Computing a View Frustum to Maximize an Object's Image Area

This paper presents a method to compute a view frustum for a 3D object viewed from a given viewpoint, such that the object is completely enclosed in the frustum and the object’s image area is also near-maximal in the given 2D rectangular viewing region. This optimization can be used to improve the resolution of shadow maps and texture maps for projective texture mapping. Instead of doing the optimization in 3D space to find a good view frustum, our method uses a 2D approach. The basic idea of our approach is as follows. First, from the given viewpoint, a conveniently-computed view frustum is used to project the 3D vertices of the object to their corresponding 2D image points. A tight 2D bounding quadrilateral is then computed to enclose these 2D image points. Next, considering the projective warp between the bounding quadrilateral and the rectangular viewing region, our method applies a technique of camera calibration to compute a new view frustum that generates an image that covers the viewing region as much as possible.