public static double Get(Seed seed, double x)
{
// Find unit grid cell containing point
var X = FastFloor(x);
// Get relative xyz coordinates of point within that cell
x -= X;
// Wrap the integer cells at 255 (smaller integer period can be introduced here)
X &= 255;
// Calculate a set of eight hashed gradient indices
var gi0 = p[X]%12;
var gi1 = p[X + 1]%12;
// The gradients of each corner are now:
// g0 = grad3[gi0];
// g1 = grad3[gi1];
// Calculate noise contributions from each of the four corners
var n0 = Dot(Grad3[gi0], x);
var n1 = Dot(Grad3[gi1], x - 1);
// Compute the fade curve value for each of x, y
var u = Fade(x);
// Interpolate along x the contributions from each of the corners
var nx = Lerp(n0, n1, u);
return nx;
}
public static double Get(Seed seed, double x, double y)
{
const double zero = 0d;
const double one = 1d;
const double two = 2d;
// Place input coordinates onto grid.
var stretchOffset = (x + y)*StretchConstant_2D;
var xs = x + stretchOffset;
var ys = y + stretchOffset;
// Floor to get grid coordinates of rhombus (stretched square) super-cell origin.
var xsFloor = Math.FastFloor(xs);
var ysFloor = Math.FastFloor(ys);
// Skew out to get actual coordinates of rhombus origin. We'll need these later.
var squishOffset = (xsFloor + ysFloor)*SquishConstant_2D;
var xFloor = xsFloor + squishOffset;
var yFloor = ysFloor + squishOffset;
// Compute grid coordinates relative to rhombus origin.
var xsFrac = xs - xsFloor;
var ysFrac = ys - ysFloor;
// Sum those together to get a value that determines which region we're in.
var fracSum = xsFrac + ysFrac;
// Positions relative to origin point.
var dx0 = x - xFloor;
var dy0 = y - yFloor;
var value = zero;
// Contribution (1,0)
var dx1 = dx0 - one - SquishConstant_2D;
var dy1 = dy0 - zero - SquishConstant_2D;
value += Gradient.Get(seed, xsFloor + 1, ysFloor, dx1, dy1);
// Contribution (0,1)
var dx2 = dx0 - zero - SquishConstant_2D;
var dy2 = dy0 - one - SquishConstant_2D;
value += Gradient.Get(seed, xsFloor, ysFloor + 1, dx2, dy2);
// Check if we're inside the triangle (2-Simplex) at (1,1)
if (fracSum > one)
{
xsFloor++;
ysFloor++;
dx0 = dx0 - one - two*SquishConstant_2D;
dy0 = dy0 - one - two*SquishConstant_2D;
}
// Contribution (0,0) or (1,1)
value += Gradient.Get(seed, xsFloor, ysFloor, dx0, dy0);
return value/NormConstant_2D;
}
public ThreadedChunkGenerator(Seed seed)
{
_in = new Queue<IChunk>();
_out = new Queue<IChunk>();
_seed = seed;
_b = new Brownian(3, 0.01, 2, 0.8);
var thread = new Thread(Run)
{
Priority = ThreadPriority.BelowNormal,
IsBackground = true
};
thread.Start();
}
public double Get(Seed seed, double x, double y, double z, Func<Seed, double, double, double, double> noise)
{
var frequency = _startFrequency;
double amplitude = 1;
double result = 0;
for (var octave = 0; octave < _octaves; ++octave)
{
result += noise(seed, x*frequency, y*frequency, z*frequency)*amplitude;
amplitude *= _persistence;
frequency *= _lacunarity;
}
return result;
}
private double extrapolate(Seed seed, int xsb, int ysb, int zsb, double dx, double dy, double dz)
{
var index = seed.Get(xsb, ysb, zsb);
var a = gradients3D[index] * dx
+ gradients3D[index + 1] * dy
+ gradients3D[index + 2] * dz;
return a;
}
private double extrapolate(Seed seed, int xsb, int ysb, double dx, double dy)
{
var seedIndex = seed.Get(xsb, ysb) & 0x0E;
return gradients2D[seedIndex] * dx
+ gradients2D[seedIndex + 1] * dy;
}
//3D OpenSimplex Noise.
public double eval(Seed seed, 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(seed, 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(seed, 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(seed, 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(seed, 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(seed, 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(seed, 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(seed, 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(seed, xsb + 1, ysb + 1, zsb + 1, dx0, dy0, dz0);
}
}
else
{ //We're inside the octahedron (Rectified 3-Simplex) in between.
double aScore;
byte aPoint;
bool aIsFurtherSide;
double bScore;
byte 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.
