This document discusses four cases for determining the closest point on an axis-aligned bounding box (AABB) to an input point P. Case 1 is when P is inside the box, in which the closest point is simply P. Case 2 is when P is near a face of the box, in which clamping P orthogonally projects it onto the closest face. Case 3 is when P is near a vertex, in which clamping yields that vertex. Case 4 is when P is near an edge, in which clamping orthogonally projects P onto that edge.