Question

I want to check a view frustum against the axis aligned bounding boxes of some objects, to check roughly whether those objects are in the field of view or not. Speed is not a big deal.

Answer 1

I figured out that building a world-space model of the view frustum and checking for bbox collisions with it was the wrong way to go about this.

A much simpler method is to go the opposite way and convert each vertex of a given bbox to screen-space, and if any vertex of the bbox is within the screen bounds then count that bbox as visible. I get the screen-space position by multiplying against the camera matrix and then accounting for perspective based on the field of view of the camera.

Here’s the code:

vertexMatrix = matrix([vertex.x,vertex.y,vertex.z,1]) 
productMatrix = (vertexMatrix * camMatrix)
pVectSS = vector(prodMatrix[0][0],prodMatrix[0][1],prodMatrix[0][2])

pointX = ((pVectSS.x/(-pVectSS.z))/tan(radians(hFOV/2)))/2.0+.5
pointY = ((pVectSS.y/(-pVectSS.z))/tan(radians(vFOV/2)))/2.0+.5

key:

 camMatrix = camera inverse world-space matrix
 pVectSS = position vector screen-space
 hFOV = horizontal field of view
 vFOV = vertical field of view