A new formulation of differential radiosity and a rendering application

Abstract

Among all the existing realistic lighting methods, the radiosity method is the only one that gives precisely an analytic solution of diffuse light exchanges. The gradient of this solution have been studied but not often used in a context of pure rendering. We present in this article a method to render a surface using the radiosity contour levels. First, we define a differential formulation of the radiosity equation which leads us to a new expression of the gradient of radiosity. We deduce from this general equation a simpler equation of this gradient in the case of a planar surface lighted by a light source reduced to a point. Then we present our method to render planar surfaces using a radial mesh that follows the contour levels of the radiosity. This method is shown to improve the quality of the rendering and decrease the number of vertices used for rendering.