A hierarchical factorization method for efficient radiosity calculations. (November 2016)

• Record Type: Journal Article
• Authors: Aguerre, José Pedro; Fernández, Eduardo
• Is Part Of: Computers & graphics. Volume 60(2016)
• Page Start: 46
• Page End: 54
• Publication Date: 2016-11
• Subjects: Computer graphics -- Periodicals; 006.6
• DOI: 10.1016/j.cag.2016.08.003
• Languages: English
• ISSNs: 0097-8493

Abstract

Abstract: The radiosity problem can be expressed as a linear system, where light interactions between patches of the scene are considered. Its resolution has been one of the main subjects in Computer Graphics, which has led to the development of methods focused on different goals. For instance, in inverse lighting problems, it is convenient to solve the radiosity equation thousands of times for static geometries. Also, this calculation needs to consider many (or infinite) light bounces to achieve accurate global illumination results. Several methods have been developed to solve the linear system by finding approximations or other representations of the radiosity matrix, because the full storage of this matrix is memory demanding. Some examples are hierarchical radiosity, progressive refinement approaches, or wavelet radiosity, which may become slow for many bounces. Recently, new direct methods have been developed based on matrix factorization. This paper introduces a novel and efficient error-bounded factorization method based on the use of multiple singular value decompositions and the Z-order curve to sort the patches of the model. This technique accelerates the factorization of in-core matrices, and allows to work with out-of-core matrices passing only one time over them. Using this method, the inverse of the radiosity matrix can be efficiently approximated, reducing the memory and time resources needed to compute radiosity with infinite bounces. In the experimental analysis, the presented method is applied to scenes up to 163 K patches. After a precomputation stage, it is used to solve the radiosity problem for fixed geometries at interactive times. Abstract : Graphical abstract: Abstract : Highlights: A new method to factorize the radiosity matrix using a hierarchical strategy. The use of the Z-order curve to accelerate the factorization. Factorization of radiosity matrices that do not fit into system memory. Accurate radiosity calculations at interactive rates for static scenes.