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(seed, 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(seed, 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(seed, 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(seed, 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(seed, 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(seed, 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(seed, 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(seed, xsv_ext1, ysv_ext1, zsv_ext1, dx_ext1, dy_ext1, dz_ext1);
}
return value / NORM_CONSTANT_3D;
}
//2D OpenSimplex Noise.
public double eval(Seed seed, 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(seed, 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(seed, 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(seed, 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(seed, xsv_ext, ysv_ext, dx_ext, dy_ext);
}
return value / NORM_CONSTANT_2D;
}
public IChunkGenerator CreateChunkGenerator(Seed seed)
{
return new ThreadedChunkGenerator(seed);
}
public static double Get(Seed seed, double x, double y, double z)
{
const double zero = 0d;
const double one = 1d;
const double two = 2d;
const double three = 3d;
// Place input coordinates on simplectic honeycomb.
var stretchOffset = (x + y + z)*StretchConstant_3D;
var xs = x + stretchOffset;
var ys = y + stretchOffset;
var zs = z + stretchOffset;
// Floor to get simplectic honeycomb coordinates of rhombohedron (stretched cube) super-cell origin.
var xsFloor = Math.FastFloor(xs);
var ysFloor = Math.FastFloor(ys);
var zsFloor = Math.FastFloor(zs);
// Skew out to get actual coordinates of rhombohedron origin. We'll need these later.
var squishOffset = (xsFloor + ysFloor + zsFloor)*SquishConstant_3D;
var xFloor = xsFloor + squishOffset;
var yFloor = ysFloor + squishOffset;
var zFloor = zsFloor + squishOffset;
// Compute simplectic honeycomb coordinates relative to rhombohedral origin.
var xsFrac = xs - xsFloor;
var ysFrac = ys - ysFloor;
var zsFrac = zs - zsFloor;
// Sum those together to get a value that determines which region we're in.
var fracSum = xsFrac + ysFrac + zsFrac;
// Positions relative to origin point.
var dx0 = x - xFloor;
var dy0 = y - yFloor;
var dz0 = z - zFloor;
var value = zero;
// Check if we're inside the tetrahedron (3-Simplex) at (0,0,0)
if (fracSum <= one)
{
// Contribution (0,0,0)
value += Gradient.Get(seed, xsFloor, ysFloor, zsFloor, dx0, dy0, dz0);
// Contribution (1,0,0)
var dx1 = dx0 - one - SquishConstant_3D;
var dy1 = dy0 - zero - SquishConstant_3D;
var dz1 = dz0 - zero - SquishConstant_3D;
value += Gradient.Get(seed, xsFloor + 1, ysFloor, zsFloor, dx1, dy1, dz1);
// Contribution (0,1,0)
var dx2 = dx0 - zero - SquishConstant_3D;
var dy2 = dy0 - one - SquishConstant_3D;
var dz2 = dz1;
value += Gradient.Get(seed, xsFloor, ysFloor + 1, zsFloor, dx2, dy2, dz2);
// Contribution (0,0,1)
var dx3 = dx2;
var dy3 = dy1;
var dz3 = dz0 - one - SquishConstant_3D;
value += Gradient.Get(seed, xsFloor, ysFloor, zsFloor + 1, dx3, dy3, dz3);
}
// Check if we're inside the tetrahedron (3-Simplex) at (1,1,1)
else if (fracSum >= two)
{
// Contribution (1,1,0)
var dx3 = dx0 - one - two*SquishConstant_3D;
var dy3 = dy0 - one - two*SquishConstant_3D;
var dz3 = dz0 - zero - two*SquishConstant_3D;
value += Gradient.Get(seed, xsFloor + 1, ysFloor + 1, zsFloor, dx3, dy3, dz3);
// Contribution (1,0,1)
var dx2 = dx3;
var dy2 = dy0 - zero - two*SquishConstant_3D;
var dz2 = dz0 - one - two*SquishConstant_3D;
value += Gradient.Get(seed, xsFloor + 1, ysFloor, zsFloor + 1, dx2, dy2, dz2);
// Contribution (0,1,1)
var dx1 = dx0 - zero - two*SquishConstant_3D;
var dy1 = dy3;
var dz1 = dz2;
value += Gradient.Get(seed, xsFloor, ysFloor + 1, zsFloor + 1, dx1, dy1, dz1);
// Contribution (1,1,1)
dx0 = dx0 - one - three*SquishConstant_3D;
dy0 = dy0 - one - three*SquishConstant_3D;
dz0 = dz0 - one - three*SquishConstant_3D;
value += Gradient.Get(seed, xsFloor + 1, ysFloor + 1, zsFloor + 1, dx0, dy0, dz0);
}
// Check if we're inside the octahedron (Rectified 3-Simplex) in between.
