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OpenSimplex2S.cs
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/**
* K.jpg's OpenSimplex 2, smooth variant ("SuperSimplex")
*
* - 2D is standard simplex, modified to support larger kernels.
* Implemented using a lookup table.
* - 3D is "Re-oriented 8-point BCC noise" which constructs an
* isomorphic BCC lattice in a much different way than usual.
*
* Multiple versions of each function are provided. See the
* documentation above each, for more info.
*/
using System.Runtime.CompilerServices;
namespace Noise
{
public class OpenSimplex2S
{
private const int PSIZE = 2048;
private const int PMASK = 2047;
private short[] perm;
private Grad2[] permGrad2;
private Grad3[] permGrad3;
public OpenSimplex2S(long seed)
{
perm = new short[PSIZE];
permGrad2 = new Grad2[PSIZE];
permGrad3 = new Grad3[PSIZE];
short[] source = new short[PSIZE];
for (short i = 0; i < PSIZE; i++)
source[i] = i;
for (int i = PSIZE - 1; i >= 0; i--)
{
seed = seed * 6364136223846793005L + 1442695040888963407L;
int r = (int)((seed + 31) % (i + 1));
if (r < 0)
r += (i + 1);
perm[i] = source[r];
permGrad2[i] = GRADIENTS_2D[perm[i]];
permGrad3[i] = GRADIENTS_3D[perm[i]];
source[r] = source[i];
}
}
/*
* Noise Evaluators
*/
/**
* 2D SuperSimplex noise, standard lattice orientation.
*/
public double Noise2(double x, double y)
{
// Get points for A2* lattice
double s = 0.366025403784439 * (x + y);
double xs = x + s, ys = y + s;
return noise2_Base(xs, ys);
}
/**
* 2D SuperSimplex noise, with Y pointing down the main diagonal.
* Might be better for a 2D sandbox style game, where Y is vertical.
* Probably slightly less optimal for heightmaps or continent maps.
*/
public double Noise2_XBeforeY(double x, double y)
{
// Skew transform and rotation baked into one.
double xx = x * 0.7071067811865476;
double yy = y * 1.224744871380249;
return noise2_Base(yy + xx, yy - xx);
}
/**
* 2D SuperSimplex noise base.
* Lookup table implementation inspired by DigitalShadow.
*/
private double noise2_Base(double xs, double ys)
{
double value = 0;
// Get base points and offsets
int xsb = fastFloor(xs), ysb = fastFloor(ys);
double xsi = xs - xsb, ysi = ys - ysb;
// Index to point list
int a = (int)(xsi + ysi);
int index =
(a << 2) |
(int)(xsi - ysi / 2 + 1 - a / 2.0) << 3 |
(int)(ysi - xsi / 2 + 1 - a / 2.0) << 4;
double ssi = (xsi + ysi) * -0.211324865405187;
double xi = xsi + ssi, yi = ysi + ssi;
// Point contributions
for (int i = 0; i < 4; i++)
{
LatticePoint2D c = LOOKUP_2D[index + i];
double dx = xi + c.dx, dy = yi + c.dy;
double attn = 2.0 / 3.0 - dx * dx - dy * dy;
if (attn <= 0) continue;
int pxm = (xsb + c.xsv) & PMASK, pym = (ysb + c.ysv) & PMASK;
Grad2 grad = permGrad2[perm[pxm] ^ pym];
double extrapolation = grad.dx * dx + grad.dy * dy;
attn *= attn;
value += attn * attn * extrapolation;
}
return value;
}
/**
* 3D Re-oriented 8-point BCC noise, classic orientation
* Proper substitute for what 3D SuperSimplex "should" be,
* in light of Forbidden Formulae.
* Use noise3_XYBeforeZ or noise3_XZBeforeY instead, wherever appropriate.
*/
public double Noise3_Classic(double x, double y, double z)
{
// Re-orient the cubic lattices via rotation, to produce the expected look on cardinal planar slices.
// If texturing objects that don't tend to have cardinal plane faces, you could even remove this.
