 2 * SQUISH_CONSTANT_4D; | |
dx_ext1 = dx0 + 1 - SQUISH_CONSTANT_4D; | |
dx_ext2 = dx0 - SQUISH_CONSTANT_4D; | |
} else | |
{ | |
xsv_ext0 = xsv_ext1 = xsv_ext2 = xsb + 1; | |
dx_ext0 = dx0 - 1 - 2 * SQUISH_CONSTANT_4D; | |
dx_ext1 = dx_ext2 = dx0 - 1 - SQUISH_CONSTANT_4D; | |
} | |
if ((c & 0x02) == 0) | |
{ | |
ysv_ext0 = ysv_ext1 = ysv_ext2 = ysb; | |
dy_ext0 = dy0 - 2 * SQUISH_CONSTANT_4D; | |
dy_ext1 = dy_ext2 = dy0 - SQUISH_CONSTANT_4D; | |
if ((c & 0x01) == 0x01) | |
{ | |
ysv_ext1 -= 1; | |
dy_ext1 += 1; | |
} else | |
{ | |
ysv_ext2 -= 1; | |
dy_ext2 += 1; | |
} | |
} else | |
{ | |
ysv_ext0 = ysv_ext1 = ysv_ext2 = ysb + 1; | |
dy_ext0 = dy0 - 1 - 2 * SQUISH_CONSTANT_4D; | |
dy_ext1 = dy_ext2 = dy0 - 1 - SQUISH_CONSTANT_4D; | |
} | |
if ((c & 0x04) == 0) | |
{ | |
zsv_ext0 = zsv_ext1 = zsv_ext2 = zsb; | |
dz_ext0 = dz0 - 2 * SQUISH_CONSTANT_4D; | |
dz_ext1 = dz_ext2 = dz0 - SQUISH_CONSTANT_4D; | |
if ((c & 0x03) == 0x03) | |
{ | |
zsv_ext1 -= 1; | |
dz_ext1 += 1; | |
} else | |
{ | |
zsv_ext2 -= 1; | |
dz_ext2 += 1; | |
} | |
} else | |
{ | |
zsv_ext0 = zsv_ext1 = zsv_ext2 = zsb + 1; | |
dz_ext0 = dz0 - 1 - 2 * SQUISH_CONSTANT_4D; | |
dz_ext1 = dz_ext2 = dz0 - 1 - SQUISH_CONSTANT_4D; | |
} | |
if ((c & 0x08) == 0) | |
{ | |
wsv_ext0 = wsv_ext1 = wsb; | |
wsv_ext2 = wsb - 1; | |
dw_ext0 = dw0 - 2 * SQUISH_CONSTANT_4D; | |
dw_ext1 = dw0 - SQUISH_CONSTANT_4D; | |
dw_ext2 = dw0 + 1 - SQUISH_CONSTANT_4D; | |
} else | |
{ | |
wsv_ext0 = wsv_ext1 = wsv_ext2 = wsb + 1; | |
dw_ext0 = dw0 - 1 - 2 * SQUISH_CONSTANT_4D; | |
dw_ext1 = dw_ext2 = dw0 - 1 - SQUISH_CONSTANT_4D; | |
} | |
} | |
//Contribution (0,0,0,0) | |
double attn0 = 2 - dx0 * dx0 - dy0 * dy0 - dz0 * dz0 - dw0 * dw0; | |
if (attn0 > 0) | |
{ | |
attn0 *= attn0; | |
value += attn0 * attn0 * extrapolate(xsb + 0, ysb + 0, zsb + 0, wsb + 0, dx0, dy0, dz0, dw0); | |
} | |
//Contribution (1,0,0,0) | |
double dx1 = dx0 - 1 - SQUISH_CONSTANT_4D; | |
double dy1 = dy0 - 0 - SQUISH_CONSTANT_4D; | |
double dz1 = dz0 - 0 - SQUISH_CONSTANT_4D; | |
double dw1 = dw0 - 0 - SQUISH_CONSTANT_4D; | |
double attn1 = 2 - dx1 * dx1 - dy1 * dy1 - dz1 * dz1 - dw1 * dw1; | |
if (attn1 > 0) | |
{ | |
attn1 *= attn1; | |
value += attn1 * attn1 * extrapolate(xsb + 1, ysb + 0, zsb + 0, wsb + 0, dx1, dy1, dz1, dw1); | |
} | |
//Contribution (0,1,0,0) | |
double dx2 = dx0 - 0 - SQUISH_CONSTANT_4D; | |
double dy2 = dy0 - 1 - SQUISH_CONSTANT_4D; | |
double dz2 = dz1; | |
double dw2 = dw1; | |
double attn2 = 2 - dx2 * dx2 - dy2 * dy2 - dz2 * dz2 - dw2 * dw2; | |
if (attn2 > 0) | |
{ | |
attn2 *= attn2; | |
value += attn2 * attn2 * extrapolate(xsb + 0, ysb + 1, zsb + 0, wsb + 0, dx2, dy2, dz2, dw2); | |
} | |
//Contribution (0,0,1,0) | |
double dx3 = dx2; | |
double dy3 = dy1; | |
double dz3 = dz0 - 1 - SQUISH_CONSTANT_4D; | |
double dw3 = dw1; | |
double attn3 = 2 - dx3 * dx3 - dy3 * dy3 - dz3 * dz3 - dw3 * dw3; | |
if (attn3 > 0) | |
{ | |
attn3 *= attn3; | |
value += attn3 * attn3 * extrapolate(xsb + 0, ysb + 0, zsb + 1, wsb + 0, dx3, dy3, dz3, dw3); | |
} | |
//Contribution (0,0,0,1) | |
double dx4 = dx2; | |
double dy4 = dy1; | |
double dz4 = dz1; | |
double dw4 = dw0 - 1 - SQUISH_CONSTANT_4D; | |
double attn4 = 2 - dx4 * dx4 - dy4 * dy4 - dz4 * dz4 - dw4 * dw4; | |
if (attn4 > 0) | |
{ | |
attn4 *= attn4; | |
value += attn4 * attn4 * extrapolate(xsb + 0, ysb + 0, zsb + 0, wsb + 1, dx4, dy4, dz4, dw4); | |
} | |
} else if (inSum >= 3) | |
{ //We're inside the pentachoron (4-Simplex) at (1,1,1,1) | |
//Determine which two of (1,1,1,0), (1,1,0,1), (1,0,1,1), (0,1,1,1) are closest. | |
sbyte aPoint = 0x0E; | |
double aScore = xins; | |
sbyte bPoint = 0x0D; | |
double bScore = yins; | |
if (aScore <= bScore && zins < bScore) | |
{ | |
bScore = zins; | |
bPoint = 0x0B; | |
} else if (aScore > bScore && zins < aScore) | |
{ | |
aScore = zins; | |
aPoint = 0x0B; | |
} | |
if (aScore <= bScore && wins < bScore) | |
{ | |
bScore = wins; | |
bPoint = 0x07; | |
} else if (aScore > bScore && wins < aScore) | |
{ | |
aScore = wins; | |
aPoint = 0x07; | |
} | |
//Now we determine the three lattice points not part of the pentachoron that may contribute. | |
//This depends on the closest two pentachoron vertices, including (0,0,0,0) | |
double uins = 4 - inSum; | |
if (uins < aScore || uins < bScore) | |
{ //(1,1,1,1) is one of the closest two pentachoron vertices. | |
sbyte c = (bScore < aScore ? bPoint : aPoint); //Our other closest vertex is the closest out of a and b. | |
if ((c & 0x01) != 0) | |
{ | |
xsv_ext0 = xsb + 2; | |
xsv_ext1 = xsv_ext2 = xsb + 1; | |
dx_ext0 = dx0 - 2 - 4 * SQUISH_CONSTANT_4D; | |
dx_ext1 = dx_ext2 = dx0 - 1 - 4 * SQUISH_CONSTANT_4D; | |
} else | |
{ | |
xsv_ext0 = xsv_ext1 = xsv_ext2 = xsb; | |
