Education, Artificial Intelligence, Computer Vision.
wrt the standard orthonormal basis and let (𝑥′, 𝑦′) be its coordinates wrt the skewed basis. Our goal is to find (𝑥′, 𝑦′). From the above figure, cos(90−θ) = y/y′ ⟹ sinθ = y/y′ ⟹ y = y′sinθ ⟹ y′= y / sinθ also, sin(90−θ) = (x - x′)/y′ ⟹ y′cosθ = x - x′ ⟹ x′ = x - y′cosθ but, y′= y / sinθ ⟹ x′ = x -