A Geometrical Approach to Modeling Reflectance Functions of Diffracting Surfaces

Modeling light reflection off surfaces, although extensively studied in computer graphics, remains a challenging problem when simulating wave phe- nomena. In particular, diffraction has received little attention until very r ecently, when an analytical model based on the wave theory of light was proposed (24). It is commonly believed in the computer graphics community that diffraction phenomena cannot be captured using a ray-based theory of light. However, an extension to geometrical optics, known as the Geometrical Theory of Diffraction (GTD), was introduced in 1962, giving a solution to the problem. In this paper, we give an introduction to the GTD and show that this theory can be successfully used to derive procedural shaders for simple diffracting sur- faces. We also discuss how the GTD can be integrated into a ray-based virtual gonio-spectro-photometer to derive Bidirectional Reflectance Distribution Func- tions incorporating diffraction effects for more general types of surfaces.

[1]  Ulrich J. Kurze,et al.  Noise reduction by barriers , 1973 .

[2]  James T. Kajiya,et al.  Anisotropic reflection models , 1985, SIGGRAPH.

[3]  Gary W. Meyer,et al.  Light Scattering Simulations using Complex Subsurface Models , 1997, Graphics Interface.

[4]  Gary W. Meyer,et al.  Wavelength dependent reflectance functions , 1994, SIGGRAPH.

[5]  A. Rajkumar,et al.  Predicting RF coverage in large environments using ray-beam tracing and partitioning tree represented geometry , 1996, Wirel. Networks.

[6]  J. Keller,et al.  Geometrical theory of diffraction. , 1962, Journal of the Optical Society of America.

[7]  Derek A. McNamara,et al.  Introduction to the Uniform Geometrical Theory of Diffraction , 1990 .

[8]  Jos Stam,et al.  Diffraction shaders , 1999, SIGGRAPH.

[9]  Lawrence B. Wolff,et al.  Ray tracing with polarization parameters , 1990, IEEE Computer Graphics and Applications.

[10]  Karl K. Turekian,et al.  Academic press, inc. , 1995, Environmental science & technology.

[11]  Pierre Poulin,et al.  A model for anisotropic reflection , 1990, SIGGRAPH.

[12]  Stephen H. Westin,et al.  Predicting reflectance functions from complex surfaces , 1992, SIGGRAPH.

[13]  R. Kouyoumjian,et al.  A uniform geometrical theory of diffraction for an edge in a perfectly conducting surface , 1974 .

[14]  Gregory J. Ward,et al.  Measuring and modeling anisotropic reflection , 1992, SIGGRAPH.

[15]  Nelson L. Max,et al.  Bidirectional reflection functions from surface bump maps , 1987, SIGGRAPH.

[16]  Gary W. Meyer,et al.  Newton’s Colors: Simulating Interference Phenomena in Realistic Image Synthesis , 1992 .

[17]  Pat Hanrahan,et al.  Reflection from layered surfaces due to subsurface scattering , 1993, SIGGRAPH.

[18]  Donald P. Greenberg,et al.  A comprehensive physical model for light reflection , 1991, SIGGRAPH.

[19]  T. Senior,et al.  Experimental detection of the edge-diffraction cone , 1972 .

[20]  W. Welford.  Principles of optics (5th Edition): M. Born, E. Wolf Pergamon Press, Oxford, 1975, pp xxviii + 808, £9.50 , 1975 .

[21]  Reinaldo A. Valenzuela,et al.  Radio propagation measurements and prediction using three-dimensional ray tracing in urban environments at 908 MHz and 1.9 GHz , 1999 .

[22]  David Irvine Laurensen.  Indoor radio channel propagation modelling by ray tracing techniques , 1994 .

[23]  Emil Wolf,et al.  Principles of Optics: Contents , 1999 .

[24]  Michael J. Wozny,et al.  Polarization and birefringency considerations in rendering , 1994, SIGGRAPH.

[25]  Maria Lurdes Dias.  Ray tracing interference color , 1991, IEEE Computer Graphics and Applications.

[26]  T. Kawai.  Sound diffraction by a many-sided barrier or pillar , 1981 .

[27]  John F. Canny,et al.  New lower bound techniques for robot motion planning problems , 1987, 28th Annual Symposium on Foundations of Computer Science (sfcs 1987).

[28]  Peter Schröder,et al.  Spherical wavelets: efficiently representing functions on the sphere , 1995, SIGGRAPH.