在服裝工業上，服裝模擬為電腦輔助設計中檢視成果的一環；而在電影產業或遊戲產業上，服裝模擬能提升整體視覺的逼真效果。而在應用上，服裝模擬除了準確性的要求外，同時也有計算效率的需求。過去的研究顯示，使用質點系統法(Particle systems)能在模擬的準確度與計算效率間取得平衡。
本研究以質點系統法為基礎，從基本幾何關係逐步推導出座標幾何分別與應變、應變能及受力的關係式，能模擬布料非等向材料特性，有別於以往的研究，此方法能運用在不規則三角網格模型上，且能處理大變形問題以模擬布料高度的柔軟性。整套模擬過程包括載入數位人台、載入數位衣版、衣片網格化、縫合模擬、垂墜模擬、碰撞檢測，以及碰撞處理。
最後，我們以C++與OpenGL開發一實作軟體實現本研究所提之服裝模擬方法，並模擬多件不同款式服裝的著裝效果，以此驗證理論之可行性。

In garment industry, cloth simulation is a visualized feedback in computer-aided draping design (CADD). Also, in movie or game industry, a fine cloth simulation can enhance visualized reality of their productions. Considering the outcomes of cloth simulation, it requires intensive computations with high accuracy and high efficiency. Related studies show that the outcomes of using particle system to simulate cloth draping can meet both requirements of accuracy and efficiency.
In this research, we implement a particle system method to simulate the anisometrical material of cloth based on geometry, strain, strain energy, and forces derived by geometric relations. Our particle system, differed from the past method, is performed with both irregular meshes and large deformation problems. A sequence of simulation handles includes digital mannequin and digital patterns loading, pieces’ triangulation, sewing settings, draping simulation, collision detection, and collision handling are presented in this thesis.
In this thesis, we present some simulation samples for different style clothes, and show that the present methods are applicable.

[1] McCartney, J., Hinds, B. K., Seow, B. L., et al., "Dedicated 3D CAD for garment modelling," Journal of Materials Processing Technology, Vol.107, No.1-3, pp.31-36, 2000.
[2] "Lectra," 2009, Lectra, <http://www.lectra.com/>, 14 July 2009.
[3] "Gerber Technology," 2009, Gerber Scientific Inc., <http://www.gerbertechnology.com/>, 14 July 2009.
[4] "TPC (HK) Limited," 2007, TPC (HK) Ltd., <http://www.tpc.com.hk/>, 14 July 2009.
[5] "旭化成 AGMS 株式會社," 2009, Asahi KASEI AGMS Corp., <http://www.agms.co.jp/>, 14 July 2009.
[6] "度卡軟件科技(上海)有限公司," 2004, DOCAD Information Technology Co. Ltd., <http://www.docad.com/>, 14 July 2009.
[7] "Fashion CAD," 2009, Cad Cam Solutions Australia Pty. Ltd., <http://www.fashioncad.net/>, 14 July 2009.
[8] Ng, H. N. and Grimsdale, R. L., "Computer graphics techniques for modeling cloth," Computer Graphics and Applications, IEEE, Vol.16, No.5, pp.28-41, 1996.
[9] Magnenat-Thalmann, N. and Volino, P., "From early draping to haute couture models: 20 years of research," The Visual Computer, Vol.21, No.8, pp.506-519, 2005.
[10] Collier, J. R., Collier, B. J., O'Toole, G., et al., "Drape prediction by means of finite-element analysis," Journal of the Textile Institute, Vol.82, No.1, pp.96-107, 1991.
[11] Eischen, J. W., Shigan, D., and Clapp, T. G., "Finite-element modeling and control of flexible fabric parts," Computer Graphics and Applications, IEEE, Vol.16, No.5, pp.71-80, 1996.
[12] Gan, L., Ly, N. G., and Steven, G. P., "A study of fabric deformation using nonlinear finite elements " Textile Research Journal, Vol.65, No.11, pp.660-668, 1995.
