struct Quaternion
	i::Float64
	j::Float64
	k::Float64
	r::Float64
	
	Quaternion(i, j, k, r) = norm([i, j, k, r]) ≈ 1 ? new(i, j, k, r) : error("Magnitude not equal to 1.") 
	Quaternion(q) = Quaternion(q[1], q[2], q[3], q[4]) 
	Quaternion() = new(0, 0, 0, 1)
	
	Quaternion(yaw, pitch, roll) = Quaternion([0 0 sin(yaw / 2) cos(yaw / 2)]) * Quaternion([0 sin(pitch / 2) 0 cos(pitch / 2)]) * Quaternion([sin(roll / 2) 0 0 cos(roll / 2)])
	
	function Quaternion(ē, ϕ)
		if sum(ē) == 0
			return Quaternion([0 0 0 cos(ϕ / 2)])
		end
		dir = normalize(ē) * sin(ϕ / 2)
		return Quaternion(dir[1], dir[2], dir[3], cos(ϕ / 2))
	end
	
end

function QuaternionMultiplication(l::Quaternion, r::Quaternion)
	R = [r.r r.k r.j r.i;
		 -r.k r.r r.i r.j;
		 r.j -r.i r.r r.k;
		 -r.i -r.j -r.k r.r]
	L = [l.i; l.j; l.k; l.r]
	return Quaternion(R * L)
	
end

Base.:*(l::Quaternion, r::Quaternion) = QuaternionMultiplication(l::Quaternion, r::Quaternion)

Base.iterate(q::Quaternion, state=1) = state > 4 ? nothing : (collect(q)[state], state + 1)
Base.length(q::Quaternion) = 4
Base.collect(q::Quaternion) = [q.i q.j q.k q.r]
Base.getindex(q::Quaternion, i) = collect(q)[i]
Base.isapprox(a::Quaternion,b::Quaternion) = isapprox(collect(a), collect(b))

LinearAlgebra.norm(q::Quaternion) = norm(collect(q))
LinearAlgebra.normalize(q::Quaternion) = collect(q) / norm(q)

export Quaternion