在圖學領域中，全域照射至今一直是個許多值得研究的課題。如何快速並精確地繪製出全域照射的影像一直是3D圖學中的最終目標。在此篇論文中，我們結合了熱輻射照射和預先計算輻射轉換法的概念。熱輻射演算法原本即是計算低頻的間接照射。之後，我們先進行預先計算，得到網線光譜基底與輻射轉換函數，再將熱輻射的計算域轉換至網線光譜基底，便可在繪圖時快速地處理低頻的間接照射。由於所有的預先計算皆是與視角及光源獨立，故在繪製時，我們能達成即時視角轉換和互動的重新打光。而在預先計算中，引入現今的繪圖硬體的加速以及實作一個階層式資料結構，便可大量地減少預先計算的時間。同時配合使用者可選擇的品質選擇，可控制我們在即時熱輻射中的虛擬點光源取樣數，而使得此篇論文同時能繪製出較精細的3D場景，或是達成一個快速繪製的全域照射預覽效果。

Global illumination now is still a good research issue in 3D graphics. How to render a photorealistic image fast remains to be a destination. In this thesis, we combine the Radiosity and the Pre-computed Radiance Transfer (PRT) to render our final image. Instead of computing the Radiosity directly on patches, we pre-compute a set of mesh spectral basis and project the computing domain onto this basis, which can calculate the low-frequency indirect lighting faster. This thesis achieves a real-time view-changing and an interactive-time relighting since all pre-computations are view-independent and light-independent. With the acceleration of graphics hardware, we apply the Bounding Volume Hierarchies (BVH) on GPU, and thus reduce the pre-computation time hugely. Finally, we make this application’s rendering quality as user-controllable for users to choose the number of virtual point light source (VPL). By this, our thesis can render the 3D scene with more accuracy, or alternatively, it can be a fast preview system for global illumination.

[1] Balog M.: Towards Optimal Combination of Shooting and Gathering Stochastic Radiosity. Central European Seminar on Computer Graphics for Students 2001.
[2] Brabec S., Annen T., Seidel H.P.: Shadow Mapping for Hemispherical and Omnidirectional Light Sources. In Proceeding of Computer Graphics International 2002
[3] Cohen, M. F., Wallace, J., and Hanrahan, P.: Radiosity and Realistic Image Synthesis. 1993: Academic Press Professional, Inc. 381.
[4] Dutr□ P.: Global Illumination Compendium. http://www.cs.kuleuven.ac.be/~phil/GI/
[5] Goldsmith J., Salmon J.: Automatic Creation of Object Hierarchies for Ray Tracing. IEEE Computer Graphics and Applications Volume 7, Issue 5, p. 14-20 (May 1987)
[6] Jensen, H. W.: Global Illumination Using Photon Maps. in Proceedings of the Eurographics Workshop on Rendering Techniques '96. 1996, Springer-Verlag: Porto, Portugal.
[7] Karni Z. and Gotsman C.: Spectral Compression of Mesh Geometry. In Proceeding of Computer Graphics, SIGGRAPH 2000, p. 279-286.
[8] Kay T.L., Kajiya J.T.: Ray Tracing Complex Scenes. ACM Computer Graphics, Volume 20, Issue 4, p. 269-278, 1986, ACM Press, New York, USA.
[9] Keller A.: Instant Radiosity. In Proceedings of Computer Graphics, Annual Conference Series, SIGGRAPH 1997, p. 49-56.
[10] Kontkanen J., Laine S.: Ambient Occlusion Fields. In Proceedings of the 2005 Symposium on Interactive 3D Graphics And Games
[11] Laine S., Saransaari H., Kontkanen J., Lehtinen J., and Aila T.: Incremental Instant Radiosity for Real-Time Indirect Illumination. Eurographics Symposium on Rendering 2007.
[12] Lin C.T., Chang C.F.: Triple Product Integral Relighting with Indirect Illumination. Master's Thesis, National Tsing Hua University, Taiwan, 2007.
[13] MeTis: http://www-users.cs.umn.edu/~karypis/metis/
[14] 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.
[15] Pozo R.: Template Numerical Toolkit (TNT). http://math.nist.gov/tnt/
[16] Segovia B., Iehl J.C., Mitanchey R. and P□roche B.: Bidirectional Instant Radiosity. In Proceedings of the 17th Eurographics Workshop on Rendering 2006
[17] Segovia B., Iehl J.C. and P□roche B.: Metropolis Instant Radiosity. In Proceedings of Eurographics 2007
[18] 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.
[19] Thrane N. and Simonsen L.O.: A Comparison of Acceleration Structures for GPU Assisted Ray Tracing. Master's thesis, University of Aarhus, Denmark, 2005.
[20] Veach E. and Guibas L.J.: Metropolis Light Transport. In Proceedings of SIGGRAPH 1997, Addison-Wesley, p. 65-76.
[21] Wallace J.R., Elmquist K.A., Haines E.A.: A Ray Tracing Algorithm for Progressive Radiosity. In Proceedings of the ACM SIGGRAPH conference 1989, p. 315 – 324
[22] Wang R., Zhu J., and Humphreys G.: Precomputed Radiance Transfer for Real-Time Indirect Lighting using A Spectral Mesh Basis. Europgraphics Symposium on Rendering 2007.
[23] Zhou K., Hu Y., Lin S., Guo B., Shum H.Y.: Precomputed Shadow Fields for Dynamic Scenes. In Proceedings of ACM SIGGRAPH 2005.