預先計算輻射轉換法為一利用預先計算好之複雜光線互動與傳遞來繪製場景的技巧。儘管只能有效的表現低頻的陰影與照明，球面調和函數是首先被採用來表現與壓縮極為龐大的預先計算資料。之後，藉由非線性小波概算的引入，預先計算輻射轉換法始得以處理高頻陰影與照明。當處理高頻信號的預先計算輻射轉換法研究多集中於直接光源與陰影的探討時，間接照明的研究多半處於被忽略的狀態。在本論文中，我們結合利用三重積積分的重新打光法與預先計算好的間接照明能量轉換函式來繪製更符合現實世界情況的場景。

Precomputed Radiance Transfer ( PRT ) is a technique used to render a scene with complex light interactions precomputed. Spherical Harmonics was first chosen to represent and compress the huge precomputed data, though it can only represent low-frequency shadows and lighting efficiently. Later, with the introduction of non-linear wavelet approximation, PRT is capable of handling all-frequency shadows and lighting. While most all-frequency PRT researches are focused on direct illumination and shadowing effects, the indirect illumination part is often neglected. In this thesis, we combine the triple product integral relighting method with precomputed indirect transfer functions to better render scenes that meet real-world conditions.

1. Cohen, M. F., Wallace, J., and Hanrahan, P., Radiosity and realistic image synthesis. 1993: Academic Press Professional, Inc. 381.
2. Veach, E. and Guibas, L. J., Metropolis light transport, in Proceedings of the 24th annual conference on Computer graphics and interactive techniques. 1997, ACM Press/Addison-Wesley Publishing Co.
3. Jensen, H. W., Global illumination using photon maps, in Proceedings of the eurographics workshop on Rendering techniques '96. 1996, Springer-Verlag: Porto, Portugal.
4. Sloan, P.-P., Kautz, J., and Snyder, J., Precomputed radiance transfer for real-time rendering in dynamic, low-frequency lighting environments, in Proceedings of the 29th annual conference on Computer graphics and interactive techniques. 2002, ACM Press: San Antonio, Texas.
5. Ng, R., Ramamoorthi, R., and Hanrahan, P., All-frequency shadows using non-linear wavelet lighting approximation, in ACM SIGGRAPH 2003 Papers. 2003, ACM Press: San Diego, California.
6. Ng, R., Ramamoorthi, R., and Hanrahan, P., Triple product wavelet integrals for all-frequency relighting, in ACM SIGGRAPH 2004 Papers. 2004, ACM Press: Los Angeles, California.
7. Blinn, J. F. and Newell, M. E., Texture and reflection in computer generated images. Commun. ACM, 1976. 19(10): p. 542-547.
8. Kautz, J. and Mccool, M. D., Approximation of Glossy Reflection with Prefiltered Environment Maps. Graphics Interface, 2000: p. 119-126.
9. Ramamoorthi, R. and Hanrahan, P., Frequency space environment map rendering, in Proceedings of the 29th annual conference on Computer graphics and interactive techniques. 2002, ACM Press: San Antonio, Texas.
10. Kautz, J., et al., Unified Approach to Prefiltered Environment Maps, in Proceedings of the Eurographics Workshop on Rendering Techniques 2000. 2000, Springer-Verlag.
11. Lehtinen, J. and Kautz, J., Matrix radiance transfer, in Proceedings of the 2003 symposium on Interactive 3D graphics. 2003, ACM Press: Monterey, California.
12. Sloan, P.-P., et al., Clustered principal components for precomputed radiance transfer. ACM Trans. Graph., 2003. 22(3): p. 382-391.
13. Wang, R., Tran, J., and Luebke, D. All-frequency Relighting of Non-diffuse Objects using Separable BRDF Approximation. in Eurographics Symposium on Rendering. 2004.
14. Wang, R., Tran, J., and Luebke, D., All-frequency relighting of glossy objects. ACM Trans. Graph., 2006. 25(2): p. 293-318.
15. Kautz, J. and Mccool, M. D. Interactive rendering with arbitrary BRDFs using separable approximations. in Eurographics Rendering Workshop. 1999.
16. Kajiya, J. T., The rendering equation, in Proceedings of the 13th annual conference on Computer graphics and interactive techniques. 1986, ACM Press.