luau-poisson-disc-sampling.luau

--[[

Copyright 2024 Cameron Campbell

Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the “Software”), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions:

The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software.

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]]

--!strict
--!native
--!optimize 2

local function PositionToIndex(rows: number, cols: number)
	return function(x: number, y: number)
		return (x - 1) * cols + y
	end
end

-- Checks To If A Point Intersects The Radius Of Another Point.
local function IsValid(
	rows: number, cols: number,
	regionX: number, regionZ: number,
	cellSize: number,
	radius: number, points: { Vector3 }, grid: { number },
	positionToIndex: (x: number, y: number) -> number
)
	return function(candidate: Vector3): boolean
		local candidateX, candidateZ = candidate.X, candidate.Z

		if candidateX >= 0 and candidateZ >= 0 and candidateX < regionX and candidateZ < regionZ then
			local cellX, cellZ = math.floor(candidateX / cellSize), math.floor(candidateZ / cellSize)
			local searchStartX, searchEndX = math.max(0, cellX - 2), math.min(cellX + 2, rows - 1)
			local searchStartZ, searchEndZ = math.max(0, cellZ - 2), math.min(cellZ + 2, cols - 1)

			for x = searchStartX, searchEndX do
				for z = searchStartZ, searchEndZ do
					local pointIndex = grid[positionToIndex(x + 1, z + 1)] - 1

					if pointIndex ~= -1 and (candidate - points[pointIndex + 1]).Magnitude < radius then
						return false
					end

				end
			end

			return true
		end

		return false
	end
end


return function(radius: number, region: Vector3, samples: number, random: Random)
	local cellSize = radius / math.sqrt(2)
	local regionX, regionZ = region.X, region.Z

	local rows, cols = math.ceil(regionX / cellSize), math.ceil(regionZ / cellSize)
	local grid: { number } = table.create(rows * (cols+1), 0)
	local points: { Vector3 } = {}
	local spawnPoints: { Vector3 } = {}

	local positionToIndex = PositionToIndex(rows, cols)
	local isValid = IsValid(rows, cols, regionX, regionZ, cellSize, radius, points, grid, positionToIndex)

	table.insert(spawnPoints, region/2)
	while #spawnPoints > 0 do
		local spawnIndex = random:NextInteger(1, #spawnPoints)
		local spawnCentre = spawnPoints[spawnIndex]
		local candidateAccepted = false

		for count = 1, samples do
			local angle = random:NextNumber() * math.pi * 2
			local dir = Vector3.new(math.sin(angle), 0, math.cos(angle))
			local candidate = spawnCentre + dir * random:NextInteger(radius, 2*radius)

			if isValid(candidate) then
				table.insert(points, candidate)
				table.insert(spawnPoints, candidate)
				grid[positionToIndex(math.ceil(candidate.X / cellSize), math.ceil(candidate.Z / cellSize))] = #points
				candidateAccepted = true
				break
			end

		end

		if not candidateAccepted then
			table.remove(spawnPoints, spawnIndex)
		end
	end

	return points
end

Example Usage

PoissonDiscSampling(
    30,   -- Radius between points.
    Vector3.new(150, 0, 150),   -- The 2d region to place points in (uses Vector3 as they are faster than Vector2).
    150,   -- The number of samples to take (Higher = More precise but slower).
    Random.new()  -- The `Random` object to use.
)