Abstract:
Traditional radiosity methods decompose surfaces into planar surface
elements that can be supposed to have uniform radiosity and emittance,
that is they approximate the unknown radiosity distribution by piecewise
constant functions. This paper, on the other hand, develops a general framework
to solve the radiosity equation numerically for any kind of function series
approximation. Having derived the general formulae, three special cases
are discussed: piecewise constant functions which lead to the traditional
methods, linear finite elements and harmonic approximations where the basis
functions are not of finite element type because they can approximate the
radiosity distribution everywhere, and thus fall into the category of global
element methods. Global element methods are able to work on the original
geometry and they can be speeded up by effective techniques, such as Fast
Fourier Transform.
Keywords:
Radiosity method, finite-element and global-element techniques, linear finite elements, variational method, Fast Fourier Transform, Ritz method.