在這篇論文裡，我們試著使用雙向材質函式來達成即時的毛髮繪製。我們的流程主要可以分為兩個部分：雙向材質函式的取得以及雙向材質函式的算圖。在取得的部分，我們不是使用傳統方法去擷取真實毛髮的材質，而是實做一套以模擬的方法產生看起來真實的毛髮。利用改變不同光源以及視點的方向，我們可以對一塊虛擬產生的毛髮樣本擷取數張圖片。這些圖片就是我們所需要的雙向材質函式的資料。而在算圖的部分，我們使用了一個能夠使用在任何物體表面有效率的雙向材質函式演算法。將第一步驟中取得的圖片重新排列然後再簡化，使得這些資料小到足以完全讀進專門處理圖形的硬體，算出最後的圖。我們的方法是由兩種性質不相近的方法所構成，而這個方法的限制產生在他們中間的資料傳遞。如果有太多長的毛髮的話，那超出某個長度的毛髮將會被剔除。在速度上來說，雖然我們的前置處理時間很長，但是毛髮生長的方式能夠受到完全的控制。使用雙向材質函式的算圖所需的時間很短，能夠即時地看見光影變化產生的影響。

We make an attempt at real-time rendering of fur using Bidirectional Texture Function (BTF). The process can be divided mainly into two parts: acquisition, and rendering of BTF. For the first part, instead of capturing real fur, we implement a basic fur rendering process to generate realistic-looking fur. Controlling the viewing and lighting parameters for the model of the fur sample, we capture serveral images. These images serve as our BTF database. For the second part, we implement an efficient BTF rendering algorithm that can be applied on arbitrary surfaces. Reading the images in the first step, we arrange and simplify them. Then the database is capable of being loaded into graphics hardware to render. Our work is a combination of two different kinds of work. The limitation falls on the bridge connecting them, the captured images of the fur sample. Too many characteristics would be cut off if the length of the fur is long. As for speed, the pre-processing time is long, but the growth of the fur is better controlled. The rendering using BTF is fast, and the instant relighting of the fur is possible.

[1] Yosuke Bando, Bing-Yu Chen, and Tomoyuki Nishita. Animating Hair with
Loosely Connected Particles. Eurographics, 2003.
[2] Armin Bruderlin. A method to generate wet and broken-up animal fur. The
Journal of Visualization and Computer Animation, pages 249–259, 2000.
[3] Agnes Daldegan, Nadia Magnenat Thalmann, Tsuneya Kurihara, and Daniel
Thalmann. An Integrated System for Modeling, Animating and Rendering
Hair. Eurographics, 1993.
[4] Martin Fuhrer, Henrik Wann Jensen, and Przemyslaw Prusinkiewicz. Modeling
hairy plants. Graphical Models, 68, 2006.
[5] Allen Van Gelder and Jane Wilhelms. An Interactive Fur Modeling Technique.
Graphics interface, 1997.
[6] Dan B Goldman. Fake Fur Rendering. Proceedings of SIGGRAPH, 1997.
[7] Farlei J. Heinen and MarceloWalter. GLFurry - An Interactive 3D Fur Modeling
System. Proceedings of the 14th Brazilian Symposium on Computer
Graphics and Image Processing, 2001.
[8] A. Iones, A. Krupkin, S. Volodarsky, and S. Zhukov. Fur and Hair: practical
modeling and rendering techniques. IEEE International Conference on
Information Visualization, 2000.
[9] James T. Kajiya and Timothy L. Kay. Rendering Fur with Three Dimensional
Textures. Computer Graphics, 23(3):271–280, July 1989.
[10] Andr´e M. LeBlanc. Rendering Hair using Pixel blending and Shadow
Buffers. The Journal of Visualization and Computer Animation, 1991.
[11] Jerome Lengyel, Emil Praun, Adam Finkelstein, and Hugues Hoppe. Realtime
Fur over Arbitrary Surfaces. Symposium on Interactive 3D graphics,
2001.
[12] Xinguo Liu, Yaohua Hu, Jingdan Zhang, Xin Tong Baining Guo, and Heung-
Yeung Shum. Synthesis and Rendering of Bidirectional Texture Functions
on Arbitrary Surfaces. IEEE Transactions on Visualization and Computer
Graphics, 10(3), May/June 2004.
[13] Nadia Magnenat-Thalmann. Photorealistic Hair Modeling, Animation, and
Rendering. SIGGRAPH Course 9, 2004.
[14] G. Mぴuller, J. Meseth, M. Sattler, R. Sarlette, and R. Klein. Acquisition,
Synthesis and Rendering of Bidirectional Texture Functions. Eurographics
State of The Art Report, 2004.
[15] Xin Tong, Jingdan Zhang, Ligang Liu, Xi Wang, Baining guo, and Heung-
Yeung Shum. Synthesis of Bidirectional Texture Functions on Arbitrary
Surfaces. ACM Transactions on Graphics, 2002.
[16] Steve Upstill. The RenderMan Companion: A Programmer’s Guide to Realistic
Computer Graphics. Addison-Wesley Professional, 1990.
[17] Kelly Ward, Florence Bertails, Tae-Yong Kim, Stephen R. Marschner,
Marie-Paule Cani, and Ming Lin. A survey on hair modeling: Styling, simulation,
and rendering. IEEE Transactions on Visualization and Computer
Graphics (TVCG), 13(2):213–34, Mar-Apr 2007.
[18] YasuhikoWatanabe and Yasuhito Suenaga. A Trigonal Prism-Based Method
for Hair Image Generation. IEEE Computer Graphics and Applications, 12,
1992.
[19] Kun Zhou, Peng Du, Lifeng Wang, Yasuyuki Matsushita, Jiaoying shi,
Baining Guo, and Heung-Yeung Shum. Decorating surfaces with Bidirectional
Texture Functions. IEEE Transactions on Visualization and Computer
Graphics, 2005.