In computer graphics we sometimes need to determine which half-space a point is located in with regards to a plane. Perhaps the most common application of this is frustum culling, where we need to resolve whether a point lies within the camera frustum by testing against all of the frustum’s planes. Mathematical Formulation For a given point \(m\) and a plane \(P\) defined by a normal vector \(\vec{N}\) and a point \(x\) on \(P\), test which half-space \(m\) lies in. Solution The derivation ...
