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.

摘要 I
Abstract II
Acknowledgement III
Table of Contents IV
List of Figures V
List of Tables VI
1. Introduction 1
2. Related Works 3
2.1 Global Illumination 3
2.2 Mesh Spectral Basis 4
3. Algorithm Overview 5
3.1 Pre-process 5
3.2 Pre-computation 5
3.3 Rendering 6
4. Mesh Spectral Basis 8
4.1 Mesh Spectral Basis Introduction 8
4.2 Mesh Spectral Basis Used for Lighting 8
4.3 Definition and Construction of Mesh Spectral Basis 9
5. Bounding Volume Hierarchies on GPU 11
5.1 Construction 11
5.2 Traversal 12
5.3 GPU Implementation 13
5.3.1 Indexing the BVH Nodes 13
5.3.2 BVH Texture 14
6. Implementation 16
6.1 Pre-Process Implementation 16
6.2 Transfer Function Implementation 17
6.2.1 Visibility and Form-Factors 17
6.2.2 Using BVH on GPU 18
6.3 User Controllable VPLs Sampling 20
6.4 Rendering Process 21
7. Results and Discussion 24
8. Conclusion and Future Work 28
Reference 29

[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.