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研究生:郭禹成
研究生(外文):Yu-Cheng Guo
論文名稱:以流場物理行為建構虛擬毛筆繪圖模型之研究
論文名稱(外文):The study of establishing a virtual Chinese-brush painting model based on physical fluid motion
指導教授:林三益林三益引用關係
指導教授(外文):San-Yih Lin
學位類別:碩士
校院名稱:國立成功大學
系所名稱:航空太空工程學系碩博士班
學門:工程學門
學類:機械工程學類
論文種類:學術論文
論文出版年:2008
畢業學年度:96
語文別:中文
論文頁數:109
中文關鍵詞:奈威爾-史托克方程式數值方法虛擬毛筆繪圖模型
外文關鍵詞:Navier-Stokes equation.virtual Chinese-brush painting
相關次數:
  • 被引用被引用:3
  • 點閱點閱:173
  • 評分評分:
  • 下載下載:28
  • 收藏至我的研究室書目清單書目收藏:1
本文研究目的在於如何利用數值方法,建立方便使用的虛擬東方毛筆繪圖模型。本文中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)計算水墨的運動,並依照毛筆幾何模型BGM(Brush Geometry Model),配合筆觸(Stroke)的運動軌跡,規範出筆觸範圍之後給予墨水源(Ink-water source)。在流場空間部分採用三階上風有限體積法,時間部分則是使用二階郎奇-庫達法(Two-step Runge-Kutta Method)來計算;此一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,及計算速度的目標之考量。
  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,使模型方面得以配合硬體之可能性。尤其在墨水源範圍規範方面,設定易於調整的毛筆幾何模型外,依據筆觸的運動軌跡,配合本文中之BMDM(Brush Motion Dynamic Model)裡的參數控制,以達到想要顯示的筆觸形狀。最後再依調整雷諾數、水量與染墨量之比例、沉澱係數,以及蒸發係數…等等,規劃出本文所希望呈現的墨韻效果,例如:擴散、吸收,以及黑邊效應等等。
This study aims to establish a handy Chinese brush model with numerical method. The simplified 2D incompressible Navier-Stokes equation with pressure term neglected is used for the calculation of the water-ink mixture motion. According to the BGM (Brush Geometry Model)and the stroke trajectory, ink-water sources are determined in the given stroke area. The third-order upstream finite volume method with two-step Runge-Kutta Method is used for the generation of flowfield grid. The stroke velocity is the key parameter in this model due to improve the calculation speed and to ensure convenience.
This study introduces the number of the controlled variables, such as , , , etc., to match the capability of the hardware for brush simulation available nowadays. Also establish an an easy-to-modulate brush model in the source area definition and the BMDM (Brush Motion Dynamic Model) variable control according to the brush motion trajectory to achieve the desired stroke geometry. The final ink diffusion effect, such as diffusion, dissipation and dark-edge effect, is modulated by adjusting Reynold’s number water-ink ratio, precipitation coefficient and vaporization coefficient.
中文摘要 I
Abstract II
符號說明 II
目錄 V
圖目錄 VIII
第一章 緒論 1
1.1 前言 1
1.2 內容大綱 5
第二章 數值方法 6
2.1 統御方程式 6
2.2 數值方法 7
2.2.1 流場之有限體積法 8
2.2.2 擴散項(Diffusive Terms) 11
2.2.3 時間積分 12
2.3 邊界條件 14
第三章 模型建立與設計 16
3.1 淺水層(Shallow fluid layer): 17
3.1-1 Source: 17
3.1-2 淺水流場 Shallow flow field: 21
3.1-3 啟動對流( Induced Advection ): 22
3. 1-4 蒸發( Evaporation ): 25
3.2 表面層(Surface Layer): 25
3. 3 毛細層(Capillary Layer): 27
3. 3-1 毛細層之吸收水量: 27
3. 3-2蒸發( Evaporation ): 28
第四章 模型使用介紹 37
4.1 紙張 ( Paper ) 37
4.2 擴散效果 ( Diffusion ) 38
4.3 筆觸 ( Stroke ) 42
4.3-1 側 43
4.3-2 勒 43
4.3-3 努 44
4.3-4 趯 45
4.3-5 策 46
4.3-6 掠 47
4.3-7 啄 48
4.3-8 磔 49
4.3-9 折 50
第五章 應用與結果 87
5.1 輔助應用程式 87
5.2 作品結果呈現 90
5.2-1 正楷體『永』字 圖[5.3] 90
5.2-2 指導老師姓名『林三益』 圖[5.4] 90
5.2-3 研究生姓名『郭禹成』 圖[5.5] 90
5.2-4 揣摩草書作品『萬里悲秋常作客』 圖[5.7] 91
5.2-5 水墨畫作品『山壑』 圖[5.8] 91
5.2-6 水墨畫作品『枝葉』 圖[5.9] 92
第六章 結論 105
參考文獻 106
自述 108
1.W. Baxter, V. Scheib, M. Lin, and D. Manocha. “DAB: Interactive Haptic Painting with 3D Virtual Brushes”. In Proceedings of ACM SIGGRAPH 01, August 2001, pp. 461-468.
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. Held June 7-9 2004, Annecy, France. pp. 45--56.
3.Crystal S. Oh, “GPU-based 3D oriental color-ink rendering”In Proceedings of the 2005 international conference on Augmented tele-existence, Pages: 142 - 147 .(2005)
4.D. Small. “Simulating Watercolor by Modeling Diffusion, Pigment, and Paper Fibers.” Proc. of SPIE '91, February 1991. 10
5.Der-Lor Way, S.-W. Huang, and Zen-Chung 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.Qinglian Guo,and Tosiyasu 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 InteractiveTechniques. ACM Press/Addison-Wesley Publishing Co.:NY, USA, 1997; 421–430.
15.Tom Van Laerhoven, “Real-time simulation of watery paint” Comp. Anim. Virtual Worlds 2005; 16: 429–439
16.Nelson S.-H. Chu, “Real-Time Painting with an Expressive Virtual Chinese Brush” ,Computer Graphics and Applications, IEEE, September/October 2004 (Vol. 24, No. 5) pp. 76-85
17.Nelson S.-H. Chu, “MoXi: Real-Time Ink Dispersion in Absorbent Paper” ACM Transactionson Graphics, Vol. 24, No. 3, August 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.Horace H.S. Ip, ”Virtual brush: a model-based synthesis of Chinese calligraphy” Computers & Graphics 24 pp. 99-113(2000)
21.詹悟,'墨',台灣省立彰化社會教育館,1994.pp.53-80.
22.賴展昌書法探索教育網 http://www.yces.chc.edu.tw/~chang/
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