public override FScheme.Value Evaluate(FSharpList <FScheme.Value> args)
{
var input = args[0];
//If we are receiving a list, we must create levels for each double in the list.
if (input.IsList)
{
throw new NotImplementedException();
}
//If we're not receiving a list, we will just assume we received one double height.
else
{
double x = ((FScheme.Value.Number)input).Item;
int i0 = SimplexHelper.FastFloor(x);
int i1 = i0 + 1;
double x0 = x - i0;
double x1 = x0 - 1.0f;
double n0, n1;
double t0 = 1.0f - x0 * x0;
t0 *= t0;
n0 = t0 * t0 * SimplexHelper.Grad(SimplexHelper.perm[i0 & 0xff], x0);
double t1 = 1.0f - x1 * x1;
t1 *= t1;
n1 = t1 * t1 * SimplexHelper.Grad(SimplexHelper.perm[i1 & 0xff], x1);
// The maximum value of this noise is 8*(3/4)^4 = 2.53125
// A factor of 0.395 scales to fit exactly within [-1,1]
return(FScheme.Value.NewNumber(0.395f * (n0 + n1)));
}
}
public override FScheme.Value Evaluate(FSharpList <FScheme.Value> args)
{
var xinput = args[0];
var yinput = args[1];
var zinput = args[2];
//If we are receiving a list, we must create levels for each double in the list.
if (xinput.IsList || yinput.IsList || zinput.IsList)
{
throw new NotImplementedException();
}
//If we're not receiving a list, we will just assume we received one double height.
else
{
double x = ((FScheme.Value.Number)xinput).Item;
double y = ((FScheme.Value.Number)yinput).Item;
double z = ((FScheme.Value.Number)zinput).Item;
// Simple skewing factors for the 3D case
const double F3 = 0.333333333f;
const double G3 = 0.166666667f;
double n0, n1, n2, n3; // Noise contributions from the four corners
// Skew the input space to determine which simplex cell we're in
double s = (x + y + z) * F3; // Very nice and simple skew factor for 3D
double xs = x + s;
double ys = y + s;
double zs = z + s;
int i = SimplexHelper.FastFloor(xs);
int j = SimplexHelper.FastFloor(ys);
int k = SimplexHelper.FastFloor(zs);
double t = (double)(i + j + k) * G3;
double X0 = i - t; // Unskew the cell origin back to (x,y,z) space
double Y0 = j - t;
double Z0 = k - t;
double x0 = x - X0; // The x,y,z distances from the cell origin
double y0 = y - Y0;
double z0 = z - Z0;
// For the 3D case, the simplex shape is a slightly irregular tetrahedron.
// Determine which simplex we are in.
int i1, j1, k1; // Offsets for second corner of simplex in (i,j,k) coords
int i2, j2, k2; // Offsets for third corner of simplex in (i,j,k) coords
/* This code would benefit from a backport from the GLSL version! */
if (x0 >= y0)
{
if (y0 >= z0)
{
i1 = 1; j1 = 0; k1 = 0; i2 = 1; j2 = 1; k2 = 0;
} // X Y Z order
else if (x0 >= z0)
{
i1 = 1; j1 = 0; k1 = 0; i2 = 1; j2 = 0; k2 = 1;
} // X Z Y order
else
{
i1 = 0; j1 = 0; k1 = 1; i2 = 1; j2 = 0; k2 = 1;
} // Z X Y order
}
else
{ // x0<y0
if (y0 < z0)
{
i1 = 0; j1 = 0; k1 = 1; i2 = 0; j2 = 1; k2 = 1;
} // Z Y X order
else if (x0 < z0)
{
i1 = 0; j1 = 1; k1 = 0; i2 = 0; j2 = 1; k2 = 1;
} // Y Z X order
else
{
i1 = 0; j1 = 1; k1 = 0; i2 = 1; j2 = 1; k2 = 0;
} // Y X Z order
}
// A step of (1,0,0) in (i,j,k) means a step of (1-c,-c,-c) in (x,y,z),
// a step of (0,1,0) in (i,j,k) means a step of (-c,1-c,-c) in (x,y,z), and
// a step of (0,0,1) in (i,j,k) means a step of (-c,-c,1-c) in (x,y,z), where
// c = 1/6.
