Verifies that a CFrame is a valid rotation matrix

ValidateRotation.lua

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

	function validateRotation(cf)
		cf = cf - cf.p

		local rx = cf.rightVector
		local ry = cf.upVector
		local rz = -cf.lookVector

		-- verify columns are unit length
		assertEq(rx.magnitude, 1)
		assertEq(ry.magnitude, 1)
		assertEq(rz.magnitude, 1)

		-- verify orthonormal basis
		assert(dot(rz, cross(rx, ry)) > 1 - EPS)
		assert(dot(rx, cross(ry, rz)) > 1 - EPS)
		assert(dot(ry, cross(rz, rx)) > 1 - EPS)

		-- verify r*r^T == I
		local _, _, _,
			qxx, qyx, qzx,
			qxy, qyy, qzy,
			qxz, qyz, qzz = (cf*cf:inverse()):components()
		
		assertEq(qxx, 1)
		assertEq(qxy, 0)
		assertEq(qxz, 0)

		assertEq(qyx, 0)
		assertEq(qyy, 1)
		assertEq(qyz, 0)

		assertEq(qzx, 0)
		assertEq(qzy, 0)
		assertEq(qzz, 1)

		print("Tests passed")
	end
end