How do I find the areas of the three projections (onto the xy, xz, and yz planes) of a rectangular prism, given it's dimensions (L, W, H), and θ and ϕ (conventional spherical angles of its rotation)?
Say when θ = 0 and ϕ = 0, L aligns with the x-axis, W with y, and H with z.
Simple problem, tough solution.