Adaptive Supersampling in Object Space Using Pyramidal Rays

We introduce a new approach to three important problems in ray tracing: antialiasing, distributed light sources, and fuzzy reflections of lights and other surfaces. For antialiasing, our approach combines the quality of supersampling with the advantages of adaptive supersampling. In adaptive supersampling, the decision to partition a ray is taken in image-space , which means that small or thin objects may be missed entirely. This is particularly problematic in animation, where the intensity of such objects may appear to vary. Our approach is based on considering pyramidal rays (pyrays) formed by the viewpoint and the pixel. We test the proximity of a pyray to the boundary of an object, and if it is close (or marginal), the pyray splits into 4 sub-pyrays; this continues recursively with each marginal sub-pyray until the estimated change in pixel intensity is sufficiently small.
The same idea also solves the problem of soft shadows from distributed light sources, which can be calculated to any required precision. Our approach also enables a method of defocusing reflected pyrays, thereby producing realistic fuzzy reflections of light sources and other objects. An interesting byproduct of our method is a substantial speedup over regular supersampling even when all pixels are supersampled. Our algorithm was implemented on polygonal and circular objects, and produced images comparable in quality to stochastic sampling, but with greatly reduced run times.