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 ρ 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.

References

1. 1.Alpert,B.,Beylkin,G.,Coifman,R.,and Rokhlin,V. Wavelet-like Bases for the Fast Solution of Second-kind Integral Equations. SIAM Journal on Scientific Computing 14, 1 (Jan 1993).
2. 2.Beylkin,G.,Coifman,R.,and Rokhlin,V.Fast Wavelet Transforms and Numerical Algorithms I. Communications on Pure and Applied Mathematics 44 (1991), 141-183.
3. 3.Blinn,J.F.,and Newell,M.E.Texture and Reflection in Computer Generated Images. Communications of the ACM 19,10 (October 1976), 542-547.
4. 4.Chen,H.,and Wu,E.-H.An Efficient Radiosity Solution for Bump Texture Generation. Computer Graphics 24, 4 (August 1990), 125-134.
5. 5.Cohen,M.,Chen,S.E.,Wallace,J.R.,and Greenberg, D.P.A Progressive Refinement Approach to Fast Radiosity Image Generation. Computer Graphics 22, 4 (August 1988), 75-84.
6. 6.Cohen,M.F.,and Greenberg,D.P.The Hemi-Cube: A Radiosity Solution for Complex Environments. Computer Graphics 19, 3 (July 1985), 31-40.
7. 7.Cohen,M.F.,Greenberg,D.P.,Immel,D.S.,and Brock,P.J.An Efficient Radiosity Approach for Realistic Image Synthesis. IEEE Computer Graphics and Applications 6, 3 (March 1986), 26-35.
8. 8.Dorsey,J.O.,Sillion,F.X.,and Greenberg,D.P. Design and Simulation of Opera Lighting and Projection Effects. Computer Graphics 25, 4 (July 1991), 41-50.
9. 9.Fournier,A.,Gunawan,A.S.,and Romanzin,C.Com-mon Illumination between Real and Computer Generated Scenes. In Proceedings of Graphics Interface 93 (1993), pp. 254-261.
10. 10.Goral,C.M.,Torrance,K.E.,Greenberg,D.P.,and Battaile,B.Modelling the Interaction of Light between Diffuse Surfaces. Computer Graphics 18, 3 (July 1984), 212-222.
11. 11.Gortler,S.,Schr ~oder,P.,Cohen,M.,and Hanrahan, P.Wavelet Radiosity. In Computer Graphics Annual Conference Series 1993 (August 1993), Siggraph, pp. 221-230.
12. 12.Hanrahan,P.,Salzman,D.,and Aupperle,L.A Rapid Hierarchical Radiosity Algorithm. Computer Graphics 25, 4 (July 1991), 197-206.
13. 13.Heckbert,P.S.Radiosity in Flatland. Computer Graphics Forum 2, 3 (1992), 181-192.
14. 14.Kajiya,J.T.The Rendering Equation. Computer Graphics 20,4 (1986), 143-150.
15. 15.Nishita,T.,and Nakamae,E.Continuous Tone Representa-tion of Three-Dimensional Objects Taking Account of Shadows and Interreflection. Computer Graphics 19, 3 (July 1985), 23-30.
16. 16.Schr ~oder,P.,Gortler,S.J.,Cohen,M.F.,and Hanrahan,P.Wavelet Projections For Radiosity. In Fourth Eurographics Workshop on Rendering (June 1993), Eurographics, pp. 105-114.
17. 17.Teller,S.,and Hanrahan,P.Global Visibility Algorithms for Illumination Computations. In Computer Graphics Annual Con-ference Series 1993 (August 1993), Siggraph, pp. 239-246.
18. 18.Troutman,R.,and Max,N.Radiosity Algorithms Using Higher-order Finite Elements. In Computer Graphics Annual Con-ference Series 1993 (August 1993), Siggraph, pp. 209-212.
19. 19.Upstill,S.The RenderMan Companion. Addison Wesley, 1992.
20. 20.Zatz,H.R.Galerkin Radiosity: A Higher-order Solution Method for Global Illumination. In Computer Graphics Annual Conference Series 1993 (August 1993), Siggraph, pp. 213-220.

Index Terms

• Applied computing

  • Physical sciences and engineering

    • Engineering

• Computing methodologies

  • Computer graphics

    • Rendering

      • Reflectance modeling

• Mathematics of computing

  • Mathematical analysis

    • Integral equations