Published on *Computer Science Department at Princeton University* (http://www.cs.princeton.edu)

Report ID:

TR-449-94

Authors:

Date:

February 1994

Pages:

16

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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.