public static NoiseSample Perlin1D(Vector3 point, float frequency)
{
point *= frequency;
int i0 = Mathf.FloorToInt(point.x);
float t0 = point.x - i0;
float t1 = t0 - 1f;
i0 &= hashMask;
int i1 = i0 + 1;
float g0 = gradients1D[hash[i0] & gradientsMask1D];
float g1 = gradients1D[hash[i1] & gradientsMask1D];
float v0 = g0 * t0;
float v1 = g1 * t1;
float dt = SmoothDerivative(t0);
float t = Smooth(t0);
float a = v0;
float b = v1 - v0;
float da = g0;
float db = g1 - g0;
NoiseSample result = new NoiseSample();
result.value = a + b * t;
result.derivative = Vector3.zero;
result.derivative.x = da + db * t + b * dt;
result.derivative *= frequency;
return(result * 2f);
}
public static NoiseSample Value1D(Vector3 point, float frequency)
{
point *= frequency;
int i0 = Mathf.FloorToInt(point.x);
float t = point.x - i0;
i0 &= hashMask;
int i1 = i0 + 1;
int h0 = hash[i0];
int h1 = hash[i1];
float dt = SmoothDerivative(t);
t = Smooth(t);
float a = h0;
float b = h1 - h0;
NoiseSample result = new NoiseSample();
result.value = a + b * t;
result.derivative = Vector3.zero;
result.derivative.x = b * dt;
result.derivative *= frequency;
return(result * (2f / hashMask) - 1f);
}
public static NoiseSample Simplex1D(Vector3 point, float frequency)
{
point *= frequency;
int ix = Mathf.FloorToInt(point.x);
NoiseSample sample = Simplex1DPart(point, ix);
sample += (Simplex1DPart(point, ix + 1));
sample.derivative *= frequency;
return(sample * (64f / 27f));
}
public static NoiseSample Perlin2D(Vector3 point, float frequency)
{
point *= frequency;
int ix0 = Mathf.FloorToInt(point.x);
int iy0 = Mathf.FloorToInt(point.y);
float tx0 = point.x - ix0;
float ty0 = point.y - iy0;
float tx1 = tx0 - 1f;
float ty1 = ty0 - 1f;
ix0 &= hashMask;
iy0 &= hashMask;
int ix1 = ix0 + 1;
int iy1 = iy0 + 1;
int h0 = hash[ix0];
int h1 = hash[ix1];
Vector2 g00 = gradients2D[hash[h0 + iy0] & gradientsMask2D];
Vector2 g10 = gradients2D[hash[h1 + iy0] & gradientsMask2D];
Vector2 g01 = gradients2D[hash[h0 + iy1] & gradientsMask2D];
Vector2 g11 = gradients2D[hash[h1 + iy1] & gradientsMask2D];
float v00 = Dot(g00, tx0, ty0);
float v10 = Dot(g10, tx1, ty0);
float v01 = Dot(g01, tx0, ty1);
float v11 = Dot(g11, tx1, ty1);
float dtx = SmoothDerivative(tx0);
float dty = SmoothDerivative(ty0);
float tx = Smooth(tx0);
float ty = Smooth(ty0);
float a = v00;
float b = v10 - v00;
float c = v01 - v00;
float d = v11 - v01 - v10 + v00;
Vector2 da = g00;
Vector2 db = g10 - g00;
Vector2 dc = g01 - g00;
Vector2 dd = g11 - g01 - g10 + g00;
NoiseSample result = new NoiseSample();
result.value = a + b * tx + (c + d * tx) * ty;
result.derivative = da + db * tx + (dc + dd * tx) * ty;
result.derivative.x += (b + d * ty) * dtx;
result.derivative.y += (c + d * tx) * dty;
result.derivative.z = 0;
result.derivative *= frequency;
return(result * sqr2);
}
private static NoiseSample SimplexValue1DPart(Vector3 point, int ix)
{
float x = point.x - ix;
float f = 1f - x * x;
float f2 = f * f;
float f3 = f * f2;
float h = hash[ix & hashMask];
NoiseSample sample = new NoiseSample();
sample.value = h * f3;
sample.derivative.x = -6f * h * x * f2;
return(sample);
}
private static NoiseSample Simplex1DPart(Vector3 point, int ix)
{
float x = point.x - ix;
float f = 1f - x * x;
float f2 = f * f;
float f3 = f * f2;
