/// <summary>Sample multi-frequency 3D Perlin Turbulence noise, also known as turbulence, tiled in all three dimensions.</summary>
/// <returns>The noise value.</returns>
/// <param name="point">Sample point in 3D.</param>
/// <param name="offset">Offset of the tiling domain.</param>
/// <param name="frequency">Base frequency.</param>
/// <param name="octaves">Amount of octaves.</param>
/// <param name="lacunarity">Frequency multiplier for successive octaves.</param>
/// <param name="persistence">Amplitude multiplier for succesive octaves.</param>
public static float SampleTurbulence3DTiledXYZ(
Vector3 point, Vector3 offset, int frequency, int octaves, int lacunarity, float persistence
)
{
int
xOffset = NoiseMath.FloorToInt(offset.x),
yOffset = NoiseMath.FloorToInt(offset.y),
zOffset = NoiseMath.FloorToInt(offset.z);
point.x += offset.x - xOffset;
point.y += offset.y - yOffset;
point.z += offset.z - zOffset;
float amplitude = 1f, range = 1f, sample = Sample3DTiledXYZ(point, xOffset, yOffset, zOffset, frequency);
float sum = sample >= 0f ? sample : -sample;
while (--octaves > 0)
{
frequency *= lacunarity;
amplitude *= persistence;
range += amplitude;
sample = Sample3DTiledXYZ(point, xOffset, yOffset, zOffset, frequency) * amplitude;
sum += sample >= 0f ? sample : -sample;
}
return(sum * (1f / range));
}
/// <summary>Sample 2D Value noise.</summary>
/// <returns>The noise value.</returns>
/// <param name="point">Sample point in 2D.</param>
/// <param name="frequency">Frequency of the noise.</param>
public static float Sample2D(Vector2 point, float frequency)
{
point.x *= frequency;
point.y *= frequency;
int ix0 = NoiseMath.FloorToInt(point.x);
int iy0 = NoiseMath.FloorToInt(point.y);
float tx = point.x - ix0;
float ty = point.y - iy0;
ix0 &= NoiseMath.hashMask;
iy0 &= NoiseMath.hashMask;
int ix1 = ix0 + 1;
int iy1 = iy0 + 1;
int h0 = NoiseMath.hash[ix0];
int h1 = NoiseMath.hash[ix1];
int h00 = NoiseMath.hash[h0 + iy0];
int h10 = NoiseMath.hash[h1 + iy0];
int h01 = NoiseMath.hash[h0 + iy1];
int h11 = NoiseMath.hash[h1 + iy1];
float a = h00;
float b = h10 - h00;
float c = h01 - h00;
float d = h11 - h01 - h10 + h00;
tx = NoiseMath.Smooth(tx);
ty = NoiseMath.Smooth(ty);
return((a + b * tx + (c + d * tx) * ty) * (1f / NoiseMath.hashMask));
}
/// <summary>Sample 2D Perlin noise, tiled in both dimensions.</summary>
/// <returns>The noise value.</returns>
/// <param name="point">Sample point in 2D.</param>
/// <param name="xOffset">X offset of the tiling domain.</param>
/// <param name="yOffset">Y offset of the tiling domain.</param>
/// <param name="frequency">Frequency of the noise.</param>
public static float Sample2DTiledXY(Vector2 point, int xOffset, int yOffset, int frequency)
{
if (frequency == 0)
{
return(0f);
}
point.x *= frequency;
point.y *= frequency;
