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wschutzer/OpenSimplexNoise.pde

Created October 26, 2025 17:27
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Parametric curve distortion in CMYK space
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OpenSimplexNoise.pde
// note : if you're on github gist and want to copy paste this code, you can click on the "Raw" button
// and then do Ctrl A, Ctrl C, Ctrl V
// (code below by Kurt Spencer, slightly modified code to run as Processing tab)
// maybe you should rather use this new (improved) version of the noise instead : https://github.com/KdotJPG/OpenSimplex2
/*
* OpenSimplex Noise in Java.
* by Kurt Spencer
*
* 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 {
private static final double STRETCH_CONSTANT_2D = -0.211324865405187; //(1/Math.sqrt(2+1)-1)/2;
private static final double SQUISH_CONSTANT_2D = 0.366025403784439; //(Math.sqrt(2+1)-1)/2;
private static final double STRETCH_CONSTANT_3D = -1.0 / 6; //(1/Math.sqrt(3+1)-1)/3;
private static final double SQUISH_CONSTANT_3D = 1.0 / 3; //(Math.sqrt(3+1)-1)/3;
private static final double STRETCH_CONSTANT_4D = -0.138196601125011; //(1/Math.sqrt(4+1)-1)/4;
private static final double SQUISH_CONSTANT_4D = 0.309016994374947; //(Math.sqrt(4+1)-1)/4;
private static final double NORM_CONSTANT_2D = 47;
private static final double NORM_CONSTANT_3D = 103;
private static final double NORM_CONSTANT_4D = 30;
private static final long DEFAULT_SEED = 0;
private short[] perm;
private short[] permGradIndex3D;
public OpenSimplexNoise() {
this(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) {
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];
}
}
//2D OpenSimplex Noise.
public 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 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.
byte aPoint = 0x01;
double aScore = xins;
byte 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.
byte 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.
byte c = (byte)(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).
byte aPoint = 0x06;
double aScore = xins;
byte 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.
byte 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.
byte c = (byte)(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;
byte aPoint;
boolean aIsFurtherSide;
double bScore;
byte bPoint;
boolean 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.
byte c = (byte)(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.
byte c = (byte)(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
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) == 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 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.
byte aPoint = 0x01;
double aScore = xins;
byte 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.
byte 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.
byte c = (byte)(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.
byte aPoint = 0x0E;
double aScore = xins;
byte 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.
byte 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.
byte c = (byte)(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;
byte aPoint;
boolean aIsBiggerSide = true;
double bScore;
byte bPoint;
boolean 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
byte c1 = (byte)(aPoint | bPoint);
byte c2 = (byte)(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.
byte c = (byte)(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"
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) == 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;
byte aPoint;
boolean aIsBiggerSide = true;
double bScore;
byte bPoint;
boolean 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
byte c1 = (byte)(aPoint & bPoint);
byte c2 = (byte)(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.
byte c = (byte)(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"
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) != 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;
}
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 int fastFloor(double x) {
int xi = (int)x;
return x < xi ? xi - 1 : xi;
}
//Gradients for 2D. They approximate the directions to the
//vertices of an octagon from the center.
private byte[] gradients2D = new byte[] {
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 byte[] gradients3D = new byte[] {
-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 byte[] gradients4D = new byte[] {
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,
};
}
Raw
sketch_251026a_cmyk_knot.pde
/* CMYK Knot Distortion
* ---------------------
* This code draws a parametric curve (a knot) drawn 3 times, one for each
* color C, M, and Y, with a slight different noise-driven distortion for each color.
*
* This work is based on the original cmyk_knot by Dave White (@davebeesandbombs)
* with added improvements.
*
* Copyright (C) 2025 Waldeck Schutzer (@infinitymathart)
*
* This program is free software: you can redistribute it and/or modify
* it under the terms of the GNU General Public License as published by
* the Free Software Foundation, either version 3 of the License, or
* (at your option) any later version.
*
* This program is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
* GNU General Public License for more details.
*
* You should have received a copy of the GNU General Public License
* along with this program. If not, see <https://www.gnu.org/licenses/>.