dx_ext0 = dx_ext1 = dx_ext2 = dx0 - 4 * SQUISH_CONSTANT_4D; | |
} | |
if ((c & 0x02) != 0) | |
{ | |
ysv_ext0 = ysv_ext1 = ysv_ext2 = ysb + 1; | |
dy_ext0 = dy_ext1 = dy_ext2 = dy0 - 1 - 4 * SQUISH_CONSTANT_4D; | |
if ((c & 0x01) != 0) | |
{ | |
ysv_ext1 += 1; | |
dy_ext1 -= 1; | |
} else | |
{ | |
ysv_ext0 += 1; | |
dy_ext0 -= 1; | |
} | |
} else | |
{ | |
ysv_ext0 = ysv_ext1 = ysv_ext2 = ysb; | |
dy_ext0 = dy_ext1 = dy_ext2 = dy0 - 4 * SQUISH_CONSTANT_4D; | |
} | |
if ((c & 0x04) != 0) | |
{ | |
zsv_ext0 = zsv_ext1 = zsv_ext2 = zsb + 1; | |
dz_ext0 = dz_ext1 = dz_ext2 = dz0 - 1 - 4 * SQUISH_CONSTANT_4D; | |
if ((c & 0x03) != 0x03) | |
{ | |
if ((c & 0x03) == 0) | |
{ | |
zsv_ext0 += 1; | |
dz_ext0 -= 1; | |
} else | |
{ | |
zsv_ext1 += 1; | |
dz_ext1 -= 1; | |
} | |
} else | |
{ | |
zsv_ext2 += 1; | |
dz_ext2 -= 1; | |
} | |
} else | |
{ | |
zsv_ext0 = zsv_ext1 = zsv_ext2 = zsb; | |
dz_ext0 = dz_ext1 = dz_ext2 = dz0 - 4 * SQUISH_CONSTANT_4D; | |
} | |
if ((c & 0x08) != 0) | |
{ | |
wsv_ext0 = wsv_ext1 = wsb + 1; | |
wsv_ext2 = wsb + 2; | |
dw_ext0 = dw_ext1 = dw0 - 1 - 4 * SQUISH_CONSTANT_4D; | |
dw_ext2 = dw0 - 2 - 4 * SQUISH_CONSTANT_4D; | |
} else | |
{ | |
wsv_ext0 = wsv_ext1 = wsv_ext2 = wsb; | |
dw_ext0 = dw_ext1 = dw_ext2 = dw0 - 4 * SQUISH_CONSTANT_4D; | |
} | |
} else | |
{ //(1,1,1,1) is not one of the closest two pentachoron vertices. | |
sbyte c = (sbyte)(aPoint & bPoint); //Our three extra vertices are determined by the closest two. | |
if ((c & 0x01) != 0) | |
{ | |
xsv_ext0 = xsv_ext2 = xsb + 1; | |
xsv_ext1 = xsb + 2; | |
dx_ext0 = dx0 - 1 - 2 * SQUISH_CONSTANT_4D; | |
dx_ext1 = dx0 - 2 - 3 * SQUISH_CONSTANT_4D; | |
dx_ext2 = dx0 - 1 - 3 * SQUISH_CONSTANT_4D; | |
} else | |
{ | |
xsv_ext0 = xsv_ext1 = xsv_ext2 = xsb; | |
dx_ext0 = dx0 - 2 * SQUISH_CONSTANT_4D; | |
dx_ext1 = dx_ext2 = dx0 - 3 * SQUISH_CONSTANT_4D; | |
} | |
if ((c & 0x02) != 0) | |
{ | |
ysv_ext0 = ysv_ext1 = ysv_ext2 = ysb + 1; | |
dy_ext0 = dy0 - 1 - 2 * SQUISH_CONSTANT_4D; | |
dy_ext1 = dy_ext2 = dy0 - 1 - 3 * SQUISH_CONSTANT_4D; | |
if ((c & 0x01) != 0) | |
{ | |
ysv_ext2 += 1; | |
dy_ext2 -= 1; | |
} else | |
{ | |
ysv_ext1 += 1; | |
dy_ext1 -= 1; | |
} | |
} else | |
{ | |
ysv_ext0 = ysv_ext1 = ysv_ext2 = ysb; | |
dy_ext0 = dy0 - 2 * SQUISH_CONSTANT_4D; | |
dy_ext1 = dy_ext2 = dy0 - 3 * SQUISH_CONSTANT_4D; | |
} | |
if ((c & 0x04) != 0) | |
{ | |
zsv_ext0 = zsv_ext1 = zsv_ext2 = zsb + 1; | |
dz_ext0 = dz0 - 1 - 2 * SQUISH_CONSTANT_4D; | |
dz_ext1 = dz_ext2 = dz0 - 1 - 3 * SQUISH_CONSTANT_4D; | |
if ((c & 0x03) != 0) | |
{ | |
zsv_ext2 += 1; | |
dz_ext2 -= 1; | |
} else | |
{ | |
zsv_ext1 += 1; | |
dz_ext1 -= 1; | |
} | |
} else | |
{ | |
zsv_ext0 = zsv_ext1 = zsv_ext2 = zsb; | |
dz_ext0 = dz0 - 2 * SQUISH_CONSTANT_4D; | |
dz_ext1 = dz_ext2 = dz0 - 3 * SQUISH_CONSTANT_4D; | |
} | |
if ((c & 0x08) != 0) | |
{ | |
wsv_ext0 = wsv_ext1 = wsb + 1; | |
wsv_ext2 = wsb + 2; | |
dw_ext0 = dw0 - 1 - 2 * SQUISH_CONSTANT_4D; | |
dw_ext1 = dw0 - 1 - 3 * SQUISH_CONSTANT_4D; | |
dw_ext2 = dw0 - 2 - 3 * SQUISH_CONSTANT_4D; | |
} else | |
{ | |
wsv_ext0 = wsv_ext1 = wsv_ext2 = wsb; | |
dw_ext0 = dw0 - 2 * SQUISH_CONSTANT_4D; | |
dw_ext1 = dw_ext2 = dw0 - 3 * SQUISH_CONSTANT_4D; | |
} | |
} | |
//Contribution (1,1,1,0) | |
double dx4 = dx0 - 1 - 3 * SQUISH_CONSTANT_4D; | |
double dy4 = dy0 - 1 - 3 * SQUISH_CONSTANT_4D; | |
double dz4 = dz0 - 1 - 3 * SQUISH_CONSTANT_4D; | |
double dw4 = dw0 - 3 * SQUISH_CONSTANT_4D; | |
double attn4 = 2 - dx4 * dx4 - dy4 * dy4 - dz4 * dz4 - dw4 * dw4; | |
if (attn4 > 0) | |
{ | |
attn4 *= attn4; | |
value += attn4 * attn4 * extrapolate(xsb + 1, ysb + 1, zsb + 1, wsb + 0, dx4, dy4, dz4, dw4); | |
} | |
//Contribution (1,1,0,1) | |
double dx3 = dx4; | |
double dy3 = dy4; | |
double dz3 = dz0 - 3 * SQUISH_CONSTANT_4D; | |
double dw3 = dw0 - 1 - 3 * SQUISH_CONSTANT_4D; | |
double attn3 = 2 - dx3 * dx3 - dy3 * dy3 - dz3 * dz3 - dw3 * dw3; | |
if (attn3 > 0) | |
{ | |
attn3 *= attn3; | |
value += attn3 * attn3 * extrapolate(xsb + 1, ysb + 1, zsb + 0, wsb + 1, dx3, dy3, dz3, dw3); | |
} | |
//Contribution (1,0,1,1) | |
double dx2 = dx4; | |
double dy2 = dy0 - 3 * SQUISH_CONSTANT_4D; | |
double dz2 = dz4; | |
double dw2 = dw3; | |
double attn2 = 2 - dx2 * dx2 - dy2 * dy2 - dz2 * dz2 - dw2 * dw2; | |
if (attn2 > 0) | |
{ | |
attn2 *= attn2; | |
value += attn2 * attn2 * extrapolate(xsb + 1, ysb + 0, zsb + 1, wsb + 1, dx2, dy2, dz2, dw2); | |
} | |
//Contribution (0,1,1,1) | |
double dx1 = dx0 - 3 * SQUISH_CONSTANT_4D; | |
double dz1 = dz4; | |
double dy1 = dy4; | |
double dw1 = dw3; | |
double attn1 = 2 - dx1 * dx1 - dy1 * dy1 - dz1 * dz1 - dw1 * dw1; | |
if (attn1 > 0) | |
{ | |
attn1 *= attn1; | |
