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...