Triangle to Axis Aligned Bounding Box

We can implement a Triangle to Axis Aligned Bounding Box (AABB) intersection test using the Separating Axis Theorem. There will be a total of 13 axes to test. These axes are:

• Three face normals of the AABB
• One face normal from the Triangle
• Nine cross products of the edges of each primitive
  

Getting ready

We can use the existing GetInterval function of the AABB. We have to write a new GetInterval function for the triangle. We also have to write a new OverlapOnAxis function to test for triangle to AABB overlap. Finally, we have to implement the actual SAT test.

How to do it…

Follow these steps to check if an AABB and triangle intersect:

1. Declare all three of the new functions in Geometry3D.h:

   Interval GetInterval(const Triangle& triangle, vec3& axis);
   bool OverlapOnAxis(const AABB& aabb, 
      const Triangle& triangle, const vec3& axis);
   bool TriangleAABB(const Triangle& t, const AABB& a);

2. Create a convenience macro in Geometry3D...