(A) parametric surface ray intersection technique

Abstract

Ray tracing is one of the most powerful techniques in computer gasphics. Many phenomena that are difficult or impossible with other techniques are simply handled with ray tracing, including shadows, reflections and refractions. The central of any ray tracing algorithms is the calculation of ray and object intersecion. In this thesis, we propose a new method to calculate the intersection of ray and parametric surface. This method solves the ray surface intersection directly using multivariate Newton iteration and overcomes the problem of initial guess for Newton iteration by interval analysis. Using hierarchical regular subdivision for parametric space, previously computed informations can be reused and substantial computation time is saved. This method is used for all kinds of parametric surface of which computation is bounded for surface and its partial derivatives. It is easily extended to many rendering applications of free form surface.