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noise.go
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package geo
import "math"
// Implemntation from https://rosettacode.org/wiki/Perlin_noise#Go and
// http://flafla2.github.io/2014/08/09/perlinnoise.html
var permutation = []int{
151, 160, 137, 91, 90, 15, 131, 13, 201, 95, 96, 53, 194, 233, 7, 225,
140, 36, 103, 30, 69, 142, 8, 99, 37, 240, 21, 10, 23, 190, 6, 148,
247, 120, 234, 75, 0, 26, 197, 62, 94, 252, 219, 203, 117, 35, 11, 32,
57, 177, 33, 88, 237, 149, 56, 87, 174, 20, 125, 136, 171, 168, 68, 175,
74, 165, 71, 134, 139, 48, 27, 166, 77, 146, 158, 231, 83, 111, 229, 122,
60, 211, 133, 230, 220, 105, 92, 41, 55, 46, 245, 40, 244, 102, 143, 54,
65, 25, 63, 161, 1, 216, 80, 73, 209, 76, 132, 187, 208, 89, 18, 169,
200, 196, 135, 130, 116, 188, 159, 86, 164, 100, 109, 198, 173, 186, 3, 64,
52, 217, 226, 250, 124, 123, 5, 202, 38, 147, 118, 126, 255, 82, 85, 212,
207, 206, 59, 227, 47, 16, 58, 17, 182, 189, 28, 42, 223, 183, 170, 213,
119, 248, 152, 2, 44, 154, 163, 70, 221, 153, 101, 155, 167, 43, 172, 9,
129, 22, 39, 253, 19, 98, 108, 110, 79, 113, 224, 232, 178, 185, 112, 104,
218, 246, 97, 228, 251, 34, 242, 193, 238, 210, 144, 12, 191, 179, 162, 241,
81, 51, 145, 235, 249, 14, 239, 107, 49, 192, 214, 31, 181, 199, 106, 157,
184, 84, 204, 176, 115, 121, 50, 45, 127, 4, 150, 254, 138, 236, 205, 93,
222, 114, 67, 29, 24, 72, 243, 141, 128, 195, 78, 66, 215, 61, 156, 180,
}
var p = append(permutation, permutation...)
// Perlin implements Perlin noise. It returns values bewtween 0 and 1.
func Perlin(x, y, z float64) float64 {
xi := int(math.Floor(x)) & 255
yi := int(math.Floor(y)) & 255
zi := int(math.Floor(z)) & 255
x -= math.Floor(x)
y -= math.Floor(y)
z -= math.Floor(z)
u := fade(x)
v := fade(y)
w := fade(z)
a := p[xi] + yi
aa := p[a] + zi
ab := p[a+1] + zi
b := p[xi+1] + yi
ba := p[b] + zi
bb := p[b+1] + zi
val := Lerp(
Lerp(
Lerp(
grad(p[aa], x, y, z),
grad(p[ba], x-1, y, z),
u),
Lerp(
grad(p[ab], x, y-1, z),
grad(p[bb], x-1, y-1, z),
u),
v),
Lerp(
Lerp(
grad(p[aa+1], x, y, z-1),
grad(p[ba+1], x-1, y, z-1),
u),
Lerp(
grad(p[ab+1], x, y-1, z-1),
grad(p[bb+1], x-1, y-1, z-1),
u),
v),
w)
// Actual range is between -1 and +1, change to 0 to +1.
return (val + 1) / 2
}
func fade(t float64) float64 {
return t * t * t * (t*(t*6-15) + 10)
}
func grad(hash int, x, y, z float64) float64 {
switch hash & 15 {
case 0, 12:
return x + y
case 1, 14:
return y - x
case 2:
return x - y
case 3:
return -x - y
case 4:
return x + z
case 5:
return z - x
case 6:
return x - z
case 7:
return -x - z
case 8:
return y + z
case 9, 13:
return z - y
case 10:
return y - z
}
// case 11, 16:
return -y - z
}
// PerlinOctave combines a number of Perlin functions, equal to octaves, of decreasing
// contribution. A persistence of 1 means each octave has equal contribution. A persistence
// of 0.5 means each octave contributes half as much as the previous one.
func PerlinOctave(x, y, z float64, octaves int, persistence float64) float64 {
total := 0.0
frequency := 1.0
amplitude := 1.0
maxValue := 0.0 // Used for normalizing result to 0.0 - 1.0
for i := 0; i < octaves; i++ {
total += Perlin(x*frequency, y*frequency, z*frequency) * amplitude
maxValue += amplitude
amplitude *= persistence
frequency *= 2
}
return total / maxValue
}