Linetest Plane

A Line segment represented by end points A and B can be parametrically expressed as follows:

S(t) = A + t(B-A) where

We can check if a line segment intersects a Plane by substituting the parametric equation of the Line into the Plane equation. If any point along the line at time t exists that satisfies the Plane equation, the Line segment and Plane intersect:

Getting ready

We are going to implement a function to test if a Line segment and a Plane intersect. This function will return a Boolean result.

How to do it…

Follow these steps to implement line testing against a plane:

1. Declare the Linetest function in Geometry3D.h:

   bool Linetest(const Plane& plane, const Line& line);

2. Implement the Linetest function in Geometry3D.cpp:

   bool Linetest(const Plane& plane, const Line& line) {
      vec3 ab = line.end - line.start;
   
      float nA = Dot(plane.normal, line.start);
      float nAB = Dot(plane.normal, ab);
   
      // If the line and plane are parallel, nAB will be 0
      //...