“Frequency space environment map rendering” by Ramamoorthi and Hanrahan

  • ©Ravi Ramamoorthi and Patrick (Pat) Hanrahan

  • ©Ravi Ramamoorthi and Patrick (Pat) Hanrahan




    Frequency space environment map rendering



    We present a new method for real-time rendering of objects with complex isotropic BRDFs under distant natural illumination, as specified by an environment map. Our approach is based on spherical frequency space analysis and includes three main contributions. Firstly, we are able to theoretically analyze required sampling rates and resolutions, which have traditionally been determined in an ad-hoc manner. We also introduce a new compact representation, which we call a spherical harmonic reflection map (SHRM), for efficient representation and rendering. Finally, we show how to rapidly prefilter the environment map to compute the SHRM—our frequency domain prefiltering algorithm is generally orders of magnitude faster than previous angular (spatial) domain approaches.


    1. BASRI, R., AND JACOBS, D. 2001. Lambertian reflectance and linear subspaces. In International Conference on Computer Vision, 383-390.Google Scholar
    2. BLINN, J., AND NEWELL, M. 1976. Texture and reflection in computer generated images. Communications of the ACM 19, 542-546. Google Scholar
    3. CABRAL, B., MAX, N., AND SPRINGMEYER, R. 1987. Bidirectional reflection functions from surface bump maps. In SIGGRAPH 87, 273-281. Google Scholar
    4. CABRAL, B., OLANO, M., AND NEMEC, P. 1999. Reflection space image based rendering. In SIGGRAPH 99, 165-170. Google Scholar
    5. DANA, K., GINNEKEN, B., NAYAR, S., AND KOENDERINK, J. 1999. Reflectance and texture of real-world surfaces. ACM Transactions on Graphics 18, 1 (January), 1-34. Google Scholar
    6. GREENE, N. 1986. Environment mapping and other applications of world projections. IEEE Computer Graphics & Applications 6, 11, 21-29. Google Scholar
    7. HAKURA, Z., SNYDER, J., AND LENGYEL, J. 2001. Parameterized environment maps. In ACM symposium on interactive 3D graphics, 203-208. Google Scholar
    8. KAJIYA, J., AND KAY, T. 1989. Rendering fur with three dimensional textures. In SIGGRAPH 89, 271-280. Google Scholar
    9. KAUTZ, J., AND MCCOOL, M. 1999. Interactive rendering with arbitrary BRDFs using separable approximations. In EGRW 99, 247-260. Google Scholar
    10. KAUTZ, J., AND MCCOOL, M. 2000. Approximation of glossy reflection with pre-filtered environment maps. In Graphics Interface, 119-126.Google Scholar
    11. KAUTZ, J., VÁZQUEZ, P., HElDRICH, W., AND SEIDEL, H. 2000. A unified approach to prefiltered environment maps. In EGRW 00, 185-196. Google Scholar
    12. KOENDERINK, J., AND VAN DOORN, A. 1998. Phenomenological description of bidirectional surface reflection. JOSA A 15, 11, 2903-2912.Google Scholar
    13. LAFORTUNE, E., FOO, S., TORRANCE, K., AND GREENBERG, D. 1997. Non-linear approximation of reflectance functions. In SIGGRAPH 97, 117-126. Google Scholar
    14. MACROBERT, T. 1948. Spherical harmonics; an elementary treatise on harmonic functions, with applications. Dover Publications.Google Scholar
    15. MALZBENDER, T., GELB, D., AND WOLTERS, H. 2001. Polynomial texture maps. In SIGGRAPH 01, 519-528. Google Scholar
    16. MARSCHNER, S., WESTIN, S., LAFORTUNE, E., TORRANCE, K., AND GREENBERG, D. 2000. Image-Based BRDF measurement including human skin. In EGRW 00, 139-152. Google Scholar
    17. MCCOOL, M., ANG, J., AND AHMAD, A. 2001. Homomorphic factorization of BRDFs for high-performance rendering. In SIGGRAPH 01, 171-178. Google Scholar
    18. MILLER, G., AND HOFFMAN, C. 1984. Illumination and reflection maps: Simulated objects in simulated and real environments. SIGGRAPH 84 Advanced Computer Graphics Animation seminar notes.Google Scholar
    19. MOHLENKAMP, M. 1999. A fast transform for spherical harmonics. The Journal of Fourier Analysis and Applications 5, 2/3, 159-184. Google Scholar
    20. NISHINO, K., SATO, Y., AND IKEUCHI, K. 1999. Eigen-texture method: Appearance compression based on 3D model. In CVPR 99, 618-624.Google Scholar
    21. PROUDFOOT, K., MARK, W., TZVETKOV, S., AND HANRAHAN, P. 2001. A real-time procedural shading system for programmable graphics hardware. In SIGGRAPH 01, 159-170. Google Scholar
    22. RAMAMOORTHI, R., AND HANRAHAN, P. 2001. An efficient representation for irradiance environment maps. In SIGGRAPH 01,497-500. Google Scholar
    23. RAMAMOORTHI, R., AND HANRAHAN, P. 2001. On the relationship between radiance and irradiance: Determining the illumination from images of a convex lambertian object. JOSA A 18, 10, 2448-2459.Google Scholar
    24. RAMAMOORTHI, R., AND HANRAHAN, P. 2001. A signal-processing framework for inverse rendering. In SIGGRAPH 01, 117-128. Google Scholar
    25. RUSINKIEWICZ, S. 1998. A new change of variables for efficient BRDF representation. In EGRW 98, 11-22.Google Scholar
    26. SCHRÖDER, P., AND SWELDENS, W. 1995. Spherical wavelets: Texture processing. In EGRW 95, 252-263.Google Scholar
    27. SILLION, F., ARVO, J., WESTIN, S., AND GREENBERG, D. 1991. A global illumination solution for general reflectance distributions. In SIGGRAPH 91, 187-196. Google Scholar
    28. TORRANCE, K., AND SPARROW, E. 1967. Theory for off-specular reflection from roughened surfaces. JOSA 57, 9, 1105-1114.Google Scholar
    29. WESTIN, S., ARVO, J., AND TORRANCE, K. 1992. Predicting reflectance functions from complex surfaces. In SIGGRAPH 92, 255-264. Google Scholar
    30. WOOD, D., AZUMA, D., ALDINGER, K., CURLESS, B., DUCHAMP, T., SALESIN, D., AND STUETZLE, W. 2000. Surface light fields for 3D photography. In SIGGRAPH 00, 287-296. Google Scholar

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