Point in triangle

We already have a definition for Triangle in Geometry3D.h, we implemented this primitive in Chapter 7, 3D Primitive Shapes . The first operation we want to perform on a triangle is testing for point containment. The containment test works by moving the triangle into the point's local space, then constructing a pyramid out of the triangle and the point. If the pyramid is flat, the point is inside the triangle. If it's not, the point is outside.

Getting ready

We are about to implement a function that will test if a point falls inside of a triangle. This function will return a simple boolean result.

How to do it…

Follow these steps to implement a point in triangle test:

1. Declare the PointInTriangle function in Geometry3D.h:

   bool PointInTriangle(const Point& p, const Triangle& t);

2. Implement the PointInTriangle function in Geometry3D.cpp:

   bool PointInTriangleNormals(const Point& p, 
   const Triangle& t) {

3. Create a temporary triangle with the size of our...