--[[ Implemented as described here: http://flafla2.github.io/2014/08/09/perlinnoise.html ]]-- local perlin = {} perlin.p = {} local bit32 = {} function bit32.band(a, b) local result = 0 local bitval = 1 while a > 0 and b > 0 do if a % 2 == 1 and b % 2 == 1 then -- test the rightmost bits result = result + bitval -- set the current bit end bitval = bitval * 2 -- shift left a = math.floor(a/2) -- shift right b = math.floor(b/2) end return result end -- Hash lookup table as defined by Ken Perlin -- This is a randomly arranged array of all numbers from 0-255 inclusive local permutation = {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 } -- p is used to hash unit cube coordinates to [0, 255] for i=0,255 do -- Convert to 0 based index table perlin.p[i] = permutation[i+1] -- Repeat the array to avoid buffer overflow in hash function perlin.p[i+256] = permutation[i+1] end -- Return range: [-1, 1] function perlin:noise(x, y, z) y = y or 0 z = z or 0 -- Calculate the "unit cube" that the point asked will be located in local xi = bit32.band(math.floor(x),255) local yi = bit32.band(math.floor(y),255) local zi = bit32.band(math.floor(z),255) -- Next we calculate the location (from 0 to 1) in that cube x = x - math.floor(x) y = y - math.floor(y) z = z - math.floor(z) -- We also fade the location to smooth the result local u = self.fade(x) local v = self.fade(y) local w = self.fade(z) -- Hash all 8 unit cube coordinates surrounding input coordinate local p = self.p local A, AA, AB, AAA, ABA, AAB, ABB, B, BA, BB, BAA, BBA, BAB, BBB A = p[xi ] + yi AA = p[A ] + zi AB = p[A+1 ] + zi AAA = p[ AA ] ABA = p[ AB ] AAB = p[ AA+1 ] ABB = p[ AB+1 ] B = p[xi+1] + yi BA = p[B ] + zi BB = p[B+1 ] + zi BAA = p[ BA ] BBA = p[ BB ] BAB = p[ BA+1 ] BBB = p[ BB+1 ] -- Take the weighted average between all 8 unit cube coordinates return self.lerp(w, self.lerp(v, self.lerp(u, self:grad(AAA,x,y,z), self:grad(BAA,x-1,y,z) ), self.lerp(u, self:grad(ABA,x,y-1,z), self:grad(BBA,x-1,y-1,z) ) ), self.lerp(v, self.lerp(u, self:grad(AAB,x,y,z-1), self:grad(BAB,x-1,y,z-1) ), self.lerp(u, self:grad(ABB,x,y-1,z-1), self:grad(BBB,x-1,y-1,z-1) ) ) ) end -- Gradient function finds dot product between pseudorandom gradient vector -- and the vector from input coordinate to a unit cube vertex perlin.dot_product = { [0x0]=function(x,y,z) return x + y end, [0x1]=function(x,y,z) return -x + y end, [0x2]=function(x,y,z) return x - y end, [0x3]=function(x,y,z) return -x - y end, [0x4]=function(x,y,z) return x + z end, [0x5]=function(x,y,z) return -x + z end, [0x6]=function(x,y,z) return x - z end, [0x7]=function(x,y,z) return -x - z end, [0x8]=function(x,y,z) return y + z end, [0x9]=function(x,y,z) return -y + z end, [0xA]=function(x,y,z) return y - z end, [0xB]=function(x,y,z) return -y - z end, [0xC]=function(x,y,z) return y + x end, [0xD]=function(x,y,z) return -y + z end, [0xE]=function(x,y,z) return y - x end, [0xF]=function(x,y,z) return -y - z end } function perlin:grad(hash, x, y, z) return self.dot_product[bit32.band(hash,0xF)](x,y,z) end -- Fade function is used to smooth final output function perlin.fade(t) return t * t * t * (t * (t * 6 - 15) + 10) end function perlin.lerp(t, a, b) return a + t * (b - a) end return perlin