value += attn1 * attn1 * extrapolate(xsb + 0, ysb + 1, zsb + 1, wsb + 1, dx1, dy1, dz1, dw1); | |
} | |
//Contribution (1,1,1,1) | |
dx0 = dx0 - 1 - 4 * SQUISH_CONSTANT_4D; | |
dy0 = dy0 - 1 - 4 * SQUISH_CONSTANT_4D; | |
dz0 = dz0 - 1 - 4 * SQUISH_CONSTANT_4D; | |
dw0 = dw0 - 1 - 4 * SQUISH_CONSTANT_4D; | |
double attn0 = 2 - dx0 * dx0 - dy0 * dy0 - dz0 * dz0 - dw0 * dw0; | |
if (attn0 > 0) | |
{ | |
attn0 *= attn0; | |
value += attn0 * attn0 * extrapolate(xsb + 1, ysb + 1, zsb + 1, wsb + 1, dx0, dy0, dz0, dw0); | |
} | |
} else if (inSum <= 2) | |
{ //We're inside the first dispentachoron (Rectified 4-Simplex) | |
double aScore; | |
sbyte aPoint; | |
bool aIsBiggerSide = true; | |
double bScore; | |
sbyte bPoint; | |
bool bIsBiggerSide = true; | |
//Decide between (1,1,0,0) and (0,0,1,1) | |
if (xins + yins > zins + wins) | |
{ | |
aScore = xins + yins; | |
aPoint = 0x03; | |
} else | |
{ | |
aScore = zins + wins; | |
aPoint = 0x0C; | |
} | |
//Decide between (1,0,1,0) and (0,1,0,1) | |
if (xins + zins > yins + wins) | |
{ | |
bScore = xins + zins; | |
bPoint = 0x05; | |
} else | |
{ | |
bScore = yins + wins; | |
bPoint = 0x0A; | |
} | |
//Closer between (1,0,0,1) and (0,1,1,0) will replace the further of a and b, if closer. | |
if (xins + wins > yins + zins) | |
{ | |
double score = xins + wins; | |
if (aScore >= bScore && score > bScore) | |
{ | |
bScore = score; | |
bPoint = 0x09; | |
} else if (aScore < bScore && score > aScore) | |
{ | |
aScore = score; | |
aPoint = 0x09; | |
} | |
} else | |
{ | |
double score = yins + zins; | |
if (aScore >= bScore && score > bScore) | |
{ | |
bScore = score; | |
bPoint = 0x06; | |
} else if (aScore < bScore && score > aScore) | |
{ | |
aScore = score; | |
aPoint = 0x06; | |
} | |
} | |
//Decide if (1,0,0,0) is closer. | |
double p1 = 2 - inSum + xins; | |
if (aScore >= bScore && p1 > bScore) | |
{ | |
bScore = p1; | |
bPoint = 0x01; | |
bIsBiggerSide = false; | |
} else if (aScore < bScore && p1 > aScore) | |
{ | |
aScore = p1; | |
aPoint = 0x01; | |
aIsBiggerSide = false; | |
} | |
//Decide if (0,1,0,0) is closer. | |
double p2 = 2 - inSum + yins; | |
if (aScore >= bScore && p2 > bScore) | |
{ | |
bScore = p2; | |
bPoint = 0x02; | |
bIsBiggerSide = false; | |
} else if (aScore < bScore && p2 > aScore) | |
{ | |
aScore = p2; | |
aPoint = 0x02; | |
aIsBiggerSide = false; | |
} | |
//Decide if (0,0,1,0) is closer. | |
double p3 = 2 - inSum + zins; | |
if (aScore >= bScore && p3 > bScore) | |
{ | |
bScore = p3; | |
bPoint = 0x04; | |
bIsBiggerSide = false; | |
} else if (aScore < bScore && p3 > aScore) | |
{ | |
aScore = p3; | |
aPoint = 0x04; | |
aIsBiggerSide = false; | |
} | |
//Decide if (0,0,0,1) is closer. | |
double p4 = 2 - inSum + wins; | |
if (aScore >= bScore && p4 > bScore) | |
{ | |
bScore = p4; | |
bPoint = 0x08; | |
bIsBiggerSide = false; | |
} else if (aScore < bScore && p4 > aScore) | |
{ | |
aScore = p4; | |
aPoint = 0x08; | |
aIsBiggerSide = false; | |
} | |
//Where each of the two closest points are determines how the extra three vertices are calculated. | |
if (aIsBiggerSide == bIsBiggerSide) | |
{ | |
if (aIsBiggerSide) | |
{ //Both closest points on the bigger side | |
sbyte c1 = (sbyte)(aPoint | bPoint); | |
sbyte c2 = (sbyte)(aPoint & bPoint); | |
if ((c1 & 0x01) == 0) | |
{ | |
xsv_ext0 = xsb; | |
xsv_ext1 = xsb - 1; | |
dx_ext0 = dx0 - 3 * SQUISH_CONSTANT_4D; | |
dx_ext1 = dx0 + 1 - 2 * SQUISH_CONSTANT_4D; | |
} else | |
{ | |
xsv_ext0 = xsv_ext1 = xsb + 1; | |
dx_ext0 = dx0 - 1 - 3 * SQUISH_CONSTANT_4D; | |
dx_ext1 = dx0 - 1 - 2 * SQUISH_CONSTANT_4D; | |
} | |
if ((c1 & 0x02) == 0) | |
{ | |
ysv_ext0 = ysb; | |
ysv_ext1 = ysb - 1; | |
dy_ext0 = dy0 - 3 * SQUISH_CONSTANT_4D; | |
dy_ext1 = dy0 + 1 - 2 * SQUISH_CONSTANT_4D; | |
} else | |
{ | |
ysv_ext0 = ysv_ext1 = ysb + 1; | |
dy_ext0 = dy0 - 1 - 3 * SQUISH_CONSTANT_4D; | |
dy_ext1 = dy0 - 1 - 2 * SQUISH_CONSTANT_4D; | |
} | |
if ((c1 & 0x04) == 0) | |
{ | |
zsv_ext0 = zsb; | |
zsv_ext1 = zsb - 1; | |
dz_ext0 = dz0 - 3 * SQUISH_CONSTANT_4D; | |
dz_ext1 = dz0 + 1 - 2 * SQUISH_CONSTANT_4D; | |
} else | |
{ | |
zsv_ext0 = zsv_ext1 = zsb + 1; | |
dz_ext0 = dz0 - 1 - 3 * SQUISH_CONSTANT_4D; | |
dz_ext1 = dz0 - 1 - 2 * SQUISH_CONSTANT_4D; | |
} | |
if ((c1 & 0x08) == 0) | |
{ | |
wsv_ext0 = wsb; | |
wsv_ext1 = wsb - 1; | |
dw_ext0 = dw0 - 3 * SQUISH_CONSTANT_4D; | |
dw_ext1 = dw0 + 1 - 2 * SQUISH_CONSTANT_4D; | |
} else | |
{ | |
wsv_ext0 = wsv_ext1 = wsb + 1; | |
dw_ext0 = dw0 - 1 - 3 * SQUISH_CONSTANT_4D; | |
dw_ext1 = dw0 - 1 - 2 * SQUISH_CONSTANT_4D; | |
} | |
//One combination is a permutation of (0,0,0,2) based on c2 | |
xsv_ext2 = xsb; | |
ysv_ext2 = ysb; | |
zsv_ext2 = zsb; | |
wsv_ext2 = wsb; | |