int ix0 = NoiseMath.FloorToInt(point.x);
int iy0 = NoiseMath.FloorToInt(point.y);
float tx0 = point.x - ix0;
float ty0 = point.y - iy0;
float tx1 = tx0 - 1f;
float ty1 = ty0 - 1f;
ix0 %= frequency;
if (ix0 < 0)
{
ix0 += frequency;
}
iy0 %= frequency;
if (iy0 < 0)
{
iy0 += frequency;
}
int ix1 = ((ix0 + 1) % frequency + xOffset) & NoiseMath.hashMask;
int iy1 = ((iy0 + 1) % frequency + yOffset) & NoiseMath.hashMask;
ix0 = (ix0 + xOffset) & NoiseMath.hashMask;
iy0 = (iy0 + yOffset) & NoiseMath.hashMask;
int h0 = NoiseMath.hash[ix0];
int h1 = NoiseMath.hash[ix1];
Vector2 g00 = NoiseMath.gradients2D[NoiseMath.hash[h0 + iy0] & NoiseMath.gradientsMask2D];
Vector2 g10 = NoiseMath.gradients2D[NoiseMath.hash[h1 + iy0] & NoiseMath.gradientsMask2D];
Vector2 g01 = NoiseMath.gradients2D[NoiseMath.hash[h0 + iy1] & NoiseMath.gradientsMask2D];
Vector2 g11 = NoiseMath.gradients2D[NoiseMath.hash[h1 + iy1] & NoiseMath.gradientsMask2D];
float v00 = NoiseMath.Dot(g00, tx0, ty0);
float v10 = NoiseMath.Dot(g10, tx1, ty0);
float v01 = NoiseMath.Dot(g01, tx0, ty1);
float v11 = NoiseMath.Dot(g11, tx1, ty1);
float a = v00;
float b = v10 - v00;
float c = v01 - v00;
float d = v11 - v01 - v10 + v00;
float tx = NoiseMath.Smooth(tx0);
float ty = NoiseMath.Smooth(ty0);
return((a + b * tx + (c + d * tx) * ty) * sqrt2);
}
/// <summary>Sample 3D Value noise.</summary>
/// <returns>The noise value.</returns>
/// <param name="point">Sample point in 3D.</param>
/// <param name="frequency">Frequency of the noise.</param>
public static float Sample3D(Vector3 point, float frequency)
{
point.x *= frequency;
point.y *= frequency;
point.z *= frequency;
int ix0 = NoiseMath.FloorToInt(point.x);
int iy0 = NoiseMath.FloorToInt(point.y);
int iz0 = NoiseMath.FloorToInt(point.z);
float tx = point.x - ix0;
float ty = point.y - iy0;
float tz = point.z - iz0;
ix0 &= NoiseMath.hashMask;
iy0 &= NoiseMath.hashMask;
iz0 &= NoiseMath.hashMask;
int ix1 = ix0 + 1;
int iy1 = iy0 + 1;
int iz1 = iz0 + 1;
int h0 = NoiseMath.hash[ix0];
int h1 = NoiseMath.hash[ix1];
int h00 = NoiseMath.hash[h0 + iy0];
int h10 = NoiseMath.hash[h1 + iy0];
int h01 = NoiseMath.hash[h0 + iy1];
int h11 = NoiseMath.hash[h1 + iy1];
int h000 = NoiseMath.hash[h00 + iz0];
int h100 = NoiseMath.hash[h10 + iz0];
int h010 = NoiseMath.hash[h01 + iz0];
int h110 = NoiseMath.hash[h11 + iz0];
int h001 = NoiseMath.hash[h00 + iz1];
int h101 = NoiseMath.hash[h10 + iz1];
int h011 = NoiseMath.hash[h01 + iz1];
int h111 = NoiseMath.hash[h11 + iz1];
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;
tx = NoiseMath.Smooth(tx);
ty = NoiseMath.Smooth(ty);
tz = NoiseMath.Smooth(tz);
return
((a + b * tx + (c + e * tx) * ty + (d + f * tx + (g + h * tx) * ty) * tz) * (1f / NoiseMath.hashMask));
}
/// <summary>Sample 2D Value noise, tiled in both dimensions.</summary>
