2 Implemented as described here:
3 http://flafla2.github.io/2014/08/09/perlinnoise.html
10 function bit32.band(a, b)
13 while a > 0 and b > 0 do
14 if a % 2 == 1 and b % 2 == 1 then -- test the rightmost bits
15 result = result + bitval -- set the current bit
17 bitval = bitval * 2 -- shift left
18 a = math.floor(a/2) -- shift right
24 -- Hash lookup table as defined by Ken Perlin
25 -- This is a randomly arranged array of all numbers from 0-255 inclusive
26 local permutation = {151,160,137,91,90,15,
27 131,13,201,95,96,53,194,233,7,225,140,36,103,30,69,142,8,99,37,240,21,10,23,
28 190, 6,148,247,120,234,75,0,26,197,62,94,252,219,203,117,35,11,32,57,177,33,
29 88,237,149,56,87,174,20,125,136,171,168, 68,175,74,165,71,134,139,48,27,166,
30 77,146,158,231,83,111,229,122,60,211,133,230,220,105,92,41,55,46,245,40,244,
31 102,143,54, 65,25,63,161, 1,216,80,73,209,76,132,187,208, 89,18,169,200,196,
32 135,130,116,188,159,86,164,100,109,198,173,186, 3,64,52,217,226,250,124,123,
33 5,202,38,147,118,126,255,82,85,212,207,206,59,227,47,16,58,17,182,189,28,42,
34 223,183,170,213,119,248,152, 2,44,154,163, 70,221,153,101,155,167, 43,172,9,
35 129,22,39,253, 19,98,108,110,79,113,224,232,178,185, 112,104,218,246,97,228,
36 251,34,242,193,238,210,144,12,191,179,162,241, 81,51,145,235,249,14,239,107,
37 49,192,214, 31,181,199,106,157,184, 84,204,176,115,121,50,45,127, 4,150,254,
38 138,236,205,93,222,114,67,29,24,72,243,141,128,195,78,66,215,61,156,180
41 -- p is used to hash unit cube coordinates to [0, 255]
43 -- Convert to 0 based index table
44 perlin.p[i] = permutation[i+1]
45 -- Repeat the array to avoid buffer overflow in hash function
46 perlin.p[i+256] = permutation[i+1]
49 -- Return range: [-1, 1]
50 function perlin:noise(x, y, z)
54 -- Calculate the "unit cube" that the point asked will be located in
55 local xi = bit32.band(math.floor(x),255)
56 local yi = bit32.band(math.floor(y),255)
57 local zi = bit32.band(math.floor(z),255)
59 -- Next we calculate the location (from 0 to 1) in that cube
64 -- We also fade the location to smooth the result
65 local u = self.fade(x)
66 local v = self.fade(y)
67 local w = self.fade(z)
69 -- Hash all 8 unit cube coordinates surrounding input coordinate
71 local A, AA, AB, AAA, ABA, AAB, ABB, B, BA, BB, BAA, BBA, BAB, BBB
88 -- Take the weighted average between all 8 unit cube coordinates
93 self:grad(BAA,x-1,y,z)
96 self:grad(ABA,x,y-1,z),
97 self:grad(BBA,x-1,y-1,z)
102 self:grad(AAB,x,y,z-1), self:grad(BAB,x-1,y,z-1)
105 self:grad(ABB,x,y-1,z-1), self:grad(BBB,x-1,y-1,z-1)
111 -- Gradient function finds dot product between pseudorandom gradient vector
112 -- and the vector from input coordinate to a unit cube vertex
113 perlin.dot_product = {
114 [0x0]=function(x,y,z) return x + y end,
115 [0x1]=function(x,y,z) return -x + y end,
116 [0x2]=function(x,y,z) return x - y end,
117 [0x3]=function(x,y,z) return -x - y end,
118 [0x4]=function(x,y,z) return x + z end,
119 [0x5]=function(x,y,z) return -x + z end,
120 [0x6]=function(x,y,z) return x - z end,
121 [0x7]=function(x,y,z) return -x - z end,
122 [0x8]=function(x,y,z) return y + z end,
123 [0x9]=function(x,y,z) return -y + z end,
124 [0xA]=function(x,y,z) return y - z end,
125 [0xB]=function(x,y,z) return -y - z end,
126 [0xC]=function(x,y,z) return y + x end,
127 [0xD]=function(x,y,z) return -y + z end,
128 [0xE]=function(x,y,z) return y - x end,
129 [0xF]=function(x,y,z) return -y - z end
131 function perlin:grad(hash, x, y, z)
132 return self.dot_product[bit32.band(hash,0xF)](x,y,z)
135 -- Fade function is used to smooth final output
136 function perlin.fade(t)
137 return t * t * t * (t * (t * 6 - 15) + 10)
140 function perlin.lerp(t, a, b)
141 return a + t * (b - a)