dx_ext2 = dx0 - 2 * SQUISH_CONSTANT_4D; | |
dy_ext2 = dy0 - 2 * SQUISH_CONSTANT_4D; | |
dz_ext2 = dz0 - 2 * SQUISH_CONSTANT_4D; | |
dw_ext2 = dw0 - 2 * SQUISH_CONSTANT_4D; | |
if ((c2 & 0x01) != 0) | |
{ | |
xsv_ext2 += 2; | |
dx_ext2 -= 2; | |
} else if ((c2 & 0x02) != 0) | |
{ | |
ysv_ext2 += 2; | |
dy_ext2 -= 2; | |
} else if ((c2 & 0x04) != 0) | |
{ | |
zsv_ext2 += 2; | |
dz_ext2 -= 2; | |
} else | |
{ | |
wsv_ext2 += 2; | |
dw_ext2 -= 2; | |
} | |
} else | |
{ //Both closest points on the smaller side | |
//One of the two extra points is (0,0,0,0) | |
xsv_ext2 = xsb; | |
ysv_ext2 = ysb; | |
zsv_ext2 = zsb; | |
wsv_ext2 = wsb; | |
dx_ext2 = dx0; | |
dy_ext2 = dy0; | |
dz_ext2 = dz0; | |
dw_ext2 = dw0; | |
//Other two points are based on the omitted axes. | |
sbyte c = (sbyte)(aPoint | bPoint); | |
if ((c & 0x01) == 0) | |
{ | |
xsv_ext0 = xsb - 1; | |
xsv_ext1 = xsb; | |
dx_ext0 = dx0 + 1 - SQUISH_CONSTANT_4D; | |
dx_ext1 = dx0 - SQUISH_CONSTANT_4D; | |
} else | |
{ | |
xsv_ext0 = xsv_ext1 = xsb + 1; | |
dx_ext0 = dx_ext1 = dx0 - 1 - SQUISH_CONSTANT_4D; | |
} | |
if ((c & 0x02) == 0) | |
{ | |
ysv_ext0 = ysv_ext1 = ysb; | |
dy_ext0 = dy_ext1 = dy0 - SQUISH_CONSTANT_4D; | |
if ((c & 0x01) == 0x01) | |
{ | |
ysv_ext0 -= 1; | |
dy_ext0 += 1; | |
} else | |
{ | |
ysv_ext1 -= 1; | |
dy_ext1 += 1; | |
} | |
} else | |
{ | |
ysv_ext0 = ysv_ext1 = ysb + 1; | |
dy_ext0 = dy_ext1 = dy0 - 1 - SQUISH_CONSTANT_4D; | |
} | |
if ((c & 0x04) == 0) | |
{ | |
zsv_ext0 = zsv_ext1 = zsb; | |
dz_ext0 = dz_ext1 = dz0 - SQUISH_CONSTANT_4D; | |
if ((c & 0x03) == 0x03) | |
{ | |
zsv_ext0 -= 1; | |
dz_ext0 += 1; | |
} else | |
{ | |
zsv_ext1 -= 1; | |
dz_ext1 += 1; | |
} | |
} else | |
{ | |
zsv_ext0 = zsv_ext1 = zsb + 1; | |
dz_ext0 = dz_ext1 = dz0 - 1 - SQUISH_CONSTANT_4D; | |
} | |
if ((c & 0x08) == 0) | |
{ | |
wsv_ext0 = wsb; | |
wsv_ext1 = wsb - 1; | |
dw_ext0 = dw0 - SQUISH_CONSTANT_4D; | |
dw_ext1 = dw0 + 1 - SQUISH_CONSTANT_4D; | |
} else | |
{ | |
wsv_ext0 = wsv_ext1 = wsb + 1; | |
dw_ext0 = dw_ext1 = dw0 - 1 - SQUISH_CONSTANT_4D; | |
} | |
} | |
} else | |
{ //One point on each "side" | |
sbyte c1, c2; | |
if (aIsBiggerSide) | |
{ | |
c1 = aPoint; | |
c2 = bPoint; | |
} else | |
{ | |
c1 = bPoint; | |
c2 = aPoint; | |
} | |
//Two contributions are the bigger-sided point with each 0 replaced with -1. | |
if ((c1 & 0x01) == 0) | |
{ | |
xsv_ext0 = xsb - 1; | |
xsv_ext1 = xsb; | |
dx_ext0 = dx0 + 1 - SQUISH_CONSTANT_4D; | |
dx_ext1 = dx0 - SQUISH_CONSTANT_4D; | |
} else | |
{ | |
xsv_ext0 = xsv_ext1 = xsb + 1; | |
dx_ext0 = dx_ext1 = dx0 - 1 - SQUISH_CONSTANT_4D; | |
} | |
if ((c1 & 0x02) == 0) | |
{ | |
ysv_ext0 = ysv_ext1 = ysb; | |
dy_ext0 = dy_ext1 = dy0 - SQUISH_CONSTANT_4D; | |
if ((c1 & 0x01) == 0x01) | |
{ | |
ysv_ext0 -= 1; | |
dy_ext0 += 1; | |
} else | |
{ | |
ysv_ext1 -= 1; | |
dy_ext1 += 1; | |
} | |
} else | |
{ | |
ysv_ext0 = ysv_ext1 = ysb + 1; | |
dy_ext0 = dy_ext1 = dy0 - 1 - SQUISH_CONSTANT_4D; | |
} | |
if ((c1 & 0x04) == 0) | |
{ | |
zsv_ext0 = zsv_ext1 = zsb; | |
dz_ext0 = dz_ext1 = dz0 - SQUISH_CONSTANT_4D; | |
if ((c1 & 0x03) == 0x03) | |
{ | |
zsv_ext0 -= 1; | |
dz_ext0 += 1; | |
} else | |
{ | |
zsv_ext1 -= 1; | |
dz_ext1 += 1; | |
} | |
} else | |
{ | |
zsv_ext0 = zsv_ext1 = zsb + 1; | |
dz_ext0 = dz_ext1 = dz0 - 1 - SQUISH_CONSTANT_4D; | |
} | |
if ((c1 & 0x08) == 0) | |
{ | |
wsv_ext0 = wsb; | |
wsv_ext1 = wsb - 1; | |
dw_ext0 = dw0 - SQUISH_CONSTANT_4D; | |
dw_ext1 = dw0 + 1 - SQUISH_CONSTANT_4D; | |
} else | |
{ | |
wsv_ext0 = wsv_ext1 = wsb + 1; | |
dw_ext0 = dw_ext1 = dw0 - 1 - SQUISH_CONSTANT_4D; | |
} | |
//One contribution is a permutation of (0,0,0,2) based on the smaller-sided point | |
xsv_ext2 = xsb; | |
ysv_ext2 = ysb; | |
zsv_ext2 = zsb; | |
wsv_ext2 = wsb; | |
dx_ext2 = dx0 - 2 * SQUISH_CONSTANT_4D; | |
dy_ext2 = dy0 - 2 * SQUISH_CONSTANT_4D; | |
dz_ext2 = dz0 - 2 * SQUISH_CONSTANT_4D; | |
dw_ext2 = dw0 - 2 * SQUISH_CONSTANT_4D; | |
if ((c2 & 0x01) != 0) | |
{ | |
xsv_ext2 += 2; | |
dx_ext2 -= 2; | |
} else if ((c2 & 0x02) != 0) | |
{ | |
ysv_ext2 += 2; | |
dy_ext2 -= 2; | |
} else if ((c2 & 0x04) != 0) | |
{ | |
zsv_ext2 += 2; | |
dz_ext2 -= 2; | |
} else | |
{ | |
wsv_ext2 += 2; | |
dw_ext2 -= 2; | |
} | |
} | |
//Contribution (1,0,0,0) | |
double dx1 = dx0 - 1 - SQUISH_CONSTANT_4D; | |
double dy1 = dy0 - 0 - SQUISH_CONSTANT_4D; | |
double dz1 = dz0 - 0 - SQUISH_CONSTANT_4D; | |
double dw1 = dw0 - 0 - SQUISH_CONSTANT_4D; | |
double attn1 = 2 - dx1 * dx1 - dy1 * dy1 - dz1 * dz1 - dw1 * dw1; | |
if (attn1 > 0) | |
{ | |
attn1 *= attn1; | |
value += attn1 * attn1 * extrapolate(xsb + 1, ysb + 0, zsb + 0, wsb + 0, dx1, dy1, dz1, dw1); | |
} | |
//Contribution (0,1,0,0) | |
double dx2 = dx0 - 0 - SQUISH_CONSTANT_4D; | |