/// <returns>The noise value.</returns>
/// <param name="point">Sample point in 2D.</param>
/// <param name="xOffset">X offset of the tiling domain.</param>
/// <param name="yOffset">Y offset of the tiling domain.</param>
/// <param name="frequency">Frequency of the noise.</param>
public static float Sample2DTiledXY(Vector2 point, int xOffset, int yOffset, int frequency)
{
if (frequency == 0)
{
return(0f);
}
point.x *= frequency;
point.y *= frequency;
int ix0 = NoiseMath.FloorToInt(point.x);
int iy0 = NoiseMath.FloorToInt(point.y);
float tx = point.x - ix0;
float ty = point.y - iy0;
ix0 %= frequency;
if (ix0 < 0)
{
ix0 += frequency;
}
iy0 %= frequency;
if (iy0 < 0)
{
iy0 += frequency;
}
int ix1 = ((ix0 + 1) % frequency + xOffset) & NoiseMath.hashMask;
int iy1 = ((iy0 + 1) % frequency + yOffset) & NoiseMath.hashMask;
ix0 = (ix0 + xOffset) & NoiseMath.hashMask;
iy0 = (iy0 + yOffset) & NoiseMath.hashMask;
int h0 = NoiseMath.hash[ix0];
int h1 = NoiseMath.hash[ix1];
int h00 = NoiseMath.hash[h0 + iy0];
int h10 = NoiseMath.hash[h1 + iy0];
int h01 = NoiseMath.hash[h0 + iy1];
int h11 = NoiseMath.hash[h1 + iy1];
float a = h00;
float b = h10 - h00;
float c = h01 - h00;
float d = h11 - h01 - h10 + h00;
tx = NoiseMath.Smooth(tx);
ty = NoiseMath.Smooth(ty);
return((a + b * tx + (c + d * tx) * ty) * (1f / NoiseMath.hashMask));
}
/// <summary>Sample multi-frequency 2D Perlin noise, tiled in both dimensions.</summary>
/// <returns>The noise value.</returns>
/// <param name="point">Sample point in 2D.</param>
/// <param name="offset">Offset of the tiling domain.</param>
/// <param name="frequency">Base frequency.</param>
/// <param name="octaves">Amount of octaves.</param>
/// <param name="lacunarity">Frequency multiplier for successive octaves.</param>
/// <param name="persistence">Amplitude multiplier for succesive octaves.</param>
public static float Sample2DTiledXY(
Vector2 point, Vector2 offset, int frequency, int octaves, int lacunarity, float persistence
)
{
int xOffset = NoiseMath.FloorToInt(offset.x), yOffset = NoiseMath.FloorToInt(offset.y);
point.x += offset.x - xOffset;
point.y += offset.y - yOffset;
float amplitude = 1f, range = 1f, sum = Sample2DTiledXY(point, xOffset, yOffset, frequency);
while (--octaves > 0)
{
frequency *= lacunarity;
amplitude *= persistence;
range += amplitude;
sum += Sample2DTiledXY(point, xOffset, yOffset, frequency) * amplitude;
}
return(sum * (0.5f / range) + 0.5f);
}
/// <summary>Sample 2D Perlin noise.</summary>
/// <returns>The noise value.</returns>
/// <param name="point">Sample point in 2D.</param>
/// <param name="frequency">Frequency of the noise.</param>
public static float Sample2D(Vector2 point, float frequency)
{
point.x *= frequency;
point.y *= frequency;
int ix0 = NoiseMath.FloorToInt(point.x);
