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--[[
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
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