宣纸上的墨水扩散模拟
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摘要
墨水扩散是一个复杂的物理现象,针对墨水在宣纸上的扩散模拟问题,提出了一个基于变系数扩散方程的模拟方法,其扩散系数由宣纸结构和随时间而减少的剩余墨水量决定。模拟分为两个阶段:宣纸结构的模拟和墨水扩散动态过程的模拟。为了模拟宣纸结构,使用一种由权重不同且方向随机的直线段均匀分布而成的加权纤维结构。墨水扩散的动态过程由变系数扩散方程来阐述,为了高效地生成扩散图像,使用Crank-Nicolson数值方法求解墨水扩散方程,并且预计算纤维结构和动态更新扩散图像。与以往类似的模拟方法相比,该方法能够生成更加自然的扩散边界,并有效地解决了边界过于平滑的问题。实验结果表明该方法能够真实地模拟不同宣纸上的墨水扩散效果。
Ink diffusion is a complex physical phenomenon. Concerning the problem of simulating ink diffusion on Xuan paper, this paper proposed a simulation method based on diffusion equation with variable coefficient, and its diffusion coefficient depended on Xuan paper structure and the residue of ink which reduced with time. There were two steps for simulation: simulating Xuan paper structure and simulating the dynamic procedure of diffusion. To simulate Xuan paper structure, a weighting fiber structure was proposed, which consisted of uniformly distributed line segments with different weights and random directions. The dynamic procedure of ink diffusion was described by the diffusion equation. To generate the diffusion image efficiently, Crank-Nicolson method was used to solve the diffusion equation, fiber structure was precomputed, and the diffusion image was updated dynamically. Compared with the previous similar simulation methods, this method rendered more natural diffusion boundary, and overcame the problem of excessively smooth boundary. The experimental results demonstrate that this approach is able to simulate the effects of ink diffusion on different Xuan paper realistically.
Ink diffusion is a complex physical phenomenon. Concerning the problem of simulating ink diffusion on Xuan paper, this paper proposed a simulation method based on diffusion equation with variable coefficient, and its diffusion coefficient depended on Xuan paper structure and the residue of ink which reduced with time. There were two steps for simulation: simulating Xuan paper structure and simulating the dynamic procedure of diffusion. To simulate Xuan paper structure, a weighting fiber structure was proposed, which consisted of uniformly distributed line segments with different weights and random directions. The dynamic procedure of ink diffusion was described by the diffusion equation. To generate the diffusion image efficiently, Crank-Nicolson method was used to solve the diffusion equation, fiber structure was precomputed, and the diffusion image was updated dynamically. Compared with the previous similar simulation methods, this method rendered more natural diffusion boundary, and overcame the problem of excessively smooth boundary. The experimental results demonstrate that this approach is able to simulate the effects of ink diffusion on different Xuan paper realistically.
引文
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[2]LEE J.Diffusion rendering of black ink paintings using new paper and ink models[J].Computers and Graphics,2001,25(2):295-308.
[3]余斌,孙济洲,白海飞,等.基于纸的物理建模的水墨画扩散效果仿真[J].系统仿真学报,2005,17(9):2305-2309.
[4]WANG X,JIAO J,SUN J.Graphical simulator for Chinese inkwash drawing[J].Transactions of Tianjin University,2002,8(1):1-7.
[5]SMALL D.Simulating watercolor by modeling diffusion,pigment,and paper fibers[C]//Proceedings of SPIE 1991:Image Handling and Reproduction Systems Integration.San Jose:International Society for Optics and Photonics,1991:140-146.
[6]CURTIS C J,ANDERSON S E,SEIMS J E,et al.Computer-generated watercolor[C]//Proceedings of the 24th Annual Conference on Computer Graphics and Interactive Techniques.New York:ACM Press,1997:421-430.
[7]KUNII T L,NOSOVSKIJ G V,HAYASHI T.A diffusion model for computer animation of diffuse ink painting[C]//CA'95:Proceedings of the Computer Animation.Washington,DC:IEEE Computer Society,1995:98-102.
[8]KUNII T L,NOSOVSKIJ G V,VECHERININ V L.Two-dimensional diffusion model for diffuse ink painting[J].International Journal of Shape Modeling,2001,7(1):45-58.
[9]WAY D L,HUANG S W,SHIH Z C.Physical-based model of ink diffusion in Chinese paintings[EB/OL].[2013-04-25].http://wenku.baidu.com/view/681ea52c0066f5335a8121cc.html.
[10]CHU N S H,TAI C L.MoXi:real-time ink dispersion in absorbent paper[J].ACM Transactions on Graphics,2005,24(3):504-511.
[11]SUCCI S.Lattice Boltzmann equation[M].Oxford:Oxford University Press,2001.
[12]CHU N S H,TAI C L.Real-time painting with an expressive virtual Chinese brush[J].Computer Graphics and Applications,2004,24(5):76-85.
[13]CHA S,PARK J,HWANG J,et al..An efficient diffusion model for viscous fingering[J].The Visual Computer,2012,28(6/7/8):563-571.
[14]WANG C M,WANG R J.Image-based color ink diffusion rendering[J].IEEE Transactions on Visualization and Computer Graphics,2007,13(2):235-246.
[15]陆金甫,关治.偏微分方程数值解法[M].北京:清华大学出版社,2004.
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