int iy0 = NoiseMath.FloorToInt(point.y);
float tx0 = point.x - ix0;
float ty0 = point.y - iy0;
float tx1 = tx0 - 1f;
float ty1 = ty0 - 1f;
ix0 &= NoiseMath.hashMask;
iy0 &= NoiseMath.hashMask;
int ix1 = ix0 + 1;
int iy1 = iy0 + 1;
int h0 = NoiseMath.hash[ix0];
int h1 = NoiseMath.hash[ix1];
Vector2 g00 = NoiseMath.gradients2D[NoiseMath.hash[h0 + iy0] & NoiseMath.gradientsMask2D];
Vector2 g10 = NoiseMath.gradients2D[NoiseMath.hash[h1 + iy0] & NoiseMath.gradientsMask2D];
Vector2 g01 = NoiseMath.gradients2D[NoiseMath.hash[h0 + iy1] & NoiseMath.gradientsMask2D];
Vector2 g11 = NoiseMath.gradients2D[NoiseMath.hash[h1 + iy1] & NoiseMath.gradientsMask2D];
float v00 = NoiseMath.Dot(g00, tx0, ty0);
float v10 = NoiseMath.Dot(g10, tx1, ty0);
float v01 = NoiseMath.Dot(g01, tx0, ty1);
float v11 = NoiseMath.Dot(g11, tx1, ty1);
float a = v00;
float b = v10 - v00;
float c = v01 - v00;
float d = v11 - v01 - v10 + v00;
float tx = NoiseMath.Smooth(tx0);
float ty = NoiseMath.Smooth(ty0);
return((a + b * tx + (c + d * tx) * ty) * sqrt2);
}
/// <summary>Sample 3D Perlin noise, tiled in the X and Y dimensions.</summary>
/// <returns>The noise value.</returns>
/// <param name="point">Sample point in 3D.</param>
/// <param name="xOffset">X offset of the tiling domain.</param>
/// <param name="yOffset">Y offset of the tiling domain.</param>
/// <param name="zOffset">Z offset of the tiling domain.</param>
/// <param name="frequency">Frequency of the noise.</param>
public static float Sample3DTiledXYZ(Vector3 point, int xOffset, int yOffset, int zOffset, int frequency)
{
if (frequency == 0)
{
return(0f);
}
point.x *= frequency;
point.y *= frequency;
point.z *= frequency;
int ix0 = NoiseMath.FloorToInt(point.x);
int iy0 = NoiseMath.FloorToInt(point.y);
int iz0 = NoiseMath.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 %= frequency;
if (ix0 < 0)
{
ix0 += frequency;
}
iy0 %= frequency;
if (iy0 < 0)
{
iy0 += frequency;
}
iz0 %= frequency;
if (iz0 < 0)
{
iz0 += frequency;
}
int ix1 = ((ix0 + 1) % frequency + xOffset) & NoiseMath.hashMask;
int iy1 = ((iy0 + 1) % frequency + yOffset) & NoiseMath.hashMask;
int iz1 = ((iz0 + 1) % frequency + zOffset) & NoiseMath.hashMask;
ix0 = (ix0 + xOffset) & NoiseMath.hashMask;
iy0 = (iy0 + yOffset) & NoiseMath.hashMask;
iz0 = (iz0 + zOffset) & NoiseMath.hashMask;
int h0 = NoiseMath.hash[ix0];
int h1 = NoiseMath.hash[ix1];
int h00 = NoiseMath.hash[h0 + iy0];
int h10 = NoiseMath.hash[h1 + iy0];
int h01 = NoiseMath.hash[h0 + iy1];
int h11 = NoiseMath.hash[h1 + iy1];
Vector3 g000 = NoiseMath.gradients3D[NoiseMath.hash[h00 + iz0] & NoiseMath.gradientsMask3D];
Vector3 g100 = NoiseMath.gradients3D[NoiseMath.hash[h10 + iz0] & NoiseMath.gradientsMask3D];
Vector3 g010 = NoiseMath.gradients3D[NoiseMath.hash[h01 + iz0] & NoiseMath.gradientsMask3D];
