Textures and Radiosity: Controlling Emission and Reflection with Texture Maps

Abstract:

In this paper we discuss the efficient and accurate incorporation of
texture maps into a hierarchical Galerkin radiosity algorithm. This
extension of the standard algorithm allows the use of textures to describe
complex reflectance and emittance patterns over surfaces, increasing the
realism and complexity of radiosity images. Previous approaches to the
inclusion of textures have either averaged the texture to yield a single
color for the radiosity computations, or exhaustively generated detail
elements---possibly as many as one per texture pixel. The former does not
capture important lighting effects due to textures, while the latter is too
expensive computationally to be practical.
To handle texture maps requires a detailed analysis of the underlying
operator equation. In particular we decompose the radiosity equation into
two steps: (i) the computation of irradiance on a surface from the
radiosities on other surfaces, and (ii) the application of the reflectance
operator $
ho$ to compute radiosities from irradiances. We then describe
an algorithm that maintains hierarchical representations of both
radiosities and textures. The numerical error involved in using these
approximations is quantifiable and a time/error tradeoff is possible. The
resulting algorithm allows texture maps to be used in radiosity
computations with very little overhead.