[13] Volino, P. and Magnenat-Thalmann, N., "Comparing Efficiency of Integration Methods for Cloth Animation," in Computer Graphics International(CGI), pp.265-274, 2001.
[14] Reeves, W. T., "Particle systems-a technique for modeling a class of fuzzy objects," in Proceedings of the 10th annual conference on Computer graphics and interactive techniques, Detroit, Michigan, United States, 1983.
[15] Breen, D. E., House, D. H., and Getto, P. H., "A physically-based particle model of woven cloth," The Visual Computer, Vol.8, No.5, pp.264-277, 1992.
[16] Breen, D. E., House, D. H., and Wozny, M. J., "Predicting the drape of woven cloth using interacting particles," in Proceedings of the 21st annual conference on Computer graphics and interactive techniques, pp.365-372, 1994.
[17] Eberhardt, B., Weber, A., and Strasser, W., "A Fast, Flexible, Particle-System Model for Cloth Draping," IEEE Comput. Graph. Appl., Vol.16, No.5, pp.52-59, 1996.
[18] Provot, X., "Deformation constraints in a mass-spring model to describe rigid cloth behavior," in Graphics Interface, pp.147-155, 1995.
[19] Choi, K. J. and Ko, H. S., "Stable but responsive cloth," in Proceedings of the 29th annual conference on Computer graphics and interactive techniques, San Antonio, Texas, 2002.
[20] 李金紋，"以質點為基礎的布料動態行為模擬"，國立成功大學工程科學系碩士論文，民國90年。
[21] 簡志霖，"布料動態模擬"，國立成功大學工業設計學系碩士論文，民國92年。
[22] 陳榮圻，"3D虛擬服裝的模擬與呈現"，國立成功大學工業設計學系碩士論文，民國94年。
[23] 陳耀昆，"三維空間中的即時旗幟動畫模擬"，輔仁大學資訊工程學系碩士論文，民國95年。
[24] 紀佳吟，"採用小波轉換加速的即時布料動態模擬"，國立交通大學多媒體工程研究所碩士論文，民國96年。
[25] Fontana, M., Rizzi, C., and Cugini, U., "3D virtual apparel design for industrial applications," Computer-Aided Design, Vol.37, No.6, pp.609-622, 2005.
[26] Hu, J., Structure and mechanics of woven fabrics, Woodhead Publishing, 2000.
[27] Volino, P., Courchesne, M., and Magnenat-Thalmann, N., "Versatile and efficient techniques for simulating cloth and other deformable objects," in Proceedings of the 22nd annual conference on Computer graphics and interactive techniques, 1995.
[28] Baraff, D. and Witkin, A., "Large steps in cloth simulation," in Proceedings of the 25th annual conference on Computer graphics and interactive techniques, pp.43-54, 1998.
[29] Volino, P. and Magnenat-Thalmann, N., "Simple linear bending stiffness in particle systems," in Proceedings of the 2006 ACM SIGGRAPH/Eurographics symposium on Computer animation, Vienna, Austria, 2006.
[30] Smith, A., Kitamura, Y., Takemura, H., et al., "A simple and efficient method for accurate collision detection among deformable polyhedral objects in arbitrary motion," in Virtual Reality Annual International Symposium, 1995. Proceedings., pp.136-145, 1995.
[31] Teschner, M., Kimmerle, S., Heidelberger, B., et al., "Collision detection for deformable objects," Computer Graphics Forum, Vol.24, No.1, pp.61-81, 2005.
[32] Hubbard, P. M., "Approximating polyhedra with spheres for time-critical collision detection," ACM Transactions on Graphics, Vol.15, No.3, pp.179-210, 1996.
[33] van den Bergen, G., "Efficient collision detection of complex deformable models using AABB trees," Journal of Graphics Tools, Vol.2, No.4, pp.1-13, 1997.
[34] Gottschalk, S., Lin, M. C., and Manocha, D., "OBBTree: a hierarchical structure for rapid interference detection," in Proceedings of the 23rd annual conference on Computer graphics and interactive techniques, pp.171-180, 1996.
