title: Barycentric parameterizations for isotropic BRDFs.
abstract: A bidirectional reflectance distribution function (BRDF) is often expressed as a function of four real variables: two spherical coordinates in each of the the "incoming" and "outgoing" directions. However, many BRDFs reduce to functions of fewer variables. For example, isotropic reflection can be represented by a function of three variables. Some BRDF models can be reduced further. In this paper, we introduce new sets of coordinates which we use to reduce the dimensionality of several well-known analytic BRDFs as well as empirically measured BRDF data. The proposed coordinate systems are barycentric with respect to a triangular support with a direct physical interpretation. One coordinate set is based on the BRDF model proposed by Lafortune. Another set, based on a model of Ward, is associated with the "halfway" vector common in analytical BRDF formulas. Through these coordinate sets we establish lower bounds on the approximation error inherent in the models on which they are based. We present a third set of coordinates, not based on any analytical model, that performs well in approximating measured data. Finally, our proposed variables suggest novel ways of constructing and visualizing BRDFs.
authors.affiliation: Department of Information and Computer Science, University of California, Irvine, Irvine, CA 92697-3425, USA. mstark@ics.uci.edu
authors.forename: Michael M
authors.initials: MM
authors.lastname: Stark
authors.forename: James
authors.initials: J
authors.lastname: Arvo
authors.forename: Brian
authors.initials: B
authors.lastname: Smits
mesh_terms: D000465:Algorithms; D016880:Anisotropy; D003196:Computer Graphics; D003198:Computer Simulation; D007089:Image Enhancement / Q000379:methods*; D007090:Image Interpretation, Computer-Assisted / Q000379:methods*; D021621:Imaging, Three-Dimensional / Q000379:methods*; D016247:Information Storage and Retrieval / Q000379:methods*; D008962:Models, Theoretical; D009716:Numerical Analysis, Computer-Assisted; D012815:Signal Processing, Computer-Assisted; D013382:Subtraction Technique; D014584:User-Computer Interface