Point and plane

We have seen the plane equation before; a point is on a plane if the result of the plane equation is 0. To find the point on the plane closest to a test point, we must project the test point onto the normal of the plane. We then subtract this new vector from the test point to get the closest point:

Getting ready

We are going to implement two functions. The first function will test whether a point is on the surface of a plane using the plane equation. The second function will find the point on a plane closest to a given test point.

How to do it…

Perform the following steps to implement point tests for a plane:

1. Declare PointOnPlane and ClosestPoint in Geometry3D.h:

   bool PointOnPlane(const Point& point, const Plane& plane);
   Point ClosestPoint(const Plane& plane, const Point& point);

2. Implement PointOnPlane in Geometry3D.cpp:

   bool PointOnPlane(const Point& point, const Plane& plane) {
       float dot = Dot(point, plane.normal);
       // To make this more robust, use...