## AABB-to-OBB

Testing if an AABB and an OBB overlap can be done using the **Separating Axis Theorem** (**SAT**). This test will require a total of 15 axes to be tested. Chapter 5, *2D Collisions*, provides an in-depth explanation of how the SAT works. The 15 axes of potential separation are:

The three axes of the AABB (world X, Y, and Z)

The three axes of the OBB (the OBB's orientation matrix)

9 axes come from the cross-products of the three axes of the AABB and the three axes of the OBB. We take the cross product of every combination of these axes. Lists these nine combinations:

AABB.XAxis x OBB.XAxis

AABB.YAxis x OBB.XAxis

AABB.ZAxis x OBB.XAxis

AABB.XAxis x OBB.YAxis

AABB.YAxis x OBB.YAxis

AABB.ZAxis x OBB.YAxis

AABB.XAxis x OBB.ZAxis

AABB.YAxis x OBB.ZAxis

AABB.ZAxis x OBB.ZAxis

Remember, the two shapes only overlap if all 15 axes overlap. If there is a single axis of separation, no intersection can happen.

### Getting ready

Because this is our first 3D SAT test, there is some groundwork to cover...