float g = gradients1D[hash[ix & hashMask] & gradientsMask1D];
float v = g * x;
NoiseSample sample = new NoiseSample();
sample.value = v * f3;
sample.derivative.x = g * f3 - 6f * v * x * f2;
return(sample);
}
public static NoiseSample Sum(NoiseMethod method, Vector3 point, float frequency, int octaves, float lacunarity, float persistance)
{
NoiseSample sum = method(point, frequency);
float amplitude = 1f;
float range = 1f;
for (int o = 1; o < octaves; o++)
{
frequency *= lacunarity;
amplitude *= persistance;
range += amplitude;
sum += method(point, frequency) * amplitude;
}
return(sum * (1f / range));
}
public static NoiseSample Value2D(Vector3 point, float frequency)
{
point *= frequency;
int ix0 = Mathf.FloorToInt(point.x);
int iy0 = Mathf.FloorToInt(point.y);
float tx = point.x - ix0;
float ty = point.y - iy0;
ix0 &= hashMask;
iy0 &= hashMask;
int ix1 = ix0 + 1;
int iy1 = iy0 + 1;
int h0 = hash[ix0];
int h1 = hash[ix1];
int h00 = hash[h0 + iy0];
int h10 = hash[h1 + iy0];
int h01 = hash[h0 + iy1];
int h11 = hash[h1 + iy1];
float dtx = SmoothDerivative(tx);
float dty = SmoothDerivative(ty);
tx = Smooth(tx);
ty = Smooth(ty);
float a = h00;
float b = h10 - h00;
float c = h01 - h00;
float d = h11 - h01 - h10 + h00;
NoiseSample result = new NoiseSample();
result.value = a + b * tx + (c + d * tx) * ty;
result.derivative = Vector3.zero;
result.derivative.x = (b + d * ty) * dtx;
result.derivative.y = (c + d * tx) * dty;
result.derivative *= frequency;
return(result * (2f / hashMask) - 1f);
}
private static NoiseSample SimplexValue2DPart(Vector3 point, int ix, int iy)
{
float unskew = (ix + iy) * squaresToTriangles;
float x = point.x - ix + unskew;
float y = point.y - iy + unskew;
float f = .5f - x * x - y * y;
NoiseSample sample = new NoiseSample();
if (f > 0f)
{
float f2 = f * f;
float f3 = f * f2;
float h = hash[hash[ix & hashMask] + iy & hashMask];
float h6f2 = -6f * h * f2;
sample.value = f3 * h;
sample.derivative.x = h6f2 * x;
sample.derivative.y = h6f2 * y;
}
return(sample);
}
private static NoiseSample Simplex2DPart(Vector3 point, int ix, int iy)
{
float unskew = (ix + iy) * squaresToTriangles;
float x = point.x - ix + unskew;
float y = point.y - iy + unskew;
float f = .5f - x * x - y * y;
NoiseSample sample = new NoiseSample();
if (f > 0f)
{
float f2 = f * f;
float f3 = f * f2;
Vector2 g = gradients2D[hash[hash[ix & hashMask] + iy & hashMask] & gradientsMask2D];
float v = Dot(g, x, y);
float v6f2 = -6f * v * f2;
sample.value = f3 * v;
sample.derivative.x = g.x * f3 + v6f2 * x;
sample.derivative.y = g.y * f3 + v6f2 * y;
}
return(sample);
}
public static NoiseSample Simplex2D(Vector3 point, float frequency)
{
point *= frequency;
float skew = (point.x + point.y) * trianglesToSquares;
float sx = point.x + skew;
float sy = point.y + skew;
int ix = Mathf.FloorToInt(sx);
int iy = Mathf.FloorToInt(sy);
NoiseSample sample = Simplex2DPart(point, ix, iy);
sample += Simplex2DPart(point, ix + 1, iy + 1);
if (sx - ix >= sy - iy)
{
sample += Simplex2DPart(point, ix + 1, iy);
}
else
{
sample += Simplex2DPart(point, ix, iy + 1);
}
sample.derivative *= frequency;
return(sample * simplexScale2D);
}
private static NoiseSample SimplexValue3DPart(Vector3 point, int ix, int iy, int iz)
{
float unskew = (ix + iy + iz) * (1f / 6f);
