Triangle to plane

There are two scenarios in which a triangle and plane intersect:

• Not every point of the triangle is on the same side of the plane
• Every point of the triangle is on the plane
  

Getting ready

We are going to implement the TrianglePlane function to test for intersection between a triangle and a plane. This function will use our existing PlaneEquation function to classify which side of the plane the triangle is on.

How to do it…

Follow these steps to test if a triangle and a plane intersect:

1. Declare the new TrianglePlane function in Geometry3D.h:

   bool TrianglePlane(const Triangle& t, const Plane& p);

2. Declare a convenience macro in Geometry3D.h:

   #define PlaneTriangle(p, t) \
       TrianglePlane(t, p)

3. Implement the TrianglePlane function in Geometry3D.cpp:

   bool TrianglePlane(const Triangle& t, const Plane& p) {

4. Check which side of the plane every point of the triangle is on:

       float side1 = PlaneEquation(t.a, p);
       float side2 = PlaneEquation(t.b, p);
       float side3...