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 ...

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