map_gen/shared/perlin_noise.lua
--[[
    Implemented as described here:
    http://flafla2.github.io/2014/08/09/perlinnoise.html
]] --

local Perlin = {}
local p = {}

-- 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
    p[i] = permutation[i + 1]
    -- Repeat the array to avoid buffer overflow in hash function
    p[i + 256] = permutation[i + 1]
end

-- Gradient function finds dot product between pseudorandom gradient vector
-- and the vector from input coordinate to a unit cube vertex
local dot_product = {
    [0x0] = function(x, y)
        return x + y
    end,
    [0x1] = function(x, y)
        return -x + y
    end,
    [0x2] = function(x, y)
        return x - y
    end,
    [0x3] = function(x, y, _)
        return -x - y
    end,
    [0x4] = function(x, _, z)
        return x + z
    end,
    [0x5] = function(x, _, z)
        return -x + z
    end,
    [0x6] = function(x, _, z)
        return x - z
    end,
    [0x7] = function(x, _, z)
        return -x - z
    end,
    [0x8] = function(_, y, z)
        return y + z
    end,
    [0x9] = function(_, y, z)
        return -y + z
    end,
    [0xA] = function(_, y, z)
        return y - z
    end,
    [0xB] = function(_, y, z)
        return -y - z
    end,
    [0xC] = function(x, y, _)
        return y + x
    end,
    [0xD] = function(_, y, z)
        return -y + z
    end,
    [0xE] = function(x, y, _)
        return y - x
    end,
    [0xF] = function(_, y, z)
        return -y - z
    end
}
local function grad(hash, x, y, z)
    return dot_product[bit32.band(hash, 0xF)](x, y, z)
end

-- Fade function is used to smooth final output
local function fade(t)
    return t * t * t * (t * (t * 6 - 15) + 10)
end

local function lerp(t, a, b)
    return a + t * (b - a)
end

-- Return range: [-1, 1]
function Perlin.noise(x, y, z)
    y = y or 0
    z = z or 0

    -- This prevents integer inputs returning 0, which causes 'straight line' artifacts.
    x = x - 0.55077056353912
    y = y - 0.131357755512
    z = z - 0.20474238274619

    -- 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 = fade(x)
    local v = fade(y)
    local w = fade(z)

    -- Hash all 8 unit cube coordinates surrounding input coordinate
    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 lerp(w, lerp(v, lerp(u, grad(AAA, x, y, z), grad(BAA, x - 1, y, z)), lerp(u, grad(ABA, x, y - 1, z), grad(BBA, x - 1, y - 1, z))), lerp(v, lerp(u, grad(AAB, x, y, z - 1), grad(BAB, x - 1, y, z - 1)), lerp(u, grad(ABB, x, y - 1, z - 1), grad(BBB, x - 1, y - 1, z - 1))))
end

return Perlin
