本文研究目的在於改良初始模型及重新設計軟體程式與數值方法，建立出更方便使用的數位東方毛筆以便數位呈現精美之國畫作品。在數值方法上採用省略壓力項之簡化二維不可壓縮奈威爾－史托克方程式(Navier－Stokes equation)來計算水墨運動。並進一步研究數位毛筆幾何模型BGM（Brush Geometry Model）模擬水墨在紙張運動行為，配合筆觸(Stroke)之運動軌跡，規範出筆觸範圍後並給予墨水源（Ink-water source）。此模型以筆觸速度為主要流場變數，如此考量是為符合兼顧方便性及計算速度之考量。
　　參考目前應用於虛擬東方毛筆繪圖之硬體設備，本研究簡化需要控制的因素，使模型之軟體方面得以與硬體搭配，達到逼近實際毛筆所呈現之筆觸形狀。隨後對於墨水規範方面，除了易於調整的數位毛筆之幾何模型外，使用者亦可選擇自己喜好的顏色進行調整毛筆粗細變化之模型，此外，也加入虛擬的紙張模型以增加其真實性。最終，依使用者需求設定參數且依據筆觸的運動軌跡，配合本文中之模型操作流程，即可完成書法、水墨畫及彩墨畫作等作品。

The aims of study are to improve the design and numerical methods,and to establish a more convenient use of the digital brush in order to digitally display the elegant works of Chinese painting.The numerical method used is a simplified 2D Navier－Stokes equation with neglected pressure term to calculate the motion of the water-ink mixture. According to the BGM （Brush Geometry Model）and trajectory of the stroke motion, one can determine the motion of ink-water on a paper.In this model ,the stroke velocity is the key parameter to compute the calculating flow speed.
Refer to the hardware devices used for the virtual East brush drawing, this study simplifies the factors of the controlled variables. The painting model matchs up each model to come up with the shape of the stroke in the real operation. We also include the models of the virtual papers to increase its authenticity.Users can also choose their own preferences to adjust the color and to select brush thickness changes in the model. Finally, users can finish calligraphic works and paintings by choosing parameters according to the demand of the users.

[1]W. Baxter, V. Scheib, M. Lin, and D. Manocha, “DAB: Interactive Haptic Painting with 3D Virtual Brushes,” Proceedings of ACM SIGGRAPH 01, pp. 461-468,2001.
[2]W. Baxter, J. Wendt, and M. Lin, “IMPaSTo: A Realistic, Interactive Model for Paint,” In the proceedings of NPAR 2004, The 3rd International Symposium on Non-Photorealistic Animation and Rendering, pp. 45-56, 2004.
[3]S. Oh , Crystal, “GPU-based 3D oriental color-ink rendering,” In Proceedings of the 2005 international conference on Augmented tele-existence, pp.142 - 147 ,2005.
[4]D. Small, “Simulating Watercolor by Modeling Diffusion, Pigment, and Paper Fibers,” Proc. of SPIE '91, February 1991. 10.
[5]D. L. Way, S. W. Huang, and Z.C. Shih, “Physical-based Model of Ink Diffusion in Chinese Paintings,” Proc. the WSCG 2003, Plzen, Czech, Feb. 2003.
[6]黃程欲, 以墨汁特性為主之水墨擴散模擬, 東海大學資訊工程與科學研究所碩士論文, 2004.
[7]郭力文, 具水墨畫風格之非真實照片式繪圖, 中原大學資訊工程研究所碩士論文, 2005.
[8]Q. Guo.and T. L. Kunii.,” "Nijimi" Rendering Algorithm for Creating Quality Black Ink Paintings,” Computer Graphics International (CGI'03), pp. 152, Tokyo, Japan, July 09 – 11,2003.
[9]R. S. Hirsh, “Higher order accurate difference solutions of fluid mechanics problem by a compact differencing technique,” J. Comput. Phy. vol-19, pp. 90-109 ,1975.
[10]S. V. Patankar, “Numerical Heat Transfer and Fluid Flows,” McGraw-Hill,1980.
[11]R. I. Issa, “Solution of the implicitly discretised fluid flow equation by operator-splitting,” J. of Comp. Phys., vol-62, pp. 40-65,1986.
[12]A. J. Chorin, “A numerical method for solving incompressible viscous flow problem,” J. Comput. Phy. vol-2, pp. 12-26,1967.
[13]D. Pan and S. R. Chakravarthy, “Unified formulation for incompressible flows,” AIAA Paper 89-0122,1989.
[14]Cassidy J. Curtis, “Computer-Generated Watercolor,”In Proceedings of the24th Annual Conference on Computer Graphics and Interactive Techniques. ACM Press/Addison-Wesley Publishing Co.:NY, USA, pp.421–430,1997.
[15]Tom Van Laerhoven, “Real-time simulation of watery paint,”, pp.429-439,2005
[16]Nelson S.-H. Chu, “Real-Time Painting with an Expressive Virtual Chinese Brush,” Computer Graphics and Applications, IEEE, Vol. 24, No. 5, pp. 76-85,2004.
[17]Nelson S.-H. Chu, “MoXi: Real-Time Ink Dispersion in Absorbent Paper,” ACM Transactionson Graphics, Vol. 24, No. 3, 2005.
[18]吳村木, 以有限體積法探討流經圓柱渦漩曳放的壓抑現象, 成功大學航空太空研究所博士論文, 1993.
[19]J. L. Chen, “The simulation of mixed convection in a vertical channel with and without local blowing/suction via revised finite volume method and simpler algorithm,” PhD. Thesis, Institute of Aeronautics and Astronautics, National Cheng Kung University, Tainan, Taiwan, R.O.C. ,1991.
[20]郭禹成, 以流場物理行為建構虛擬毛筆繪圖模型之研究, 成功大學航空太空研究所碩士論文, 2008.
[21]郭禹昌, 三維虛擬毛筆繪圖模型之研究, 成功大學航空太空研究所碩士論文, 2010.
[22]Horace H.S. Ip, ”Virtual brush: a model-based synthesis of Chinese calligraphy,” Computers & Graphics 24 pp. 99-113,2000.
[23]詹悟, 墨, 台灣省立彰化社會教育館, pp.53-80, 1994.
[24]賴展昌書法探索教育網, http://www.yces.chc.edu.tw/~chang/
[25]維基百科, 自由的百科全書, http://zh.wikipedia.org/zh-tw/
[26]國家文化網, http://www.nationculture.com/
[27]360圖片, 墨水畫圖片參考網, http://st.haoso.com/i?src=corr&q=%E7%AE%80%E5%8D%95%E6%B0%B4%E5%A2%A8%E7%94%BB%E5%8A%A8%E7%89%A9%E6%88%AA%E5%9B%BE&pq=%E7%AE%80%E5%8D%95%E6%B0%B4%E5%A2%A8%E7%94%BB%E5%8A%A8%E7%89%A9%E8%A7%A3%E5%9B%BE