// Orthonormal rotation. Not a skew transform.
double r = (2.0 / 3.0) * (x + y + z);
double xr = r - x, yr = r - y, zr = r - z;
// Evaluate both lattices to form a BCC lattice.
return noise3_BCC(xr, yr, zr);
}
/**
* 3D Re-oriented 8-point BCC noise, with better visual isotropy in (X, Y).
* Recommended for 3D terrain and time-varied animations.
* The Z coordinate should always be the "different" coordinate in your use case.
* If Y is vertical in world coordinates, call noise3_XYBeforeZ(x, z, Y) or use noise3_XZBeforeY.
* If Z is vertical in world coordinates, call noise3_XYBeforeZ(x, y, Z).
* For a time varied animation, call noise3_XYBeforeZ(x, y, T).
*/
public double Noise3_XYBeforeZ(double x, double y, double z)
{
// Re-orient the cubic lattices without skewing, to make X and Y triangular like 2D.
// Orthonormal rotation. Not a skew transform.
double xy = x + y;
double s2 = xy * -0.211324865405187;
double zz = z * 0.577350269189626;
double xr = x + s2 - zz, yr = y + s2 - zz;
double zr = xy * 0.577350269189626 + zz;
// Evaluate both lattices to form a BCC lattice.
return noise3_BCC(xr, yr, zr);
}
/**
* 3D Re-oriented 8-point BCC noise, with better visual isotropy in (X, Z).
* Recommended for 3D terrain and time-varied animations.
* The Y coordinate should always be the "different" coordinate in your use case.
* If Y is vertical in world coordinates, call noise3_XZBeforeY(x, Y, z).
* If Z is vertical in world coordinates, call noise3_XZBeforeY(x, Z, y) or use noise3_XYBeforeZ.
* For a time varied animation, call noise3_XZBeforeY(x, T, y) or use noise3_XYBeforeZ.
*/
public double Noise3_XZBeforeY(double x, double y, double z)
{
// Re-orient the cubic lattices without skewing, to make X and Z triangular like 2D.
// Orthonormal rotation. Not a skew transform.
double xz = x + z;
double s2 = xz * -0.211324865405187;
double yy = y * 0.577350269189626;
double xr = x + s2 - yy; double zr = z + s2 - yy;
double yr = xz * 0.577350269189626 + yy;
// Evaluate both lattices to form a BCC lattice.
return noise3_BCC(xr, yr, zr);
}
/**
* Generate overlapping cubic lattices for 3D Re-oriented BCC noise.
* Lookup table implementation inspired by DigitalShadow.
* It was actually faster to narrow down the points in the loop itself,
* than to build up the index with enough info to isolate 8 points.
*/
private double noise3_BCC(double xr, double yr, double zr)
{
// Get base and offsets inside cube of first lattice.
int xrb = fastFloor(xr), yrb = fastFloor(yr), zrb = fastFloor(zr);
double xri = xr - xrb, yri = yr - yrb, zri = zr - zrb;
// Identify which octant of the cube we're in. This determines which cell
// in the other cubic lattice we're in, and also narrows down one point on each.
int xht = (int)(xri + 0.5), yht = (int)(yri + 0.5), zht = (int)(zri + 0.5);
int index = (xht << 0) | (yht << 1) | (zht << 2);
// Point contributions
double value = 0;
LatticePoint3D c = LOOKUP_3D[index];
while (c != null)