double x1 = x0 - i1 + G3; // Offsets for second corner in (x,y,z) coords
double y1 = y0 - j1 + G3;
double z1 = z0 - k1 + G3;
double x2 = x0 - i2 + 2.0f * G3; // Offsets for third corner in (x,y,z) coords
double y2 = y0 - j2 + 2.0f * G3;
double z2 = z0 - k2 + 2.0f * G3;
double x3 = x0 - 1.0f + 3.0f * G3; // Offsets for last corner in (x,y,z) coords
double y3 = y0 - 1.0f + 3.0f * G3;
double z3 = z0 - 1.0f + 3.0f * G3;
// Wrap the integer indices at 256, to avoid indexing perm[] out of bounds
int ii = i % 256;
int jj = j % 256;
int kk = k % 256;
// Calculate the contribution from the four corners
double t0 = 0.6f - x0 * x0 - y0 * y0 - z0 * z0;
if (t0 < 0.0f)
{
n0 = 0.0f;
}
else
{
t0 *= t0;
n0 = t0 * t0 * SimplexHelper.Grad(SimplexHelper.perm[ii + SimplexHelper.perm[jj + SimplexHelper.perm[kk]]], x0, y0, z0);
}
double t1 = 0.6f - x1 * x1 - y1 * y1 - z1 * z1;
if (t1 < 0.0f)
{
n1 = 0.0f;
}
else
{
t1 *= t1;
n1 = t1 * t1 * SimplexHelper.Grad(SimplexHelper.perm[ii + i1 + SimplexHelper.perm[jj + j1 + SimplexHelper.perm[kk + k1]]], x1, y1, z1);
}
double t2 = 0.6f - x2 * x2 - y2 * y2 - z2 * z2;
if (t2 < 0.0f)
{
n2 = 0.0f;
}
else
{
t2 *= t2;
n2 = t2 * t2 * SimplexHelper.Grad(SimplexHelper.perm[ii + i2 + SimplexHelper.perm[jj + j2 + SimplexHelper.perm[kk + k2]]], x2, y2, z2);
}
double t3 = 0.6f - x3 * x3 - y3 * y3 - z3 * z3;
if (t3 < 0.0f)
{
n3 = 0.0f;
}
else
{
t3 *= t3;
n3 = t3 * t3 * SimplexHelper.Grad(SimplexHelper.perm[ii + 1 + SimplexHelper.perm[jj + 1 + SimplexHelper.perm[kk + 1]]], x3, y3, z3);
}
// Add contributions from each corner to get the final noise value.
// The result is scaled to stay just inside [-1,1]
return(FScheme.Value.NewNumber(32.0f * (n0 + n1 + n2 + n3))); // TODO: The scale factor is preliminary!
}
}
public override FScheme.Value Evaluate(FSharpList <FScheme.Value> args)
{
var xinput = args[0];
var yinput = args[1];
//If we are receiving a list, we must create levels for each double in the list.
if (xinput.IsList || yinput.IsList)
{
throw new NotImplementedException();
}
//If we're not receiving a list, we will just assume we received one double height.
else
{
double x = ((FScheme.Value.Number)xinput).Item;
double y = ((FScheme.Value.Number)yinput).Item;
const double F2 = 0.366025403f; // F2 = 0.5*(sqrt(3.0)-1.0)
const double G2 = 0.211324865f; // G2 = (3.0-Math.sqrt(3.0))/6.0
double n0, n1, n2; // Noise contributions from the three corners
// Skew the input space to determine which simplex cell we're in
double s = (x + y) * F2; // Hairy factor for 2D
double xs = x + s;
double ys = y + s;
int i = SimplexHelper.FastFloor(xs);
int j = SimplexHelper.FastFloor(ys);
double t = (double)(i + j) * G2;
double X0 = i - t; // Unskew the cell origin back to (x,y) space
double Y0 = j - t;
double x0 = x - X0; // The x,y distances from the cell origin
double y0 = y - Y0;
// For the 2D case, the simplex shape is an equilateral triangle.
// Determine which simplex we are in.
int i1, j1; // Offsets for second (middle) corner of simplex in (i,j) coords
if (x0 > y0)
{
i1 = 1; j1 = 0;
} // lower triangle, XY order: (0,0)->(1,0)->(1,1)
else
{
i1 = 0; j1 = 1;
} // upper triangle, YX order: (0,0)->(0,1)->(1,1)
// A step of (1,0) in (i,j) means a step of (1-c,-c) in (x,y), and
// a step of (0,1) in (i,j) means a step of (-c,1-c) in (x,y), where
// c = (3-sqrt(3))/6
double x1 = x0 - i1 + G2; // Offsets for middle corner in (x,y) unskewed coords
double y1 = y0 - j1 + G2;
double x2 = x0 - 1.0f + 2.0f * G2; // Offsets for last corner in (x,y) unskewed coords
double y2 = y0 - 1.0f + 2.0f * G2;
// Wrap the integer indices at 256, to avoid indexing perm[] out of bounds
int ii = i % 256;
int jj = j % 256;
// Calculate the contribution from the three corners
double t0 = 0.5f - x0 * x0 - y0 * y0;
if (t0 < 0.0f)
{
n0 = 0.0f;
}
else
{
t0 *= t0;
n0 = t0 * t0 * SimplexHelper.Grad(SimplexHelper.perm[ii + SimplexHelper.perm[jj]], x0, y0);
}
double t1 = 0.5f - x1 * x1 - y1 * y1;
if (t1 < 0.0f)
{
n1 = 0.0f;
}
else
{
t1 *= t1;
n1 = t1 * t1 * SimplexHelper.Grad(SimplexHelper.perm[ii + i1 + SimplexHelper.perm[jj + j1]], x1, y1);
}
double t2 = 0.5f - x2 * x2 - y2 * y2;
if (t2 < 0.0f)
{
n2 = 0.0f;
}
else
{
t2 *= t2;
n2 = t2 * t2 * SimplexHelper.Grad(SimplexHelper.perm[ii + 1 + SimplexHelper.perm[jj + 1]], x2, y2);
}
// Add contributions from each corner to get the final noise value.
// The result is scaled to return values in the interval [-1,1].
return(FScheme.Value.NewNumber(40.0f * (n0 + n1 + n2))); // TODO: The scale factor is preliminary!
}
}