Numerical analysis of the radiosity equation using the collocation method
General stability and convergence results for the collocation solution of the radiosity equation when a surface \(S\) is occluded, are given. Particular attention is paid to the use of discontinuity meshing for both piecewise constant and piecewise linear approximants. The possibility of superconvergence of the approximating solutions is considered. Two different surfaces are used to illustrate the variety of behaviours which can occur in the radiosity solution. The numerical integration of the collocation integrals is examined. There are difficulties in such integrations when the integration element is close to an edge of surface. A near-analytic approximation procedure for such integrals is proposed. Experimental calculations are given.
scientific article; zbMATH DE number 1533612