ON SUPERCONVERGENT SPLINE COLLOCATION METHODS FOR THE RADIOSITY EQUATION
Sanda Micula · 2006
In this paper we study collocation methods based on piecewise polynomial interpolation for the radiosity equation. We give a brief outline of this equation and its properties. With a special choice of interior nodes, we show that interpolation of degree r of the solution leads to an error in the collocation method of O h r+1 , where h is the mesh size of the triangulation. We conclude the paper by giving superconvergence results, considering separately the case where r is odd and the case where r is even. 1. The radiosity equation Radiosity is a method of describing illumination based on a detailed analysis of light reflections o diuse surfaces. It is typically used to render images of the interior of buildings. In computer graphics, the computation of lighting can be done via radiosity. 1.1. Definition. Properties Radiosity is defined as being the energy per unit solid angle that leaves a sur- face. The radiosity equation is a mathematical model for the brightness of a collection of one or more surfaces. The equation is