double dy2 = dy0 - 1 - SQUISH_CONSTANT_4D; | |
double dz2 = dz1; | |
double dw2 = dw1; | |
double attn2 = 2 - dx2 * dx2 - dy2 * dy2 - dz2 * dz2 - dw2 * dw2; | |
if (attn2 > 0) | |
{ | |
attn2 *= attn2; | |
value += attn2 * attn2 * extrapolate(xsb + 0, ysb + 1, zsb + 0, wsb + 0, dx2, dy2, dz2, dw2); | |
} | |
//Contribution (0,0,1,0) | |
double dx3 = dx2; | |
double dy3 = dy1; | |
double dz3 = dz0 - 1 - SQUISH_CONSTANT_4D; | |
double dw3 = dw1; | |
double attn3 = 2 - dx3 * dx3 - dy3 * dy3 - dz3 * dz3 - dw3 * dw3; | |
if (attn3 > 0) | |
{ | |
attn3 *= attn3; | |
value += attn3 * attn3 * extrapolate(xsb + 0, ysb + 0, zsb + 1, wsb + 0, dx3, dy3, dz3, dw3); | |
} | |
//Contribution (0,0,0,1) | |
double dx4 = dx2; | |
double dy4 = dy1; | |
double dz4 = dz1; | |
double dw4 = dw0 - 1 - SQUISH_CONSTANT_4D; | |
double attn4 = 2 - dx4 * dx4 - dy4 * dy4 - dz4 * dz4 - dw4 * dw4; | |
if (attn4 > 0) | |
{ | |
attn4 *= attn4; | |
value += attn4 * attn4 * extrapolate(xsb + 0, ysb + 0, zsb + 0, wsb + 1, dx4, dy4, dz4, dw4); | |
} | |
//Contribution (1,1,0,0) | |
double dx5 = dx0 - 1 - 2 * SQUISH_CONSTANT_4D; | |
double dy5 = dy0 - 1 - 2 * SQUISH_CONSTANT_4D; | |
double dz5 = dz0 - 0 - 2 * SQUISH_CONSTANT_4D; | |
double dw5 = dw0 - 0 - 2 * SQUISH_CONSTANT_4D; | |
double attn5 = 2 - dx5 * dx5 - dy5 * dy5 - dz5 * dz5 - dw5 * dw5; | |
if (attn5 > 0) | |
{ | |
attn5 *= attn5; | |
value += attn5 * attn5 * extrapolate(xsb + 1, ysb + 1, zsb + 0, wsb + 0, dx5, dy5, dz5, dw5); | |
} | |
//Contribution (1,0,1,0) | |
double dx6 = dx0 - 1 - 2 * SQUISH_CONSTANT_4D; | |
double dy6 = dy0 - 0 - 2 * SQUISH_CONSTANT_4D; | |
double dz6 = dz0 - 1 - 2 * SQUISH_CONSTANT_4D; | |
double dw6 = dw0 - 0 - 2 * SQUISH_CONSTANT_4D; | |
double attn6 = 2 - dx6 * dx6 - dy6 * dy6 - dz6 * dz6 - dw6 * dw6; | |
if (attn6 > 0) | |
{ | |
attn6 *= attn6; | |
value += attn6 * attn6 * extrapolate(xsb + 1, ysb + 0, zsb + 1, wsb + 0, dx6, dy6, dz6, dw6); | |
} | |
//Contribution (1,0,0,1) | |
double dx7 = dx0 - 1 - 2 * SQUISH_CONSTANT_4D; | |
double dy7 = dy0 - 0 - 2 * SQUISH_CONSTANT_4D; | |
double dz7 = dz0 - 0 - 2 * SQUISH_CONSTANT_4D; | |
double dw7 = dw0 - 1 - 2 * SQUISH_CONSTANT_4D; | |
double attn7 = 2 - dx7 * dx7 - dy7 * dy7 - dz7 * dz7 - dw7 * dw7; | |
if (attn7 > 0) | |
{ | |
attn7 *= attn7; | |
value += attn7 * attn7 * extrapolate(xsb + 1, ysb + 0, zsb + 0, wsb + 1, dx7, dy7, dz7, dw7); | |
} | |
//Contribution (0,1,1,0) | |
double dx8 = dx0 - 0 - 2 * SQUISH_CONSTANT_4D; | |
double dy8 = dy0 - 1 - 2 * SQUISH_CONSTANT_4D; | |
double dz8 = dz0 - 1 - 2 * SQUISH_CONSTANT_4D; | |
double dw8 = dw0 - 0 - 2 * SQUISH_CONSTANT_4D; | |
double attn8 = 2 - dx8 * dx8 - dy8 * dy8 - dz8 * dz8 - dw8 * dw8; | |
if (attn8 > 0) | |
{ | |
attn8 *= attn8; | |
value += attn8 * attn8 * extrapolate(xsb + 0, ysb + 1, zsb + 1, wsb + 0, dx8, dy8, dz8, dw8); | |
} | |
//Contribution (0,1,0,1) | |
double dx9 = dx0 - 0 - 2 * SQUISH_CONSTANT_4D; | |
double dy9 = dy0 - 1 - 2 * SQUISH_CONSTANT_4D; | |
double dz9 = dz0 - 0 - 2 * SQUISH_CONSTANT_4D; | |
double dw9 = dw0 - 1 - 2 * SQUISH_CONSTANT_4D; | |
double attn9 = 2 - dx9 * dx9 - dy9 * dy9 - dz9 * dz9 - dw9 * dw9; | |
if (attn9 > 0) | |
{ | |
attn9 *= attn9; | |
value += attn9 * attn9 * extrapolate(xsb + 0, ysb + 1, zsb + 0, wsb + 1, dx9, dy9, dz9, dw9); | |
} | |
//Contribution (0,0,1,1) | |
double dx10 = dx0 - 0 - 2 * SQUISH_CONSTANT_4D; | |
double dy10 = dy0 - 0 - 2 * SQUISH_CONSTANT_4D; | |
double dz10 = dz0 - 1 - 2 * SQUISH_CONSTANT_4D; | |
double dw10 = dw0 - 1 - 2 * SQUISH_CONSTANT_4D; | |
double attn10 = 2 - dx10 * dx10 - dy10 * dy10 - dz10 * dz10 - dw10 * dw10; | |
if (attn10 > 0) | |
{ | |
attn10 *= attn10; | |
value += attn10 * attn10 * extrapolate(xsb + 0, ysb + 0, zsb + 1, wsb + 1, dx10, dy10, dz10, dw10); | |
} | |
} else | |
{ //We're inside the second dispentachoron (Rectified 4-Simplex) | |
double aScore; | |
sbyte aPoint; | |
bool aIsBiggerSide = true; | |
double bScore; | |
sbyte bPoint; | |
bool bIsBiggerSide = true; | |
//Decide between (0,0,1,1) and (1,1,0,0) | |
if (xins + yins < zins + wins) | |
{ | |
aScore = xins + yins; | |
aPoint = 0x0C; | |
} else | |
{ | |
aScore = zins + wins; | |
aPoint = 0x03; | |
} | |
//Decide between (0,1,0,1) and (1,0,1,0) | |
if (xins + zins < yins + wins) | |
{ | |
bScore = xins + zins; | |
bPoint = 0x0A; | |
} else | |
{ | |
bScore = yins + wins; | |
bPoint = 0x05; | |
} | |
//Closer between (0,1,1,0) and (1,0,0,1) will replace the further of a and b, if closer. | |
if (xins + wins < yins + zins) | |
{ | |
double score = xins + wins; | |
if (aScore <= bScore && score < bScore) | |
{ | |
bScore = score; | |
bPoint = 0x06; | |
} else if (aScore > bScore && score < aScore) | |
{ | |
