radial and square fall off functions to filter perlin noise

--[[

This module generates normalized fall off to filter perlin noise with, there are 2 types of filter:
- Radial
- Square

these work with my map generation implementation which is found under it
--]]

-- module script
local FallOffMap = {}

function FallOffMap.GenerateCircularFallOff(value1: number, value2: number, theMapSize)

    local radius = .5^2
    local widthFallOff = math.abs(value1/theMapSize * 2 - 1)
    local lengthFallOff = math.abs(value2/theMapSize * 2 - 1)


    local result = math.clamp(math.sqrt(widthFallOff^2  + lengthFallOff^2), 0, 1)
    return result
end


function FallOffMap.GenerateSquareFallOff(value1: number, value2: number, theMapSize)
    local widthFallOff = math.abs(value1/theMapSize * 2 - 1)
    local lengthFallOff = math.abs(value2/theMapSize * 2 - 1)
    local result = math.max(widthFallOff, lengthFallOff)

    return math.clamp(result, 0, 1)
end


-- smooths out both the circular and square filters, substract the return value with the perlin noise value
function FallOffMap.Transform(theFallOffResult, anOffset, aSmoothValue)

    local a = aSmoothValue
    local b = anOffset
    local value = theFallOffResult
    return math.pow(value, a)/(math.pow(value, a)+math.pow(b - b * value, a))
end

return FallOffMap


-- another module script

--[[

This module serves as the map class constructor, it uses an Open source perlin noise library found here:
https://devforum.roblox.com/t/perlin-noise-library-module-4d-and-octaves/600192
--]]
local Map = {}
Map.__index = Map

function Map.new(theMapGenValueMap: table, aTile, theTerrainTypesMap: table)
    local self = setmetatable({}, Map)
    self.MapSize = theMapGenValueMap.MapSize
    self.TileSize = theMapGenValueMap.TileSize

    local seed = theMapGenValueMap.Seed
    local amplitude = theMapGenValueMap.Amplitude
    local scale = theMapGenValueMap.Scale
    local octaves = theMapGenValueMap.Octaves
    local persistence = theMapGenValueMap.Persistence

    local fallOffOffset = theMapGenValueMap.FallOffOffset
    local fallOffPower = theMapGenValueMap.FallOffSmoothness

    for i = 1, self.MapSize do
        for j = 1, self.MapSize do
            -- Noise and fall off calculations
            local noiseResult  = PerlinNoise.new({(i + seed) * scale, (j + seed) * scale}, amplitude, octaves, persistence)
            local fallOff = FallOffMap.GenerateSquareFallOff(i, j , self.MapSize)
            noiseResult  -= FallOffMap.Transform(fallOff, fallOffOffset, fallOffPower)
            noiseResult  = math.clamp(noiseResult  + 0.5 , 0, 1)

            -- It needs the tile to be an object, if you dont want that, instance a base part here
            local tile = aTile.Asset:Clone()
            tile.Size = Vector3.new(self.TileSize, self.TileSize, self.TileSize)
            tile.Position = Vector3.new(i * tile.Size.X, tile.Size.Y, j * tile.Size.Z)
            tile.Name = fallOff

            tile.Color = Color3.new(noiseResult , noiseResult , noiseResult )
            tile.Parent = workspace
        end
    end

    return self
end