float x = point.x - ix + unskew;
float y = point.y - iy + unskew;
float z = point.z - iz + unskew;
float f = 0.5f - x * x - y * y - z * z;
NoiseSample sample = new NoiseSample();
if (f > 0f)
{
float f2 = f * f;
float f3 = f * f2;
float h = hash[hash[hash[ix & hashMask] + iy & hashMask] + iz & hashMask];
float h6f2 = -6f * h * f2;
sample.value = f3 * h;
sample.derivative.x = h6f2 * x;
sample.derivative.y = h6f2 * y;
sample.derivative.z = h6f2 * z;
}
return(sample);
}
private static NoiseSample Simplex3DPart(Vector3 point, int ix, int iy, int iz)
{
float unskew = (ix + iy + iz) * (1f / 6f);
float x = point.x - ix + unskew;
float y = point.y - iy + unskew;
float z = point.z - iz + unskew;
float f = 0.5f - x * x - y * y - z * z;
NoiseSample sample = new NoiseSample();
if (f > 0f)
{
float f2 = f * f;
float f3 = f * f2;
Vector3 g = simplexGradients3D[hash[hash[hash[ix & hashMask] + iy & hashMask] + iz & hashMask] & simplexGradientsMask3D];
float v = Dot(g, x, y, z);
float v6f2 = -6f * v * f2;
sample.value = f3 * v;
sample.derivative.x = g.x * f3 + v6f2 * x;
sample.derivative.y = g.y * f3 + v6f2 * y;
sample.derivative.z = g.z * f3 + v6f2 * z;
}
return(sample);
}
public static NoiseSample Simplex3D(Vector3 point, float frequency)
{
point *= frequency;
float skew = (point.x + point.y + point.z) * (1f / 3f);
float sx = point.x + skew;
float sy = point.y + skew;
float sz = point.z + skew;
int ix = Mathf.FloorToInt(sx);
int iy = Mathf.FloorToInt(sy);
int iz = Mathf.FloorToInt(sz);
NoiseSample sample = Simplex3DPart(point, ix, iy, iz);
sample += Simplex3DPart(point, ix + 1, iy + 1, iz + 1);
float x = sx - ix;
float y = sy - iy;
float z = sz - iz;
if (x >= y)
{
if (x >= z)
{
sample += Simplex3DPart(point, ix + 1, iy, iz);
if (y >= z)
{
sample += Simplex3DPart(point, ix + 1, iy + 1, iz);
}
else
{
sample += Simplex3DPart(point, ix + 1, iy, iz + 1);
}
}
else
{
sample += Simplex3DPart(point, ix, iy, iz + 1);
sample += Simplex3DPart(point, ix + 1, iy, iz + 1);
}
}
else
{
if (y >= z)
{
sample += Simplex3DPart(point, ix, iy + 1, iz);
if (x >= z)
{
sample += Simplex3DPart(point, ix + 1, iy + 1, iz);
}
else
{
sample += Simplex3DPart(point, ix, iy + 1, iz + 1);
}
}
else
{
sample += Simplex3DPart(point, ix, iy, iz + 1);
sample += Simplex3DPart(point, ix, iy + 1, iz + 1);
}
}
sample.derivative *= frequency;
return(sample * simplexScale3D);
}
public static NoiseSample Perlin3D(Vector3 point, float frequency)
{
point *= frequency;
int ix0 = Mathf.FloorToInt(point.x);
int iy0 = Mathf.FloorToInt(point.y);
int iz0 = Mathf.FloorToInt(point.z);
float tx0 = point.x - ix0;
float ty0 = point.y - iy0;
float tz0 = point.z - iz0;
float tx1 = tx0 - 1f;
float ty1 = ty0 - 1f;
float tz1 = tz0 - 1f;
ix0 &= hashMask;
iy0 &= hashMask;
iz0 &= hashMask;
int ix1 = ix0 + 1;
int iy1 = iy0 + 1;
int iz1 = iz0 + 1;
int h0 = hash[ix0];
int h1 = hash[ix1];
int h00 = hash[h0 + iy0];
int h10 = hash[h1 + iy0];
int h01 = hash[h0 + iy1];
int h11 = hash[h1 + iy1];
Vector3 g000 = gradients3D[hash[h00 + iz0] & gradientsMask3D];
Vector3 g001 = gradients3D[hash[h00 + iz1] & gradientsMask3D];
Vector3 g010 = gradients3D[hash[h01 + iz0] & gradientsMask3D];
Vector3 g011 = gradients3D[hash[h01 + iz1] & gradientsMask3D];
Vector3 g100 = gradients3D[hash[h10 + iz0] & gradientsMask3D];
