Radar Approach – Testing Points II

Up to this point the required computations to compute the value of p in the camera referential coordinates, pc have been detailed. It is also assumed at this point that the pc.z has a value that is between nearDist and farDist, so its time to check the other coordinates, namely pc.y and pc.x.

Consider now a side view of the frustum in 2D to simplify the diagram. The horizontal arrow shows the value of pc.z. At that distance from the camera, pc.z the view frustum has a height h.

where a is the vertical field of view angle.

This implies that, for the Y coordinate of pc to be inside the view frustum,

	-h/2 < pc.y <  h/2

or, in algorithmic style,

	if (-h/2 > pc.y || pc.y  >  h/2)
		return(OUTSIDE)

The width of the frustum can be computed based on the height as

	w = h * ratio;

So the X component of pc can be tested with the following if statement:

	if (-w/2 > pc.x || pc.x  >  w/2)
		return(OUTSIDE)

The following figure, although a little bit complex ( ;-> ) provides some information about the components of pc.

This method should be faster than the previous approaches where six planes are tested. In here, only a dot product is performed for each pair of planes, whereas in the previous approaches a dot product was performed for every plane, in the worst case scenario. See the next section for an implementation.