ComfyFactorio/utils/perlin_noise.lua

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

local band = bit32.band
local floor = math.floor
local Perlin = {}
local p = {}
local b = 'ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789+/'

local function decode(data)
    data = string.gsub(data, '[^' .. b .. '=]', '')
    return (data:gsub(
        '.',
        function(x)
            if (x == '=') then
                return ''
            end
            local r, f = '', (b:find(x) - 1)
            for i = 6, 1, -1 do
                r = r .. (f % 2 ^ i - f % 2 ^ (i - 1) > 0 and '1' or '0')
            end
            return r
        end
    ):gsub(
        '%d%d%d?%d?%d?%d?%d?%d?',
        function(x)
            if (#x ~= 8) then
                return ''
            end
            local c = 0
            for i = 1, 8 do
                c = c + (x:sub(i, i) == '1' and 2 ^ (8 - i) or 0)
            end
            return string.char(c)
        end
    ))
end

-- Hash lookup table as defined by Ken Perlin
-- This is a randomly arranged array of all numbers from 0-255 inclusive
local permutation =
    loadstring(
    decode(
        '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'
    )
)()

-- 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, bit)
    return dot_product[band(hash, bit)](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, bs)
    return a + t * (bs - a)
end

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

    -- This prevents integer inputs returning 0, which casues '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 = band(floor(x), 255)
    local yi = band(floor(y), 255)
    local zi = band(floor(z), 255)

    -- Next we calculate the location (from 0 to 1) in that cube
    x = x - floor(x)
    y = y - floor(y)
    z = z - 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, bit), grad(BAA, x - 1, y, z, bit)), lerp(u, grad(ABA, x, y - 1, z), grad(BBA, x - 1, y - 1, z, bit))),
        lerp(v, lerp(u, grad(AAB, x, y, z - 1, bit), grad(BAB, x - 1, y, z - 1)), lerp(u, grad(ABB, x, y - 1, z - 1, bit), grad(BBB, x - 1, y - 1, z - 1, bit)))
    )
end

return Perlin