5.1 研究總結
在本論文中，我們使用了以光子映射法為基礎的全域照明方法及多項式貼圖 法，對場景進行光源照度的計算，並提出了光子密度圖，將場景照度結果轉為以 空間光子密度的表示方法，這使得數量龐大的光子資料得以減少，以利於多項式 的計算。之後將光源移動的位置及其對應的光子密度圖之變化關係，經由三次方 多項式計算以求得空間中每一取樣點之二十個多項式係數，並將其儲存於多項式 照度圖中，用來還原對應於光源位置的光子密度圖。有了這些準備，便可在給定 新的光源位置後，很快的計算出整個場景的照明亮度。由實驗中得知，經過上述 的程序處理，可加速取得全域照明計算之結果，省略光源發散光子計算的步驟，
縮減大量計算時間。
此外，經由我們觀察測試場景的結果，在場景中以較細的空間分割而形成的 取樣cell，可得到較精確的空間照明數值，但過多的取樣cell卻會導致較長的計算時 間。另外，隨著光源的取樣點增加，空間中每一取樣cell之光子密度變化也隨之複 雜，由於是使用多項方程式來進行結果逼近，因此從圖 27中可以看到如此將會損 失一些細微的數值變化，這樣的結果會造成彩現時陰影部份的細節消失，而呈現 出較為模糊的影子。在加速計算方面，於建立多項式照度圖時，我們可以將未與 物體表面接觸的取樣cell忽略，這些取樣cell通常像是空間中的間隙，如此便可加速 多項式照度圖的計算及處理。
5.2 未來工作
我們提出一個新的方法採用多項式近似的方式來進行全域照明計算，延著這 個方向，將有許多課題可以被提出研究。其中一個為加入可變動的視角，這需要 加快處理本篇論文所提的方法。此外，由於多項式計算方式單純，亦可將整體執 行架構於硬體上，應用GPU硬體加速計算，相信對速度上的提昇會有很大的助益。
另一方面，相對於場景中光源位置變動，物體位置改變更常見於實際的應用，因 此，加入對物體變動的全域照明計算亦為一重要的方向。
參考文獻
[Bli78] BLINN J. F.: Computer display of curved surfaces. PhD thesis, 1978.
[DHT*00] DEBEVEC P., HAWKINS T., TCHOU C., DUIKER H.-P., SAROKIN W., SAGAR M.: Acquiring the reflectance field of a human face. In SIGGRAPH ’00: Proceedings of the 27th annual conference on Computer graphics and interactive techniques (New York, NY, USA, 2000), ACM Press/Addison-Wesley Publishing Co., pp. 145–156.
[DMG99] DISCHLER J.-M., MOSTEFAOUI L., GHAZANFARPOUR D.: Radiosity including complex surfaces and geometric textures using solid
irradiance and virtual surfaces. Computers & Graphics 23, 4 (1999), 507–524.
[EHY95] EPSTEIN R., HALLINAN P. W., YUILLE A. L.: 5 +/- 2 eigenimages suffice: An empircal investigation of low-dimensional lighting models, 1995.
IEEE Workshop on Physics-Based Vision.
[HSA91] HANRAHAN P., SALZMAN D., AUPPERLE L.: A rapid hierarchical radiosity algorithm. In SIGGRAPH ’91: Proceedings of the 18th annual conference on Computer graphics and interactive techniques (New York, NY, USA, 1991), ACM Press, pp. 197–206.
[Jen95] JENSEN H. W.: Importance driven path tracing using the photon
map. In Rendering Techniques ’95 (1995), pp. 326–335. (Proceedings of the Sixth Eurographics Workshop on Rendering).
[Jen96] JENSEN H. W.: Global illumination using photon maps. In
Proceedings of the eurographics workshop on Rendering techniques ’96 (London, UK, 1996), Springer-Verlag, pp. 21–30.
[Jen97] JENSEN H. W.: Rendering caustics on non-lambertian surfaces.
Comput. Graph. Forum 16, 1 (1997), 57–64.
[Jen01] JENSEN H. W.: Realistic image synthesis using Photon Mapping. A.
K. Peters, Ltd., Natick, MA, USA, 2001.
[LTG93] LISCHINSKI D., TAMPIERI F., GREENBERG D. P.: Combining hierarchical radiosity and discontinuity meshing. In SIGGRAPH ’93:
Proceedings of the 20th annual conference on Computer graphics and interactive techniques (New York, NY, USA, 1993), ACM Press, pp.
199–208.
[Kaj86] KAJIYA J. T.: The rendering equation. In Computer Graphics (SIGGRAPH ’86 Proceedings) (Aug. 1986), vol. 20, pp. 143–150.
[LW93] LAFORTUNE E. P., WILLEMS Y. D.: Bidirectional path tracing. In
3rd International Conference on Computational Graphics and Visualization Techniques (Compugraphics) ’93 (Alvor, Portugal, 1993), Santo H. P., (Ed.), pp. 145–153.
[LW96] LAFORTUNE E. P., WILLEMS Y. D.: Rendering participating media with bidirectional path tracing. In Rendering Techniques ’96 (Proceedings of the Seventh Eurographics Workshop on Rendering) (New York, NY, 1996), Springer-Verlag/Wien, pp. 91–100.
[MGW01] MALZBENDER T., GELB D., WOLTERS H.: Polynomial texture maps. In SIGGRAPH ’01: Proceedings of the 28th annual conference on Computer graphics and interactive techniques (New York, NY, USA, 2001), ACM Press, pp. 519–528.
[PDC*03] PURCELL T. J., DONNER C., CAMMARANO M., JENSEN H. W., HANRAHAN P.: Photon Mapping on programmable graphics hardware. In HWWS ’03: Proceedings of the ACM SIGGRAPH/EUROGRAPHICS conference on Graphics hardware (Aire-la-Ville, Switzerland, Switzerland, 2003), Eurographics Association, pp. 41–50.
[TSH97] TEO P. C., SIMONCELLI E. P., HEEGER D. J.: Efficient Linear Rerendering for Interactive Lighting Design. Tech. rep., 1997. Stanford Computer Science Department Technical Report STAN-CS-TN-97-60.
[VG94] VEACH E., GUIBAS L.: Bidirectional estimators for light transport.
In Proceedings of the 5th Eurographics Workshop on Rendering ’94 (Darmstadt, Germany, jun 1994), pp. 147–162.
in complex and highly occluded environments. In EGRW ’03:
Proceedings of the 14th Eurographics workshop on Rendering (Aire-la-Ville, Switzerland, Switzerland, 2003), Eurographics Association, pp. 74–81.
[WKB*02] WALD I., KOLLIG T., BENTHIN C., KELLER A., SLUSALLEK P.: Interactive global illumination using fast ray tracing. In EGRW ’02:
Proceedings of the 13th Eurographics workshop on Rendering
(Aire-la-Ville, Switzerland, Switzerland, 2002), Eurographics Association, pp. 15–24.
[Wat00] WATT A.: 3D Computer Graphics. Addison-Wesley, 2000, pp. 349.
[WS03] WAND M., STRASSER W.: Real-time caustics. Comput. Graph.
Forum 22, 3 (2003), 611–620.
[WWW] architecture models. http://www.3dcafe.com.