Comparison of Finite Element Bases for Global Illumination in Image Synthesis

Finite element bases defined by sampling points were used by J. Lehtinen in 2008 for the efficient computation of global illumination in virtual scenes. The bases provide smooth approximations for the radiosity and spontaneous emission functions, leading to a discrete version of Kajiya´s rendering equation. Unlike methods that are based on surface subdivision, Lehtinen´s method can cope with arbitrarily complex geometries. In this paper we present an experimental validation of Lehtinen´s meshless method by comparing its results with an independent numerical solution of the rendering equation on a simple three-dimensional scene. We also compare Lehtinen´s special finite-element basis with two other similar bases that are often used for meshless data interpolation, namely a radial basis with a Gaussian mother function, and Shepard´s inverse-square-distance weighted interpolation. The results confirm the superiority of Lehtinen´s basis and clarify why the other two bases provide inferior-looking results.