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