init commit

src/AstroHelper.jl

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+module AstroHelper
+using LinearAlgebra
+
+
+include("Quaternions.jl")
+
+end # module

src/Quaternions.jl

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+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(ē, ϕ) = Quaternion(vcat(if sum(ē) == 0 ? [0 0 0] : ē / norm(ē) * sin(ϕ / 2),cos(ϕ / 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) = (q.i, 1)
+Base.iterate(q::Quaternion, state=1) = state > 4 ? nothing : ([q.i q.j q.k q.r][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)
+# q = Quaternion([1,-2,2], -2 * pi / 3) * Quaternion([0,0,0,1])
+
+# println(q[3])