Rational z-buffer for decreasing a likelihood of z-buffer collisions

Abstract

A 'Rational Z-Buffer' provides various techniques for reducing artifacts when rendering graphics using z-buffers. In particular, the Rational Z-Buffer reduces the likelihood of z-buffer collisions when using hardware or software z-buffer algorithms to render graphics by delaying homogenous division of pixels until after occlusion testing. Further, occlusion testing between any two pixels, pand p, is accomplished by comparing rational depth values, r={z, w} and r={z, w}, for pixel pand pto determine which pixels are visible. Depth values are compared by determining whether the expression zw<zwis true. If true, then pixel poccludes pixel pin clipping cube space relative to an image-plane defined by a particular viewpoint and the field of view. Further, since homogeneous division by w is not performed prior to occlusion testing, rational depth values are uniformly distributed clipping-cube space, thereby significantly reducing potential z collisions relative to conventional z-buffer testing.