Fast Radiosity Solutions for Environments with High Average Reflectance

In radiosity algorithms the average radiance of Lambertian patches is approximated by solving a linear system with unknowns. When is small (i.e. fewer than thousands of patches), general matrix methods like Gauss-Siedel can be used where the explicit matrix can be pre-computed and stored [5]. When is large, progressive techniques are used where the matrix rows or elements are recomputed as needed [4]. When is very large (i.e. hundreds of thousands of patches), stochastic techniques can avoid computing or storing the elements of the matrix [10]. In applications where is small enough to store the entire matrix in main memory, general matrix techniques will be faster than progressive techniques . For “massing studies” [8] the lighting can be examined on simple geometric approximations of the environment being designed, and can be very small. When the color scheme and lighting are being designed, the computationally expensive part (form factors) of the matrix in the linear system can be reused as the material properties are changed. For these applications the fastest possible general matrix solution is desirable. This paper examines the Chebyshev method for solving linear systems, which for environments with high average reflectance can converge faster than the methods usually used in radiosity problems. We discuss some important characteristics of the linear systems in radiosity applications. We also look for solution methods that converge in small amounts of time, as opposed to a small number of iterations. For this discussion we assume a conventional RISC architecture, where coherent memory access is vital.