Point In Frustum

Perhaps the easyest frustum test to perform is the Point In Frustum test. Actually, we've implemented this functionality before. The only difference is, now we will formally include it in our collision library.

The Algorithm

The algorithm here is simple, it's essentially just a half-space test. A half space test is very similar to the DistanceFromPlane function we wrote, except instead of adding plane.Distance at the end, we subtract it. Once you can do a half-space test, doing the actual intersection is easy, loop trough all of the frustum planes, and do a half space test between the point and each plane. If any of the half space tests are less than 0, return false immediateley. IF they are all 0 or greater you can return true by default.

On Your Own

Add the following function to the Collisions class:

public static float HalfSpaceTest(Point point, Plane plane) {
    // TODO: Implement this!
}

public static bool Intersects(Plane[] frustum, Point point) {
    // TODO: Implement this!
}

public static bool Intersects(Point point, Plane[] frustum) {
    return Intersects(frustum, point);
}

And provide an implementation for it!

Unit Test

Add the following unit test at the end of the Initialize function in CameraSample.

if (!Collisions.Intersects(new Point(), camera.Frustum)) {
    System.Console.WriteLine("Error with point in frustum! 0");
}
if (Collisions.Intersects(new Point(-5000,-5000,-5000), camera.Frustum)) {
    System.Console.WriteLine("Error with point in frustum! 1");
}
if (!Collisions.Intersects(new Point(2, 30, 4), camera.Frustum)) {
    System.Console.WriteLine("Error with point in frustum! 2");
}