Cheap bounding-volume tests reject most pairs; only the survivors get the exact, more expensive polygon test. Shown in 2D, because the idea is the same in 3D. Companion to notes/09.
Grey outlines are bounding volumes. Orange: the bounding volumes overlap but the shapes do not, a false positive the exact test must clean up. Red: a real collision, found with the separating axis theorem. Each body's polygon is stored once in local coordinates and placed with a model matrix, and the collision test uses exactly the same matrix.