aScore = score; | |
aPoint = 0x06; | |
} | |
} else | |
{ | |
double score = yins + zins; | |
if (aScore <= bScore && score < bScore) | |
{ | |
bScore = score; | |
bPoint = 0x09; | |
} else if (aScore > bScore && score < aScore) | |
{ | |
aScore = score; | |
aPoint = 0x09; | |
} | |
} | |
//Decide if (0,1,1,1) is closer. | |
double p1 = 3 - inSum + xins; | |
if (aScore <= bScore && p1 < bScore) | |
{ | |
bScore = p1; | |
bPoint = 0x0E; | |
bIsBiggerSide = false; | |
} else if (aScore > bScore && p1 < aScore) | |
{ | |
aScore = p1; | |
aPoint = 0x0E; | |
aIsBiggerSide = false; | |
} | |
//Decide if (1,0,1,1) is closer. | |
double p2 = 3 - inSum + yins; | |
if (aScore <= bScore && p2 < bScore) | |
{ | |
bScore = p2; | |
bPoint = 0x0D; | |
bIsBiggerSide = false; | |
} else if (aScore > bScore && p2 < aScore) | |
{ | |
aScore = p2; | |
aPoint = 0x0D; | |
aIsBiggerSide = false; | |
} | |
//Decide if (1,1,0,1) is closer. | |
double p3 = 3 - inSum + zins; | |
if (aScore <= bScore && p3 < bScore) | |
{ | |
bScore = p3; | |
bPoint = 0x0B; | |
bIsBiggerSide = false; | |
} else if (aScore > bScore && p3 < aScore) | |
{ | |
aScore = p3; | |
aPoint = 0x0B; | |
aIsBiggerSide = false; | |
} | |
//Decide if (1,1,1,0) is closer. | |
double p4 = 3 - inSum + wins; | |
if (aScore <= bScore && p4 < bScore) | |
{ | |
bScore = p4; | |
bPoint = 0x07; | |
bIsBiggerSide = false; | |
} else if (aScore > bScore && p4 < aScore) | |
{ | |
aScore = p4; | |
aPoint = 0x07; | |
aIsBiggerSide = false; | |
} | |
//Where each of the two closest points are determines how the extra three vertices are calculated. | |
if (aIsBiggerSide == bIsBiggerSide) | |
{ | |
if (aIsBiggerSide) | |
{ //Both closest points on the bigger side | |
sbyte c1 = (sbyte)(aPoint & bPoint); | |
sbyte c2 = (sbyte)(aPoint | bPoint); | |
//Two contributions are permutations of (0,0,0,1) and (0,0,0,2) based on c1 | |
xsv_ext0 = xsv_ext1 = xsb; | |
ysv_ext0 = ysv_ext1 = ysb; | |
zsv_ext0 = zsv_ext1 = zsb; | |
wsv_ext0 = wsv_ext1 = wsb; | |
dx_ext0 = dx0 - SQUISH_CONSTANT_4D; | |
dy_ext0 = dy0 - SQUISH_CONSTANT_4D; | |
dz_ext0 = dz0 - SQUISH_CONSTANT_4D; | |
dw_ext0 = dw0 - SQUISH_CONSTANT_4D; | |
dx_ext1 = dx0 - 2 * SQUISH_CONSTANT_4D; | |
dy_ext1 = dy0 - 2 * SQUISH_CONSTANT_4D; | |
dz_ext1 = dz0 - 2 * SQUISH_CONSTANT_4D; | |
dw_ext1 = dw0 - 2 * SQUISH_CONSTANT_4D; | |
if ((c1 & 0x01) != 0) | |
{ | |
xsv_ext0 += 1; | |
dx_ext0 -= 1; | |
xsv_ext1 += 2; | |
dx_ext1 -= 2; | |
} else if ((c1 & 0x02) != 0) | |
{ | |
ysv_ext0 += 1; | |
dy_ext0 -= 1; | |
ysv_ext1 += 2; | |
dy_ext1 -= 2; | |
} else if ((c1 & 0x04) != 0) | |
{ | |
zsv_ext0 += 1; | |
dz_ext0 -= 1; | |
zsv_ext1 += 2; | |
dz_ext1 -= 2; | |
} else | |
{ | |
wsv_ext0 += 1; | |
dw_ext0 -= 1; | |
wsv_ext1 += 2; | |
dw_ext1 -= 2; | |
} | |
//One contribution is a permutation of (1,1,1,-1) based on c2 | |
xsv_ext2 = xsb + 1; | |
ysv_ext2 = ysb + 1; | |
zsv_ext2 = zsb + 1; | |
wsv_ext2 = wsb + 1; | |
dx_ext2 = dx0 - 1 - 2 * SQUISH_CONSTANT_4D; | |
dy_ext2 = dy0 - 1 - 2 * SQUISH_CONSTANT_4D; | |
dz_ext2 = dz0 - 1 - 2 * SQUISH_CONSTANT_4D; | |
dw_ext2 = dw0 - 1 - 2 * SQUISH_CONSTANT_4D; | |
if ((c2 & 0x01) == 0) | |
{ | |
xsv_ext2 -= 2; | |
dx_ext2 += 2; | |
} else if ((c2 & 0x02) == 0) | |
{ | |
ysv_ext2 -= 2; | |
dy_ext2 += 2; | |
} else if ((c2 & 0x04) == 0) | |
{ | |
zsv_ext2 -= 2; | |
dz_ext2 += 2; | |
} else | |
{ | |
wsv_ext2 -= 2; | |
dw_ext2 += 2; | |
} | |
} else | |
{ //Both closest points on the smaller side | |
//One of the two extra points is (1,1,1,1) | |
xsv_ext2 = xsb + 1; | |
ysv_ext2 = ysb + 1; | |
zsv_ext2 = zsb + 1; | |
wsv_ext2 = wsb + 1; | |
dx_ext2 = dx0 - 1 - 4 * SQUISH_CONSTANT_4D; | |
dy_ext2 = dy0 - 1 - 4 * SQUISH_CONSTANT_4D; | |
dz_ext2 = dz0 - 1 - 4 * SQUISH_CONSTANT_4D; | |
dw_ext2 = dw0 - 1 - 4 * SQUISH_CONSTANT_4D; | |
//Other two points are based on the shared axes. | |
sbyte c = (sbyte)(aPoint & bPoint); | |
if ((c & 0x01) != 0) | |
{ | |
xsv_ext0 = xsb + 2; | |
xsv_ext1 = xsb + 1; | |
dx_ext0 = dx0 - 2 - 3 * SQUISH_CONSTANT_4D; | |
dx_ext1 = dx0 - 1 - 3 * SQUISH_CONSTANT_4D; | |
} else | |
{ | |
xsv_ext0 = xsv_ext1 = xsb; | |
dx_ext0 = dx_ext1 = dx0 - 3 * SQUISH_CONSTANT_4D; | |
} | |
if ((c & 0x02) != 0) | |
{ | |
ysv_ext0 = ysv_ext1 = ysb + 1; | |
dy_ext0 = dy_ext1 = dy0 - 1 - 3 * SQUISH_CONSTANT_4D; | |
if ((c & 0x01) == 0) | |
{ | |
ysv_ext0 += 1; | |
dy_ext0 -= 1; | |
} else | |
{ | |
ysv_ext1 += 1; | |
dy_ext1 -= 1; | |
} | |
} else | |
{ | |
ysv_ext0 = ysv_ext1 = ysb; | |
dy_ext0 = dy_ext1 = dy0 - 3 * SQUISH_CONSTANT_4D; | |
} | |
if ((c & 0x04) != 0) | |
{ | |
zsv_ext0 = zsv_ext1 = zsb + 1; | |
dz_ext0 = dz_ext1 = dz0 - 1 - 3 * SQUISH_CONSTANT_4D; | |
if ((c & 0x03) == 0) | |
{ | |
zsv_ext0 += 1; | |