{
double dxr = xri + c.dxr, dyr = yri + c.dyr, dzr = zri + c.dzr;
double attn = 0.75 - dxr * dxr - dyr * dyr - dzr * dzr;
if (attn < 0)
{
c = c.NextOnFailure;
}
else
{
int pxm = (xrb + c.xrv) & PMASK, pym = (yrb + c.yrv) & PMASK, pzm = (zrb + c.zrv) & PMASK;
Grad3 grad = permGrad3[perm[perm[pxm] ^ pym] ^ pzm];
double extrapolation = grad.dx * dxr + grad.dy * dyr + grad.dz * dzr;
attn *= attn;
value += attn * attn * extrapolation;
c = c.NextOnSuccess;
}
}
return value;
}
/*
* Utility
*/
[MethodImpl(MethodImplOptions.AggressiveInlining)]
private static int fastFloor(double x)
{
int xi = (int)x;
return x < xi ? xi - 1 : xi;
}
/*
* Lookup Tables & Gradients
*/
private static LatticePoint2D[] LOOKUP_2D;
private static LatticePoint3D[] LOOKUP_3D;
private const double N2 = 0.05481866495625118;
private const double N3 = 0.2781926117527186;
private static Grad2[] GRADIENTS_2D;
private static Grad3[] GRADIENTS_3D;
static OpenSimplex2S() {
LOOKUP_2D = new LatticePoint2D[8 * 4];
LOOKUP_3D = new LatticePoint3D[8];
for (int i = 0; i < 8; i++)
{
int i1, j1, i2, j2;
if ((i & 1) == 0)
{
if ((i & 2) == 0) { i1 = -1; j1 = 0; } else { i1 = 1; j1 = 0; }
if ((i & 4) == 0) { i2 = 0; j2 = -1; } else { i2 = 0; j2 = 1; }
}
else
{
if ((i & 2) != 0) { i1 = 2; j1 = 1; } else { i1 = 0; j1 = 1; }
if ((i & 4) != 0) { i2 = 1; j2 = 2; } else { i2 = 1; j2 = 0; }
}
LOOKUP_2D[i * 4 + 0] = new LatticePoint2D(0, 0);
LOOKUP_2D[i * 4 + 1] = new LatticePoint2D(1, 1);
LOOKUP_2D[i * 4 + 2] = new LatticePoint2D(i1, j1);
LOOKUP_2D[i * 4 + 3] = new LatticePoint2D(i2, j2);
}
for (int i = 0; i < 8; i++)
{
int i1, j1, k1, i2, j2, k2;
i1 = (i >> 0) & 1; j1 = (i >> 1) & 1; k1 = (i >> 2) & 1;
i2 = i1 ^ 1; j2 = j1 ^ 1; k2 = k1 ^ 1;
// The two points within this octant, one from each of the two cubic half-lattices.
LatticePoint3D c0 = new LatticePoint3D(i1, j1, k1, 0);
LatticePoint3D c1 = new LatticePoint3D(i1 + i2, j1 + j2, k1 + k2, 1);
// (1, 0, 0) vs (0, 1, 1) away from octant.
LatticePoint3D c2 = new LatticePoint3D(i1 ^ 1, j1, k1, 0);
LatticePoint3D c3 = new LatticePoint3D(i1, j1 ^ 1, k1 ^ 1, 0);
// (1, 0, 0) vs (0, 1, 1) away from octant, on second half-lattice.
LatticePoint3D c4 = new LatticePoint3D(i1 + (i2 ^ 1), j1 + j2, k1 + k2, 1);
LatticePoint3D c5 = new LatticePoint3D(i1 + i2, j1 + (j2 ^ 1), k1 + (k2 ^ 1), 1);
// (0, 1, 0) vs (1, 0, 1) away from octant.
LatticePoint3D c6 = new LatticePoint3D(i1, j1 ^ 1, k1, 0);
LatticePoint3D c7 = new LatticePoint3D(i1 ^ 1, j1, k1 ^ 1, 0);
// (0, 1, 0) vs (1, 0, 1) away from octant, on second half-lattice.
LatticePoint3D c8 = new LatticePoint3D(i1 + i2, j1 + (j2 ^ 1), k1 + k2, 1);
LatticePoint3D c9 = new LatticePoint3D(i1 + (i2 ^ 1), j1 + j2, k1 + (k2 ^ 1), 1);
// (0, 0, 1) vs (1, 1, 0) away from octant.
LatticePoint3D cA = new LatticePoint3D(i1, j1, k1 ^ 1, 0);
LatticePoint3D cB = new LatticePoint3D(i1 ^ 1, j1 ^ 1, k1, 0);
// (0, 0, 1) vs (1, 1, 0) away from octant, on second half-lattice.
