Fraktality

-- Given a knot sequence p[1<=i<=n], solve for a sequence of cubic
-- splines s[1<=i<=n-1] such that the square of acceleration is minimized.

local gamma = {
	0.50000000000000000, 0.28571428571428571, 0.26923076923076923, 0.26804123711340206,
	0.26795580110497238, 0.26794966691339748, 0.26794922649742166, 0.26794919487697295,
	0.26794919260672685, 0.26794919244373052, 0.26794919243202791, 0.26794919243118770,
	0.26794919243112737, 0.26794919243112304, 0.26794919243112273, 0.26794919243112271,
}
local gammaLimit = gamma[#gamma]

Fraktality

--[[
local fooInterlock = Interlock.new()

function foo()
	local lock = fooInterlock:takeLock()

	coroutine.yield()
	
	if not lock:hasLock() then
		return

Fraktality

-- Perform a breadth first traversal of an instance's descendant tree.
--
-- >  for obj in scanBF(root) do
-- >     print(obj)
-- >  end

local function scanBF(root)
	local queue = {} -- Queue containing stacks of children
	local qIdx0 = 1 -- Queue front index
	local qIdx1 = 0 -- Queue back index

Fraktality

local Connection = {} do
	Connection.__index = Connection

	function Connection.new(hook, signal)
		return setmetatable({
			_hook = hook,
			_signal = signal,
			_connected = true,
		}, Connection)
	end

Fraktality

local RunService = game:GetService("RunService")

-- compile an oriented bounding box into a scaled CFrame
local function compileBBox(cframe: CFrame, size: Vector3)
	return CFrame.fromMatrix(
		cframe.Position,
		cframe.XVector/size.X,
		cframe.YVector/size.Y,
		cframe.ZVector/size.Z
	):Inverse()

Fraktality

local function bbox(part)
	local size = part.Size
	local inv = part.CFrame:inverse()

	local wx = size*inv.XVector
	local wy = size*inv.YVector
	local wz = size*inv.ZVector

	return Vector3.new(
		math.abs(wx.x) + math.abs(wx.y) + math.abs(wx.z),

Fraktality

local pi    = math.pi
local abs   = math.abs
local atan2 = math.atan2
local cos   = math.cos
local sqrt  = math.sqrt
local sign  = math.sign

local EPS = 1e-9

local function cbrt(x)

Fraktality

local function waitForFirst(...)
	local shunt = Instance.new("BindableEvent")
	local slots = {...}
	
	local function fire(...)
		for i = 1, #slots do
			slots[i]:Disconnect()
		end
		return shunt:Fire(...)
	end

Fraktality

local validateRotation do
	local dot = Vector3.new().Dot
	local cross = Vector3.new().Cross
	local abs = math.abs

	local EPS = 1e-4

	local function assertEq(value, expected)
		assert(abs(value - expected) < EPS)
	end

Fraktality

-- Various ways of testing a screen point against a GuiBase2d
-- Note: Rounded rect corner radius is inferred from SliceCenter.Min.X

local cos = math.cos
local min = math.min
local rad = math.rad
local sin = math.sin

return {
	-- Axis-aligned rectangle