Vector3 g110 = NoiseMath.gradients3D[NoiseMath.hash[h11 + iz0] & NoiseMath.gradientsMask3D];
Vector3 g001 = NoiseMath.gradients3D[NoiseMath.hash[h00 + iz1] & NoiseMath.gradientsMask3D];
Vector3 g101 = NoiseMath.gradients3D[NoiseMath.hash[h10 + iz1] & NoiseMath.gradientsMask3D];
Vector3 g011 = NoiseMath.gradients3D[NoiseMath.hash[h01 + iz1] & NoiseMath.gradientsMask3D];
Vector3 g111 = NoiseMath.gradients3D[NoiseMath.hash[h11 + iz1] & NoiseMath.gradientsMask3D];
float v000 = NoiseMath.Dot(g000, tx0, ty0, tz0);
float v100 = NoiseMath.Dot(g100, tx1, ty0, tz0);
float v010 = NoiseMath.Dot(g010, tx0, ty1, tz0);
float v110 = NoiseMath.Dot(g110, tx1, ty1, tz0);
float v001 = NoiseMath.Dot(g001, tx0, ty0, tz1);
float v101 = NoiseMath.Dot(g101, tx1, ty0, tz1);
float v011 = NoiseMath.Dot(g011, tx0, ty1, tz1);
float v111 = NoiseMath.Dot(g111, tx1, ty1, tz1);
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 - v100 + v000;
float g = v011 - v001 - v010 + v000;
float h = v111 - v011 - v101 + v001 - v110 + v010 + v100 - v000;
float tx = NoiseMath.Smooth(tx0);
float ty = NoiseMath.Smooth(ty0);
float tz = NoiseMath.Smooth(tz0);
return(a + b * tx + (c + e * tx) * ty + (d + f * tx + (g + h * tx) * ty) * tz);
}
/// <summary>Sample 3D Perlin noise.</summary>
/// <returns>The noise value.</returns>
/// <param name="point">Sample point in 3D.</param>
/// <param name="frequency">Frequency of the noise.</param>
public static float Sample3D(Vector3 point, float frequency)
{
point.x *= frequency;
point.y *= frequency;
point.z *= frequency;
int ix0 = NoiseMath.FloorToInt(point.x);
int iy0 = NoiseMath.FloorToInt(point.y);
int iz0 = NoiseMath.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 &= NoiseMath.hashMask;
iy0 &= NoiseMath.hashMask;
iz0 &= NoiseMath.hashMask;
int ix1 = ix0 + 1;
int iy1 = iy0 + 1;
int iz1 = iz0 + 1;
int h0 = NoiseMath.hash[ix0];
int h1 = NoiseMath.hash[ix1];
int h00 = NoiseMath.hash[h0 + iy0];
int h10 = NoiseMath.hash[h1 + iy0];
int h01 = NoiseMath.hash[h0 + iy1];
int h11 = NoiseMath.hash[h1 + iy1];
Vector3 g000 = NoiseMath.gradients3D[NoiseMath.hash[h00 + iz0] & NoiseMath.gradientsMask3D];
Vector3 g100 = NoiseMath.gradients3D[NoiseMath.hash[h10 + iz0] & NoiseMath.gradientsMask3D];
Vector3 g010 = NoiseMath.gradients3D[NoiseMath.hash[h01 + iz0] & NoiseMath.gradientsMask3D];
Vector3 g110 = NoiseMath.gradients3D[NoiseMath.hash[h11 + iz0] & NoiseMath.gradientsMask3D];
Vector3 g001 = NoiseMath.gradients3D[NoiseMath.hash[h00 + iz1] & NoiseMath.gradientsMask3D];
Vector3 g101 = NoiseMath.gradients3D[NoiseMath.hash[h10 + iz1] & NoiseMath.gradientsMask3D];
Vector3 g011 = NoiseMath.gradients3D[NoiseMath.hash[h01 + iz1] & NoiseMath.gradientsMask3D];
Vector3 g111 = NoiseMath.gradients3D[NoiseMath.hash[h11 + iz1] & NoiseMath.gradientsMask3D];
float v000 = NoiseMath.Dot(g000, tx0, ty0, tz0);