dz_ext0 -= 1; | |
} else | |
{ | |
zsv_ext1 += 1; | |
dz_ext1 -= 1; | |
} | |
} else | |
{ | |
zsv_ext0 = zsv_ext1 = zsb; | |
dz_ext0 = dz_ext1 = dz0 - 3 * SQUISH_CONSTANT_4D; | |
} | |
if ((c & 0x08) != 0) | |
{ | |
wsv_ext0 = wsb + 1; | |
wsv_ext1 = wsb + 2; | |
dw_ext0 = dw0 - 1 - 3 * SQUISH_CONSTANT_4D; | |
dw_ext1 = dw0 - 2 - 3 * SQUISH_CONSTANT_4D; | |
} else | |
{ | |
wsv_ext0 = wsv_ext1 = wsb; | |
dw_ext0 = dw_ext1 = dw0 - 3 * SQUISH_CONSTANT_4D; | |
} | |
} | |
} else | |
{ //One point on each "side" | |
sbyte c1, c2; | |
if (aIsBiggerSide) | |
{ | |
c1 = aPoint; | |
c2 = bPoint; | |
} else | |
{ | |
c1 = bPoint; | |
c2 = aPoint; | |
} | |
//Two contributions are the bigger-sided point with each 1 replaced with 2. | |
if ((c1 & 0x01) != 0) | |
{ | |
xsv_ext0 = xsb + 2; | |
xsv_ext1 = xsb + 1; | |
dx_ext0 = dx0 - 2 - 3 * SQUISH_CONSTANT_4D; | |
dx_ext1 = dx0 - 1 - 3 * SQUISH_CONSTANT_4D; | |
} else | |
{ | |
xsv_ext0 = xsv_ext1 = xsb; | |
dx_ext0 = dx_ext1 = dx0 - 3 * SQUISH_CONSTANT_4D; | |
} | |
if ((c1 & 0x02) != 0) | |
{ | |
ysv_ext0 = ysv_ext1 = ysb + 1; | |
dy_ext0 = dy_ext1 = dy0 - 1 - 3 * SQUISH_CONSTANT_4D; | |
if ((c1 & 0x01) == 0) | |
{ | |
ysv_ext0 += 1; | |
dy_ext0 -= 1; | |
} else | |
{ | |
ysv_ext1 += 1; | |
dy_ext1 -= 1; | |
} | |
} else | |
{ | |
ysv_ext0 = ysv_ext1 = ysb; | |
dy_ext0 = dy_ext1 = dy0 - 3 * SQUISH_CONSTANT_4D; | |
} | |
if ((c1 & 0x04) != 0) | |
{ | |
zsv_ext0 = zsv_ext1 = zsb + 1; | |
dz_ext0 = dz_ext1 = dz0 - 1 - 3 * SQUISH_CONSTANT_4D; | |
if ((c1 & 0x03) == 0) | |
{ | |
zsv_ext0 += 1; | |
dz_ext0 -= 1; | |
} else | |
{ | |
zsv_ext1 += 1; | |
dz_ext1 -= 1; | |
} | |
} else | |
{ | |
zsv_ext0 = zsv_ext1 = zsb; | |
dz_ext0 = dz_ext1 = dz0 - 3 * SQUISH_CONSTANT_4D; | |
} | |
if ((c1 & 0x08) != 0) | |
{ | |
wsv_ext0 = wsb + 1; | |
wsv_ext1 = wsb + 2; | |
dw_ext0 = dw0 - 1 - 3 * SQUISH_CONSTANT_4D; | |
dw_ext1 = dw0 - 2 - 3 * SQUISH_CONSTANT_4D; | |
} else | |
{ | |
wsv_ext0 = wsv_ext1 = wsb; | |
dw_ext0 = dw_ext1 = dw0 - 3 * SQUISH_CONSTANT_4D; | |
} | |
//One contribution is a permutation of (1,1,1,-1) based on the smaller-sided point | |
xsv_ext2 = xsb + 1; | |
ysv_ext2 = ysb + 1; | |
zsv_ext2 = zsb + 1; | |
wsv_ext2 = wsb + 1; | |
dx_ext2 = dx0 - 1 - 2 * SQUISH_CONSTANT_4D; | |
dy_ext2 = dy0 - 1 - 2 * SQUISH_CONSTANT_4D; | |
dz_ext2 = dz0 - 1 - 2 * SQUISH_CONSTANT_4D; | |
dw_ext2 = dw0 - 1 - 2 * SQUISH_CONSTANT_4D; | |
if ((c2 & 0x01) == 0) | |
{ | |
xsv_ext2 -= 2; | |
dx_ext2 += 2; | |
} else if ((c2 & 0x02) == 0) | |
{ | |
ysv_ext2 -= 2; | |
dy_ext2 += 2; | |
} else if ((c2 & 0x04) == 0) | |
{ | |
zsv_ext2 -= 2; | |
dz_ext2 += 2; | |
} else | |
{ | |
wsv_ext2 -= 2; | |
dw_ext2 += 2; | |
} | |
} | |
//Contribution (1,1,1,0) | |
double dx4 = dx0 - 1 - 3 * SQUISH_CONSTANT_4D; | |
double dy4 = dy0 - 1 - 3 * SQUISH_CONSTANT_4D; | |
double dz4 = dz0 - 1 - 3 * SQUISH_CONSTANT_4D; | |
double dw4 = dw0 - 3 * SQUISH_CONSTANT_4D; | |
double attn4 = 2 - dx4 * dx4 - dy4 * dy4 - dz4 * dz4 - dw4 * dw4; | |
if (attn4 > 0) | |
{ | |
attn4 *= attn4; | |
value += attn4 * attn4 * extrapolate(xsb + 1, ysb + 1, zsb + 1, wsb + 0, dx4, dy4, dz4, dw4); | |
} | |
//Contribution (1,1,0,1) | |
double dx3 = dx4; | |
double dy3 = dy4; | |
double dz3 = dz0 - 3 * SQUISH_CONSTANT_4D; | |
double dw3 = dw0 - 1 - 3 * SQUISH_CONSTANT_4D; | |
double attn3 = 2 - dx3 * dx3 - dy3 * dy3 - dz3 * dz3 - dw3 * dw3; | |
if (attn3 > 0) | |
{ | |
attn3 *= attn3; | |
value += attn3 * attn3 * extrapolate(xsb + 1, ysb + 1, zsb + 0, wsb + 1, dx3, dy3, dz3, dw3); | |
} | |
//Contribution (1,0,1,1) | |
double dx2 = dx4; | |
double dy2 = dy0 - 3 * SQUISH_CONSTANT_4D; | |
double dz2 = dz4; | |
double dw2 = dw3; | |
double attn2 = 2 - dx2 * dx2 - dy2 * dy2 - dz2 * dz2 - dw2 * dw2; | |
if (attn2 > 0) | |
{ | |
attn2 *= attn2; | |
value += attn2 * attn2 * extrapolate(xsb + 1, ysb + 0, zsb + 1, wsb + 1, dx2, dy2, dz2, dw2); | |
} | |
//Contribution (0,1,1,1) | |
double dx1 = dx0 - 3 * SQUISH_CONSTANT_4D; | |
double dz1 = dz4; | |
double dy1 = dy4; | |
double dw1 = dw3; | |
double attn1 = 2 - dx1 * dx1 - dy1 * dy1 - dz1 * dz1 - dw1 * dw1; | |
if (attn1 > 0) | |
{ | |
attn1 *= attn1; | |
value += attn1 * attn1 * extrapolate(xsb + 0, ysb + 1, zsb + 1, wsb + 1, dx1, dy1, dz1, dw1); | |
} | |
//Contribution (1,1,0,0) | |
double dx5 = dx0 - 1 - 2 * SQUISH_CONSTANT_4D; | |
double dy5 = dy0 - 1 - 2 * SQUISH_CONSTANT_4D; | |
double dz5 = dz0 - 0 - 2 * SQUISH_CONSTANT_4D; | |
double dw5 = dw0 - 0 - 2 * SQUISH_CONSTANT_4D; | |
double attn5 = 2 - dx5 * dx5 - dy5 * dy5 - dz5 * dz5 - dw5 * dw5; | |
if (attn5 > 0) | |
{ | |
attn5 *= attn5; | |
value += attn5 * attn5 * extrapolate(xsb + 1, ysb + 1, zsb + 0, wsb + 0, dx5, dy5, dz5, dw5); | |
} | |