else
{
// Contribution (1,0,0)
var dx1 = dx0 - one - SquishConstant_3D;
var dy1 = dy0 - zero - SquishConstant_3D;
var dz1 = dz0 - zero - SquishConstant_3D;
value += Gradient.Get(seed, xsFloor + 1, ysFloor, zsFloor, dx1, dy1, dz1);
// Contribution (0,1,0)
var dx2 = dx0 - zero - SquishConstant_3D;
var dy2 = dy0 - one - SquishConstant_3D;
var dz2 = dz1;
value += Gradient.Get(seed, xsFloor, ysFloor + 1, zsFloor, dx2, dy2, dz2);
// Contribution (0,0,1)
var dx3 = dx2;
var dy3 = dy1;
var dz3 = dz0 - one - SquishConstant_3D;
value += Gradient.Get(seed, xsFloor, ysFloor, zsFloor + 1, dx3, dy3, dz3);
// Contribution (1,1,0)
var dx4 = dx0 - one - two*SquishConstant_3D;
var dy4 = dy0 - one - two*SquishConstant_3D;
var dz4 = dz0 - zero - two*SquishConstant_3D;
value += Gradient.Get(seed, xsFloor + 1, ysFloor + 1, zsFloor, dx4, dy4, dz4);
// Contribution (1,0,1)
var dx5 = dx4;
var dy5 = dy0 - zero - two*SquishConstant_3D;
var dz5 = dz0 - one - two*SquishConstant_3D;
value += Gradient.Get(seed, xsFloor + 1, ysFloor, zsFloor + 1, dx5, dy5, dz5);
// Contribution (0,1,1)
var dx6 = dx0 - zero - two*SquishConstant_3D;
var dy6 = dy4;
var dz6 = dz5;
value += Gradient.Get(seed, xsFloor, ysFloor + 1, zsFloor + 1, dx6, dy6, dz6);
}
return value/NormConstant_3D;
}
private const double StretchConstant_4D = -0.138196601125011; //(1/Math.Sqrt(4+1)-1)/4;
#endregion Fields
#region Methods
public static double Get(Seed seed, double x)
{
throw new NotImplementedException();
}
private void InitializeChunkGenerators(uint chunkGeneratorCount)
{
_chunkGeneratorCount = chunkGeneratorCount;
_nextChunkGeneratorIndex = 0;
_chunkGenerators = new IChunkGenerator[_chunkGeneratorCount];
var seed = new Seed(CryptoRand.NextInt64());
for (var i = 0; i < _chunkGeneratorCount; ++i)
{
_chunkGenerators[i] = _chunkFactory.CreateChunkGenerator(seed);
}
}
public static double Get(Seed seed, double x, double y, double z)
{
// Find unit grid cell containing point
var X = FastFloor(x);
var Y = FastFloor(y);
var Z = FastFloor(z);
// Get relative xyz coordinates of point within that cell
x -= X;
y -= Y;
z -= Z;
// Wrap the integer cells at 255 (smaller integer period can be introduced here)
X &= 255;
Y &= 255;
Z &= 255;
// Calculate a set of eight hashed gradient indices
var gi000 = p[X + p[Y + p[Z]]]%12;
var gi001 = p[X + p[Y + p[Z + 1]]]%12;
var gi010 = p[X + p[Y + 1 + p[Z]]]%12;
var gi011 = p[X + p[Y + 1 + p[Z + 1]]]%12;
var gi100 = p[X + 1 + p[Y + p[Z]]]%12;
var gi101 = p[X + 1 + p[Y + p[Z + 1]]]%12;
var gi110 = p[X + 1 + p[Y + 1 + p[Z]]]%12;
var gi111 = p[X + 1 + p[Y + 1 + p[Z + 1]]]%12;
// The gradients of each corner are now:
// g000 = grad3[gi000];
// g001 = grad3[gi001];
// g010 = grad3[gi010];
// g011 = grad3[gi011];
// g100 = grad3[gi100];
// g101 = grad3[gi101];
// g110 = grad3[gi110];
// g111 = grad3[gi111];
// Calculate noise contributions from each of the eight corners
var n000 = Dot(Grad3[gi000], x, y, z);
var n100 = Dot(Grad3[gi100], x - 1, y, z);
var n010 = Dot(Grad3[gi010], x, y - 1, z);
var n110 = Dot(Grad3[gi110], x - 1, y - 1, z);
var n001 = Dot(Grad3[gi001], x, y, z - 1);
var n101 = Dot(Grad3[gi101], x - 1, y, z - 1);
var n011 = Dot(Grad3[gi011], x, y - 1, z - 1);
var n111 = Dot(Grad3[gi111], x - 1, y - 1, z - 1);
// Compute the fade curve value for each of x, y, z
var u = Fade(x);
var v = Fade(y);
var w = Fade(z);
// Interpolate along x the contributions from each of the corners
var nx00 = Lerp(n000, n100, u);
var nx01 = Lerp(n001, n101, u);
var nx10 = Lerp(n010, n110, u);
var nx11 = Lerp(n011, n111, u);
// Interpolate the four results along y
var nxy0 = Lerp(nx00, nx10, v);
var nxy1 = Lerp(nx01, nx11, v);
// Interpolate the two last results along z
var nxyz = Lerp(nxy0, nxy1, w);
return nxyz;
}