float v100 = NoiseMath.Dot(g100, tx1, ty0, tz0);
float v010 = NoiseMath.Dot(g010, tx0, ty1, tz0);
float v110 = NoiseMath.Dot(g110, tx1, ty1, tz0);
float v001 = NoiseMath.Dot(g001, tx0, ty0, tz1);
float v101 = NoiseMath.Dot(g101, tx1, ty0, tz1);
float v011 = NoiseMath.Dot(g011, tx0, ty1, tz1);
float v111 = NoiseMath.Dot(g111, tx1, ty1, tz1);
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 - v100 + v000;
float g = v011 - v001 - v010 + v000;
float h = v111 - v011 - v101 + v001 - v110 + v010 + v100 - v000;
float tx = NoiseMath.Smooth(tx0);
float ty = NoiseMath.Smooth(ty0);
float tz = NoiseMath.Smooth(tz0);
return(a + b * tx + (c + e * tx) * ty + (d + f * tx + (g + h * tx) * ty) * tz);
}
/// <summary>Sample 3D Value noise, tiled in all three dimensions.</summary>
/// <returns>The noise value.</returns>
/// <param name="point">Sample point in 3D.</param>
/// <param name="xOffset">X offset of the tiling domain.</param>
/// <param name="yOffset">Y offset of the tiling domain.</param>
/// <param name="zOffset">Z offset of the tiling domain.</param>
/// <param name="frequency">Frequency of the noise.</param>
public static float Sample3DTiledXYZ(Vector3 point, int xOffset, int zOffset, int yOffset, int frequency)
{
if (frequency == 0)
{
return(0f);
}
point.x *= frequency;
point.y *= frequency;
point.z *= frequency;
int ix0 = NoiseMath.FloorToInt(point.x);
int iy0 = NoiseMath.FloorToInt(point.y);
int iz0 = NoiseMath.FloorToInt(point.z);
float tx = point.x - ix0;
float ty = point.y - iy0;
float tz = point.z - iz0;
ix0 %= frequency;
if (ix0 < 0)
{
ix0 += frequency;
}
iy0 %= frequency;
if (iy0 < 0)
{
iy0 += frequency;
}
iz0 %= frequency;
if (iz0 < 0)
{
iz0 += frequency;
}
int ix1 = ((ix0 + 1) % frequency + xOffset) & NoiseMath.hashMask;
int iy1 = ((iy0 + 1) % frequency + yOffset) & NoiseMath.hashMask;
int iz1 = ((iz0 + 1) % frequency + zOffset) & NoiseMath.hashMask;
ix0 = (ix0 + xOffset) & NoiseMath.hashMask;
iy0 = (iy0 + yOffset) & NoiseMath.hashMask;
iz0 = (iz0 + zOffset) & NoiseMath.hashMask;
int h0 = NoiseMath.hash[ix0];
int h1 = NoiseMath.hash[ix1];
int h00 = NoiseMath.hash[h0 + iy0];
int h10 = NoiseMath.hash[h1 + iy0];
int h01 = NoiseMath.hash[h0 + iy1];
int h11 = NoiseMath.hash[h1 + iy1];
int h000 = NoiseMath.hash[h00 + iz0];
int h100 = NoiseMath.hash[h10 + iz0];
int h010 = NoiseMath.hash[h01 + iz0];
int h110 = NoiseMath.hash[h11 + iz0];
int h001 = NoiseMath.hash[h00 + iz1];
int h101 = NoiseMath.hash[h10 + iz1];
int h011 = NoiseMath.hash[h01 + iz1];
int h111 = NoiseMath.hash[h11 + iz1];
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;
tx = NoiseMath.Smooth(tx);
ty = NoiseMath.Smooth(ty);
tz = NoiseMath.Smooth(tz);
return
((a + b * tx + (c + e * tx) * ty + (d + f * tx + (g + h * tx) * ty) * tz) * (1f / NoiseMath.hashMask));
}