*/
final boolean recording = true;
final boolean small = true;
final int frameWidth = small ? 800 : (recording ? 2160 : 540);
final float fac = 1.0*frameWidth/540; // Scale reference factor
final float aspect = 1.0; // 1350.0/1080; // 1920.0/1080;
final int frameHeight = int(aspect * frameWidth);
final int duration = 5; //Seconds
final int fps = 30; // Frames Per Second
final float num_frames = fps*duration;
final float numFrames = fps*duration;
// Motion blur:
final int samplesPerFrame = 5;
final float shutterAngle = 0.5;
int[][] result;
float t, c;
PFont courier;
OpenSimplexNoise noise;
float ease(float p) {
return 3*p*p - 2*p*p*p;
}
float ease(float p, float g) {
if (p < 0.5)
return 0.5 * pow(2*p, g);
else
return 1 - 0.5 * pow(2*(1 - p), g);
}
float mn = .5*sqrt(3), ia = atan(sqrt(.5));
void push() {
pushMatrix();
pushStyle();
}
void pop(){
popStyle();
popMatrix();
}
void draw() {
if(!recording){
t = mouseX*1.0/width;
c = mouseY*1.0/height;
if(mousePressed)
println(c);
draw_();
}
else {
for (int i=0; i<width*height; i++)
for (int a=0; a<3; a++)
result[i][a] = 0;
c = 0;
for (int sa=0; sa<samplesPerFrame; sa++) {
t = map(frameCount-1 + sa*shutterAngle/samplesPerFrame, 0, numFrames, 0, 1);
draw_();
loadPixels();
for (int i=0; i<pixels.length; i++) {
result[i][0] += pixels[i] >> 16 & 0xff;
result[i][1] += pixels[i] >> 8 & 0xff;
result[i][2] += pixels[i] & 0xff;
}
}
loadPixels();
for (int i=0; i<pixels.length; i++)
pixels[i] = 0xff << 24 |
int(result[i][0]*1.0/samplesPerFrame) << 16 |
int(result[i][1]*1.0/samplesPerFrame) << 8 |
int(result[i][2]*1.0/samplesPerFrame);
updatePixels();
saveFrame("/tmp/r/frame_####.png");
if (frameCount==numFrames)
exit();
}
}
//////////////////////////////////////////////////////////////////////////////
final int n = int(1200*fac);
final float h = 1e-4;
final float R = 120*fac; // major radius
final float zoom = 0.4f; // global scale on screen
// TODO: Try new parametric curves here!
// Note: parameter q ranges from 0 to PI
PVector s(float q)
{
q*=2; // extend range to 2 PI
float a = 3 + cos(5*q);
float x = a*cos(2*q);
float y = a*sin(2*q);
return new PVector(x,y).mult(R*zoom);
}
// Define the tangent vector to the curve
PVector ts(float q)
{
return s(q+h).sub(s(q-h)).div(h);
}
// Define the normalized tangent vector to the curve
PVector nts(float q)
{
return ts(q).normalize();
}
// Define the normalized normal vector to the curve
PVector nns(float q)
{
PVector v = nts(q);
return new PVector(v.y, -v.x);
}
final float dr = 1;
final int nw = 72/2;
final float nscl = 0.001;
final float tscl = 0.1;
void drawCurve(float ph, color c)
{
float amt, th;
noFill();
stroke(c);
beginShape();
for(int i=0; i<n; i++){
th = PI*i/n;
amt = map(cos(2*th-TWO_PI*t),1,-1,0,1);
amt = 30*fac*ease(constrain(1.7*amt-0.7,0,1),4.5);
amt *= sin(nw*th+ph+dr*TWO_PI*t);
PVector pt = s(th); // point on curve
amt *= (float)noise.eval(nscl*pt.x, nscl*pt.y, tscl*cos(2*TWO_PI*t+ph), tscl*sin(2*TWO_PI*t+ph));
PVector delta = nns(th).mult(amt); // scaled normal vector
vertex(pt.x + delta.x, pt.y + delta.y);
}
endShape(CLOSE);
noStroke();
final int nsteps = 20;
for(int k=0; k<=nsteps; k++)
{
PVector pt = s(PI*(t+0.75+0.0005*ph));
color c1 = color(hue(c),saturation(c),brightness(c),100/nsteps);
fill(c1);
circle(pt.x, pt.y, k*fac);
}
/*
PVector pt = s(2*t);
PVector v = nts(2*t).mult(50);
PVector w = nns(2*t).mult(50);
line(pt.x, pt.y, pt.x + v.x, pt.y + v.y);
line(pt.x, pt.y, pt.x + w.x, pt.y + w.y);
*/
}
void settings()
{
size(frameWidth, frameHeight, P2D); // Use P2D renderer for shader support
smooth(8);
}
void setup() {
// size(540,540,P3D);
blendMode(ADD); // blendMode(MULTIPLY);
result = new int[width*height][3];
rectMode(CENTER);
noFill();
strokeWeight(7);
courier = createFont("Courier New",10*fac,true);
noise = new OpenSimplexNoise(1337);
}
float x, y, z, tt;
int N = 12;
void draw_() {
color c;
background(0); //background(250);
push();
translate(width/2, height/2);
translate(0,12);
scale(1);
strokeWeight(3*fac);
colorMode(HSB, 100);
c = color(50, 100, 100); // Cyan
drawCurve(0, c);
c = color(83, 100, 100); // Magenta
drawCurve(TWO_PI/3, c);
c = color(16, 100, 100); // Yellow
drawCurve(2*TWO_PI/3, c);
pop();
postDraw();
}
void postDraw()
{
push();
// texts
translate(width/2,height/2);
fill(255);stroke(255);
textAlign(CENTER, CENTER);
textFont(courier);
text("@infinitymathart | 2025",0.0*width,0.41*height);
pop();
}
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