A fast matrix--vector multiplication method for solving the radiosity equation
This paper is devoted to the numerical solution of the radiosity equation in the unoccluded case, which takes the form \[ u(P) - {\rho (P) \over \pi} \int_S u(Q) {\cos \Theta_P \cos \Theta_Q \over |P-Q|^2} dS_Q = E(P),\quad P \in S , \tag{1} \] with \(u(P)\) the radiosity, \(E(P)\) the emissivity and \(\rho (P)\) the reflectivity at \(P \in S\). Furthermore, \(\Theta_p\) is the angle between the inner normal to \(S\) at \(P\) and \(Q-P\), and the surface \(S\) need not to be connected and is usually only piecewise smooth. The authors discuss stability and convergence of the centroid collocation method applied to (1). They present a fast iteration method for the solution of the corresponding linear system using fewer than \(O(n^2)\) operations. A detailed numerical example shows a large speedup compared to direct solvers for the radiosity equation. The restriction to unoccluded surfaces will be removed in a later paper.
scientific article; zbMATH DE number 1419502