Vector3 g101 = gradients3D[hash[h10 + iz1] & gradientsMask3D];
Vector3 g110 = gradients3D[hash[h11 + iz0] & gradientsMask3D];
Vector3 g111 = gradients3D[hash[h11 + iz1] & gradientsMask3D];
float v000 = Dot(g000, tx0, ty0, tz0);
float v001 = Dot(g001, tx0, ty0, tz1);
float v010 = Dot(g010, tx0, ty1, tz0);
float v011 = Dot(g011, tx0, ty1, tz1);
float v100 = Dot(g100, tx1, ty0, tz0);
float v101 = Dot(g101, tx1, ty0, tz1);
float v110 = Dot(g110, tx1, ty1, tz0);
float v111 = Dot(g111, tx1, ty1, tz1);
float dtx = SmoothDerivative(tx0);
float dty = SmoothDerivative(ty0);
float dtz = SmoothDerivative(tz0);
float tx = Smooth(tx0);
float ty = Smooth(ty0);
float tz = Smooth(tz0);
float a = v000;
float b = v100 - v000;
float c = v010 - v000;
float d = v001 - v000;
float e = v110 - v010 - v100 + v000;
float f = v101 - v001 - v010 + v000;
float g = v011 - v001 - v010 + v000;
float h = v111 - v011 - v101 + v001 - v001 - v110 + v010 + v100 - v000;
Vector3 da = g000;
Vector3 db = g100 - g000;
Vector3 dc = g010 - g000;
Vector3 dd = g001 - g000;
Vector3 de = g110 - g010 - g100 + g000;
Vector3 df = g101 - g001 - g100 + g000;
Vector3 dg = g011 - g001 - g010 + g000;
Vector3 dh = g111 - g011 - g001 + g001 - g110 + g010 + g100 - g000;
NoiseSample result = new NoiseSample();
result.value = a + b * tx + (c + e * tx) * ty + (d + f * tx + (g + h * tx) * ty) * tz;
result.derivative = da + db * tx + (dc + de * tx) * ty + (dd + df * tx + (dg + dh * tx) * ty) * tz;
result.derivative.x += (b + e * ty + (f + h * ty) * tz) * dtx;
result.derivative.y += (c + e * tx + (g + h * tx) * tz) * dty;
result.derivative.z += (d + f * tx + (g + h * tx) * ty) * dtz;
result.derivative *= frequency;
return(result);
}
public static NoiseSample Value3D(Vector3 point, float frequency)
{
point *= frequency;
int ix0 = Mathf.FloorToInt(point.x);
int iy0 = Mathf.FloorToInt(point.y);
int iz0 = Mathf.FloorToInt(point.z);
float tx = point.x - ix0;
float ty = point.y - iy0;
float tz = point.z - iz0;
ix0 &= hashMask;
iy0 &= hashMask;
iz0 &= hashMask;
int ix1 = ix0 + 1;
int iy1 = iy0 + 1;
int iz1 = iz0 + 1;
int h0 = hash[ix0];
int h1 = hash[ix1];
int h00 = hash[h0 + iy0];
int h10 = hash[h1 + iy0];
int h01 = hash[h0 + iy1];
int h11 = hash[h1 + iy1];
int h000 = hash[h00 + iz0];
int h001 = hash[h00 + iz1];
int h010 = hash[h01 + iz0];
int h011 = hash[h01 + iz1];
int h100 = hash[h10 + iz0];
int h101 = hash[h10 + iz1];
int h110 = hash[h11 + iz0];
int h111 = hash[h11 + iz1];
float dtx = SmoothDerivative(tx);
float dty = SmoothDerivative(ty);
float dtz = SmoothDerivative(tz);
tx = Smooth(tx);
ty = Smooth(ty);
tz = Smooth(tz);
float a = h000;
float b = h100 - h000;
float c = h010 - h000;
float d = h001 - h000;
float e = h110 - h010 - h100 + h000;
float f = h101 - h001 - h100 + h000;
float g = h011 - h001 - h010 + h000;
float h = h111 - h011 - h101 + h001 - h110 + h010 + h100 - h000;
NoiseSample result = new NoiseSample();
result.value = a + b * tx + (c + e * tx) * ty + (d + f * tx + (g + h * tx) * ty) * tz;
result.derivative = Vector3.zero;
result.derivative.x = (b + e * ty + (f + h * ty) * tz) * dtx;
result.derivative.y = (c + e * tx + (g + h * tx) * tz) * dty;
result.derivative.z = (d + f * tx + (g + h * tx) * ty) * dtz;
result.derivative *= frequency;
return(result * (2f / hashMask) - 1f);
}