Triangle to sphere

To test if a sphere and a triangle intersect, we must first find the point on the triangle that is closest to the center of the sphere. If the distance between the center of the sphere and the closest point is less than the radius of the sphere, we have an intersection:

Getting ready

We are about to implement a function that tests if a triangle and sphere intersect. This function will return a Boolean result. We avoid the expensive square root operation involved in finding distance by checking squared distance against squared radius.

How to do it…

Follow these steps to implement a test for checking if a triangle and sphere intersect:

1. Declare the TriangleSphere function in Geometry3D.h:

   bool TriangleSphere(const Triangle& t, const Sphere& s);

2. Declare the SphereTriangle convenience macro in Geometry3D.h:

   #define SphereTriangle(s, t) \
       TriangleSphere(t, s)

3. Implement the TriangleSphere function in Geometry3D.cpp:

   bool TriangleSphere(const Triangle& t, const Sphere...