LatticePoint3D cC = new LatticePoint3D(i1 + i2, j1 + j2, k1 + (k2 ^ 1), 1);
LatticePoint3D cD = new LatticePoint3D(i1 + (i2 ^ 1), j1 + (j2 ^ 1), k1 + k2, 1);
// First two points are guaranteed.
c0.NextOnFailure = c0.NextOnSuccess = c1;
c1.NextOnFailure = c1.NextOnSuccess = c2;
// If c2 is in range, then we know c3 and c4 are not.
c2.NextOnFailure = c3; c2.NextOnSuccess = c5;
c3.NextOnFailure = c4; c3.NextOnSuccess = c4;
// If c4 is in range, then we know c5 is not.
c4.NextOnFailure = c5; c4.NextOnSuccess = c6;
c5.NextOnFailure = c5.NextOnSuccess = c6;
// If c6 is in range, then we know c7 and c8 are not.
c6.NextOnFailure = c7; c6.NextOnSuccess = c9;
c7.NextOnFailure = c8; c7.NextOnSuccess = c8;
// If c8 is in range, then we know c9 is not.
c8.NextOnFailure = c9; c8.NextOnSuccess = cA;
c9.NextOnFailure = c9.NextOnSuccess = cA;
// If cA is in range, then we know cB and cC are not.
cA.NextOnFailure = cB; cA.NextOnSuccess = cD;
cB.NextOnFailure = cC; cB.NextOnSuccess = cC;
// If cC is in range, then we know cD is not.
cC.NextOnFailure = cD; cC.NextOnSuccess = null;
cD.NextOnFailure = cD.NextOnSuccess = null;
LOOKUP_3D[i] = c0;
}
GRADIENTS_2D = new Grad2[PSIZE];
Grad2[] grad2 = {
new Grad2( 0.130526192220052, 0.99144486137381),
new Grad2( 0.38268343236509, 0.923879532511287),
new Grad2( 0.608761429008721, 0.793353340291235),
new Grad2( 0.793353340291235, 0.608761429008721),
new Grad2( 0.923879532511287, 0.38268343236509),
new Grad2( 0.99144486137381, 0.130526192220051),
new Grad2( 0.99144486137381, -0.130526192220051),
new Grad2( 0.923879532511287, -0.38268343236509),
new Grad2( 0.793353340291235, -0.60876142900872),
new Grad2( 0.608761429008721, -0.793353340291235),
new Grad2( 0.38268343236509, -0.923879532511287),
new Grad2( 0.130526192220052, -0.99144486137381),
new Grad2(-0.130526192220052, -0.99144486137381),
new Grad2(-0.38268343236509, -0.923879532511287),
new Grad2(-0.608761429008721, -0.793353340291235),
new Grad2(-0.793353340291235, -0.608761429008721),
new Grad2(-0.923879532511287, -0.38268343236509),
new Grad2(-0.99144486137381, -0.130526192220052),
new Grad2(-0.99144486137381, 0.130526192220051),
new Grad2(-0.923879532511287, 0.38268343236509),
new Grad2(-0.793353340291235, 0.608761429008721),
new Grad2(-0.608761429008721, 0.793353340291235),
new Grad2(-0.38268343236509, 0.923879532511287),
new Grad2(-0.130526192220052, 0.99144486137381)
};
for (int i = 0; i < grad2.Length; i++)
{
grad2[i].dx /= N2; grad2[i].dy /= N2;
}
for (int i = 0; i < PSIZE; i++)
{
GRADIENTS_2D[i] = grad2[i % grad2.Length];
}
GRADIENTS_3D = new Grad3[PSIZE];
Grad3[] grad3 = {
new Grad3(-2.22474487139, -2.22474487139, -1.0),
new Grad3(-2.22474487139, -2.22474487139, 1.0),
new Grad3(-3.0862664687972017, -1.1721513422464978, 0.0),
new Grad3(-1.1721513422464978, -3.0862664687972017, 0.0),
new Grad3(-2.22474487139, -1.0, -2.22474487139),
new Grad3(-2.22474487139, 1.0, -2.22474487139),
new Grad3(-1.1721513422464978, 0.0, -3.0862664687972017),
new Grad3(-3.0862664687972017, 0.0, -1.1721513422464978),
new Grad3(-2.22474487139, -1.0, 2.22474487139),
new Grad3(-2.22474487139, 1.0, 2.22474487139),
