Theoretical Developments on Polygonal Approximation of Parametric Surfaces for Ray Tracing

Abstract

Some theoretical extensions are brought to Koparkar and Mudur s method which deals with a polygonal approximation of parametric surfaces using potential extrema. The proposed extensions allow the determination of both the existence and the equation of a curve solution of potential extrema. Solutions are given to solve the crack problem and to avoid the artificats due to an inexact ray-surface intersection point near the silhouette or on the higher curvature regions. Moreover, two methods of ray tracing surfaces are proposed.