//Contribution (1,0,1,0) | |
double dx6 = dx0 - 1 - 2 * SQUISH_CONSTANT_4D; | |
double dy6 = dy0 - 0 - 2 * SQUISH_CONSTANT_4D; | |
double dz6 = dz0 - 1 - 2 * SQUISH_CONSTANT_4D; | |
double dw6 = dw0 - 0 - 2 * SQUISH_CONSTANT_4D; | |
double attn6 = 2 - dx6 * dx6 - dy6 * dy6 - dz6 * dz6 - dw6 * dw6; | |
if (attn6 > 0) | |
{ | |
attn6 *= attn6; | |
value += attn6 * attn6 * extrapolate(xsb + 1, ysb + 0, zsb + 1, wsb + 0, dx6, dy6, dz6, dw6); | |
} | |
//Contribution (1,0,0,1) | |
double dx7 = dx0 - 1 - 2 * SQUISH_CONSTANT_4D; | |
double dy7 = dy0 - 0 - 2 * SQUISH_CONSTANT_4D; | |
double dz7 = dz0 - 0 - 2 * SQUISH_CONSTANT_4D; | |
double dw7 = dw0 - 1 - 2 * SQUISH_CONSTANT_4D; | |
double attn7 = 2 - dx7 * dx7 - dy7 * dy7 - dz7 * dz7 - dw7 * dw7; | |
if (attn7 > 0) | |
{ | |
attn7 *= attn7; | |
value += attn7 * attn7 * extrapolate(xsb + 1, ysb + 0, zsb + 0, wsb + 1, dx7, dy7, dz7, dw7); | |
} | |
//Contribution (0,1,1,0) | |
double dx8 = dx0 - 0 - 2 * SQUISH_CONSTANT_4D; | |
double dy8 = dy0 - 1 - 2 * SQUISH_CONSTANT_4D; | |
double dz8 = dz0 - 1 - 2 * SQUISH_CONSTANT_4D; | |
double dw8 = dw0 - 0 - 2 * SQUISH_CONSTANT_4D; | |
double attn8 = 2 - dx8 * dx8 - dy8 * dy8 - dz8 * dz8 - dw8 * dw8; | |
if (attn8 > 0) | |
{ | |
attn8 *= attn8; | |
value += attn8 * attn8 * extrapolate(xsb + 0, ysb + 1, zsb + 1, wsb + 0, dx8, dy8, dz8, dw8); | |
} | |
//Contribution (0,1,0,1) | |
double dx9 = dx0 - 0 - 2 * SQUISH_CONSTANT_4D; | |
double dy9 = dy0 - 1 - 2 * SQUISH_CONSTANT_4D; | |
double dz9 = dz0 - 0 - 2 * SQUISH_CONSTANT_4D; | |
double dw9 = dw0 - 1 - 2 * SQUISH_CONSTANT_4D; | |
double attn9 = 2 - dx9 * dx9 - dy9 * dy9 - dz9 * dz9 - dw9 * dw9; | |
if (attn9 > 0) | |
{ | |
attn9 *= attn9; | |
value += attn9 * attn9 * extrapolate(xsb + 0, ysb + 1, zsb + 0, wsb + 1, dx9, dy9, dz9, dw9); | |
} | |
//Contribution (0,0,1,1) | |
double dx10 = dx0 - 0 - 2 * SQUISH_CONSTANT_4D; | |
double dy10 = dy0 - 0 - 2 * SQUISH_CONSTANT_4D; | |
double dz10 = dz0 - 1 - 2 * SQUISH_CONSTANT_4D; | |
double dw10 = dw0 - 1 - 2 * SQUISH_CONSTANT_4D; | |
double attn10 = 2 - dx10 * dx10 - dy10 * dy10 - dz10 * dz10 - dw10 * dw10; | |
if (attn10 > 0) | |
{ | |
attn10 *= attn10; | |
value += attn10 * attn10 * extrapolate(xsb + 0, ysb + 0, zsb + 1, wsb + 1, dx10, dy10, dz10, dw10); | |
} | |
} | |
//First extra vertex | |
double attn_ext0 = 2 - dx_ext0 * dx_ext0 - dy_ext0 * dy_ext0 - dz_ext0 * dz_ext0 - dw_ext0 * dw_ext0; | |
if (attn_ext0 > 0) | |
{ | |
attn_ext0 *= attn_ext0; | |
value += attn_ext0 * attn_ext0 * extrapolate(xsv_ext0, ysv_ext0, zsv_ext0, wsv_ext0, dx_ext0, dy_ext0, dz_ext0, dw_ext0); | |
} | |
//Second extra vertex | |
double attn_ext1 = 2 - dx_ext1 * dx_ext1 - dy_ext1 * dy_ext1 - dz_ext1 * dz_ext1 - dw_ext1 * dw_ext1; | |
if (attn_ext1 > 0) | |
{ | |
attn_ext1 *= attn_ext1; | |
value += attn_ext1 * attn_ext1 * extrapolate(xsv_ext1, ysv_ext1, zsv_ext1, wsv_ext1, dx_ext1, dy_ext1, dz_ext1, dw_ext1); | |
} | |
//Third extra vertex | |
double attn_ext2 = 2 - dx_ext2 * dx_ext2 - dy_ext2 * dy_ext2 - dz_ext2 * dz_ext2 - dw_ext2 * dw_ext2; | |
if (attn_ext2 > 0) | |
{ | |
attn_ext2 *= attn_ext2; | |
value += attn_ext2 * attn_ext2 * extrapolate(xsv_ext2, ysv_ext2, zsv_ext2, wsv_ext2, dx_ext2, dy_ext2, dz_ext2, dw_ext2); | |
} | |
return value / NORM_CONSTANT_4D; | |
} | |
#endregion | |
#region private | |
private double extrapolate(int xsb, int ysb, double dx, double dy) | |
{ | |
int index = perm [(perm [xsb & 0xFF] + ysb) & 0xFF] & 0x0E; | |
return gradients2D [index] * dx | |
+ gradients2D [index + 1] * dy; | |
} | |
private double extrapolate(int xsb, int ysb, int zsb, double dx, double dy, double dz) | |
{ | |
int index = permGradIndex3D [(perm [(perm [xsb & 0xFF] + ysb) & 0xFF] + zsb) & 0xFF]; | |
return gradients3D [index] * dx | |
+ gradients3D [index + 1] * dy | |
+ gradients3D [index + 2] * dz; | |
} | |
private double extrapolate(int xsb, int ysb, int zsb, int wsb, double dx, double dy, double dz, double dw) | |
{ | |
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; | |
} | |
private static int fastFloor(double x) | |
{ | |
int xi = (int)x; | |
return x < xi ? xi - 1 : xi; | |
} | |
#endregion | |
#region private data | |
//Gradients for 2D. They approximate the directions to the | |
//vertices of an octagon from the center. | |
private static sbyte[] gradients2D = new sbyte[] | |
{ | |
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. | |
private static sbyte[] gradients3D = new sbyte[] | |
{ | |
-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. | |
private static sbyte[] gradients4D = new sbyte[] | |
{ | |
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, | |
}; | |
#endregion | |
} |
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