[35] Klosowski, J. T., Held, M., Mitchell, J. S. B., et al., "Efficient collision detection using bounding volume hierarchies of k-DOPs," IEEE Transactions on Visualization and Computer Graphics, Vol.4, No.1, pp.21-36, 1998.
[36] Volino, P. and Magnenat-Thalmann, N., "Efficient self-collision detection on smoothly discretized surface animations using geometrical shape regularity," Computer Graphics Forum, Vol.13, No.3, pp.155-166, 1994.
[37] Volino, P. and Magnenat-Thalmann, N., "Collision and self-collision detection : robust and efficient techniques for highly deformable surfaces," in Eurographics Workshop on Animation and Simulation, pp.105-108, 1995.
[38] Provot, X., "Collision and self-collision handling in cloth model dedicated to design garment," in Graphics Interface, pp.177-189, 1997.
[39] Moore, M. and Wilhelms, J., "Collision detection and response for computer animation," SIGGRAPH Comput. Graph., Vol.22, No.4, pp.289-298, 1988.
[40] Huh, S., Metaxas, D. N., and Badler, N. I., "Collision resolutions in cloth simulation," in Computer Animation, 2001. The Fourteenth Conference on Computer Animation. Proceedings, pp.122-127, 2001.
[41] Bridson, R., Fedkiw, R., and Anderson, J., "Robust treatment of collisions, contact and friction for cloth animation," ACM Transactions on Graphics, Vol.21, No.3, pp.594-603, 2002.
[42] Volino, P. and Magnenat-Thalmann, N., "Accurate collision response on polygonal meshes," in Computer Animation 2000. Proceedings, pp.154-163, 2000.
[43] Ho-Le, K., "Finite element mesh generation methods: a review and classification," Computer-Aided Design, Vol.20, No.1, pp.27-38, 1988.
[44] O'Rourke, J., Computational geometry in C, Cambridge University, 1993.
[45] Alfonzetti, S., Coco, S., Cavalieri, S., et al., "Automatic mesh generation by the let-it-grow neural network," IEEE Transactions on Magnetics, Vol.32, No.3, pp.1349-1352, 1996.
[46] Cavendish, J. C., Field, D. A., and Frey, W. H., "An apporach to automatic three-dimensional finite element mesh generation," International Journal for Numerical Methods in Engineering, Vol.21, No.2, pp.329-347, 1985.
[47] Kikuchi, N., "Adaptive grid-design methods for finite element analysis," Computer Methods in Applied Mechanics and Engineering, Vol.55, No.1-2, pp.129-160, 1986.
[48] Min, W., Tangt, Z., Zhang, Z., et al., "Automatic mesh generation for multiply connected planar regions based on mesh grading propagation," Computer-Aided Design, Vol.28, No.9, pp.671-681, 1996.
[49] Bykat, A., "Design of a recursive, shape controlling mesh generator," International Journal for Numerical Methods in Engineering, Vol.19, No.9, pp.1375-1390, 1983.
[50] Choi, K. J. and Ko, H. S., "Research problems in clothing simulation," Computer-Aided Design, Vol.37, No.6, pp.585-592, 2005.
[51] Leong, I. F., "Automatic feature extraction and anthropometry from marker-less scanned human body," Doctoral Dissertation, Mechanical Engineering, National Cheng Kung University, Tainan, Taiwan, 2009.
[52] ANSI/AAMA 292, "American national standard for pattern data interchange: data format", American National Standards Institute, 1993
[53] "Autodesk," 2009, Autodesk Inc., <http://www.autodesk.com.tw/>, 14 July 2009.
[54] Gerald, C. F. and Wheatley, P. O., Applied Numerical Analysis, 7th ed. Pearson Education, 2004.
[55] Volino, P. and Magnenat-Thalmann, N., Virtual Clothing: Theory and Practice, Springer, 1998.