Integration Methods for Galerkin Radiosity Couplings

Computing energy transfer between objects is the most expensive operation in radiosity systems. This energy transfer operation, known as the irradiance operator, is an integral that, in general, must be calculated numerically. We perform a study of numerical integration techniques to increase the speed of this computation without severely compromising fidelity. A theoretical discussion of numerical integration is presented followed by details of the studied methods. The results of our study give us insight into greatly reducing the cost of the irradiance operator while maintaining accuracy. An adaptive method for choosing Gauss quadrature rules is presented, and our performance analysis of the new adaptive algorithm shows that it can be up to 10 times faster than previous methods. 1 Introduction The radiosity equation can be written as a simplification of the rendering equation, introduced by Kajiya [8], by assuming that all surfaces are perfectly diffuse (Lambertian): B(x) ..