new Grad3(-3.0862664687972017, 0.0, 1.1721513422464978),
new Grad3(-1.1721513422464978, 0.0, 3.0862664687972017),
new Grad3(-2.22474487139, 2.22474487139, -1.0),
new Grad3(-2.22474487139, 2.22474487139, 1.0),
new Grad3(-1.1721513422464978, 3.0862664687972017, 0.0),
new Grad3(-3.0862664687972017, 1.1721513422464978, 0.0),
new Grad3(-1.0, -2.22474487139, -2.22474487139),
new Grad3( 1.0, -2.22474487139, -2.22474487139),
new Grad3( 0.0, -3.0862664687972017, -1.1721513422464978),
new Grad3( 0.0, -1.1721513422464978, -3.0862664687972017),
new Grad3(-1.0, -2.22474487139, 2.22474487139),
new Grad3( 1.0, -2.22474487139, 2.22474487139),
new Grad3( 0.0, -1.1721513422464978, 3.0862664687972017),
new Grad3( 0.0, -3.0862664687972017, 1.1721513422464978),
new Grad3(-1.0, 2.22474487139, -2.22474487139),
new Grad3( 1.0, 2.22474487139, -2.22474487139),
new Grad3( 0.0, 1.1721513422464978, -3.0862664687972017),
new Grad3( 0.0, 3.0862664687972017, -1.1721513422464978),
new Grad3(-1.0, 2.22474487139, 2.22474487139),
new Grad3( 1.0, 2.22474487139, 2.22474487139),
new Grad3( 0.0, 3.0862664687972017, 1.1721513422464978),
new Grad3( 0.0, 1.1721513422464978, 3.0862664687972017),
new Grad3( 2.22474487139, -2.22474487139, -1.0),
new Grad3( 2.22474487139, -2.22474487139, 1.0),
new Grad3( 1.1721513422464978, -3.0862664687972017, 0.0),
new Grad3( 3.0862664687972017, -1.1721513422464978, 0.0),
new Grad3( 2.22474487139, -1.0, -2.22474487139),
new Grad3( 2.22474487139, 1.0, -2.22474487139),
new Grad3( 3.0862664687972017, 0.0, -1.1721513422464978),
new Grad3( 1.1721513422464978, 0.0, -3.0862664687972017),
new Grad3( 2.22474487139, -1.0, 2.22474487139),
new Grad3( 2.22474487139, 1.0, 2.22474487139),
new Grad3( 1.1721513422464978, 0.0, 3.0862664687972017),
new Grad3( 3.0862664687972017, 0.0, 1.1721513422464978),
new Grad3( 2.22474487139, 2.22474487139, -1.0),
new Grad3( 2.22474487139, 2.22474487139, 1.0),
new Grad3( 3.0862664687972017, 1.1721513422464978, 0.0),
new Grad3( 1.1721513422464978, 3.0862664687972017, 0.0)
};
for (int i = 0; i < grad3.Length; i++)
{
grad3[i].dx /= N3; grad3[i].dy /= N3; grad3[i].dz /= N3;
}
for (int i = 0; i < PSIZE; i++)
{
GRADIENTS_3D[i] = grad3[i % grad3.Length];
}
}
private class LatticePoint2D
{
public int xsv, ysv;
public double dx, dy;
public LatticePoint2D(int xsv, int ysv)
{
this.xsv = xsv; this.ysv = ysv;
double ssv = (xsv + ysv) * -0.211324865405187;
this.dx = -xsv - ssv;
this.dy = -ysv - ssv;
}
}
private class LatticePoint3D
{
public double dxr, dyr, dzr;
public int xrv, yrv, zrv;
public LatticePoint3D NextOnFailure, NextOnSuccess;
public LatticePoint3D(int xrv, int yrv, int zrv, int lattice)
{
this.dxr = -xrv + lattice * 0.5; this.dyr = -yrv + lattice * 0.5; this.dzr = -zrv + lattice * 0.5;
this.xrv = xrv + lattice * 1024; this.yrv = yrv + lattice * 1024; this.zrv = zrv + lattice * 1024;
}
}
private class Grad2
{
public double dx, dy;
public Grad2(double dx, double dy)
{
this.dx = dx; this.dy = dy;
}
}
private class Grad3
{
public double dx, dy, dz;
public Grad3(double dx, double dy, double dz)
{
this.dx = dx; this.dy = dy; this.dz = dz;
}
}
}
}