Application of Variational Calculus in Radiosity Method

Szirmay-Kalos László
Department of Process Control, Technical University of Budapest,
Budapest, Muegyetem rkp. 11, H-1111, HUNGARY


The original radiosity method searches for the radiosity distribution in a piecewise constant function form.Using this stepwise constant assumption about the radiosity distribution,  the integral equation describing the energy transfer is transformed to a linear equation system. Higher order radiosity method means the approximation of the radiosity distribution by more complex functions, as for example, by piecewise linear, harmonic, wavelet, etc. function series with unknown coefficients. Due to higher order approximation, the number of the unknown variables can be significantly smaller than the number of constant steps in the original method. This paper discusses the conversion of the integral equation to an equivalent variational problem which can result in a linear equation system for the unknown coefficients. Three function bases are examined in detail in this framework:piecewise constant, piecewise linear and harmonic approximations.


Radiosity method, integral equations, Ritz's method.