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Theory and Application of Specular Path Perturbation

Summary: Theory and Application
of Specular Path Perturbation
Min Chen James Arvo
California Institute of Technology
January 30, 2001
In this paper we apply perturbation methods to the problem of computing specular
reflections in curved surfaces. The key idea is to generate families of closely related op­
tical paths by expanding a given path into a high­dimensional Taylor series. Our path
perturbation method is based on closed­form expressions for linear and higher­order
approximations of ray paths, which are derived using Fermat's Variation Principle
and the Implicit Function Theorem. The perturbation formula presented here holds
for general multiple­bounce reflection paths and provides a mathematical foundation
for exploiting path coherence in ray tracing acceleration techniques and incremental
rendering. To illustrate its use, we describe an algorithm for fast approximation of
specular reflections on curved surfaces; the resulting images are of high accuracy and
nearly indistinguishable from ray traced images.
Keywords: perturbation theory, implicit surfaces, optics, ray tracing, specular re­


Source: Arvo, Jim - Departments of Information and Computer Science & Electrical and Computer Engineering, University of California, Irvine


Collections: Computer Technologies and Information Sciences