在這本論文中，我們為模擬3D環境中的可變形物體而提出一變形的方法，我們的目標包括：(1) 即時變形效能，(2) 在複雜的場景中仍能維持變形計算的穩定性，及 (3) 易於應用於各種模型。
我們以剛體做為物體變形後復原的形狀，每一個剛體上的點稱做目標點或目標粒子，剛體擁用物理行為並受外力的影響。我們的方法沒有使用模型的網格做為變形的依據。我們是利用粒子系統控制可變形模型的外形。每個粒子與其相對應的目標點之間存在一個力量，將粒子拉回目標點的位置，所以可變形模型最終會回復原來的形狀並在過程中產生變形的樣子。
我們的貢獻包括：(1) 改進記憶體及計算量上的效益，(2) 變形演算法在維持互動式環境的穩定性，及 (3) 具有對各種模型提供“載入即模擬”的特性。

In this paper, we propose a deformation method for modeling non-rigid objects in a game-like environment or 3D virtual environment. The studying goals include: (1) providing high-speed run-time performance, (2) maintaining the stability of deformation computation in a complex scene, and (3) deploying all kinds of models to our approach easily.
We use a rigid body to maintain the shape of a model; a point on a rigid body is called a goal position or goal particle. A rigid body has physical behaviors and is affected by external forces. We use particle system to control the appearance of a deformable object. There forces among particles and its corresponding goal positions to pull the particles back, so the deformable object will finally return to its original shape and make deformed appearance.
Our contributions include: (1) improving the efficiency in terms of memory and computational complexity, and (2) maintaining the stability of the dynamic simulation, for games and interactive applications, and (3) "plug and simulate" characteristic to handle a large variety of objects.

[1] Bourg D., Physics for Game Developers, Sebastopol, O’Reilly, 2002.
[2] Desbrun M. and M. P. Gascuel, "Animating soft substances withimplicit surfaces," in Proc. 22nd Anal. Conf. on Computer graphics and interactive techniques, Los Angeles, Sep. 1995, pp.287-290.
[3] Desbrun M. and M. P. Gascuel, "A new paradigm for animating highly deformable bodies," in Proc. Eurographics Workshop on Computer Animation and Simulation, Poitiers, Aug. 1996, pp.61-76.
[4] Dubenne G., M. Desbrun, M. P. Cani, and A. P. Barr, "Dynamic real-time deformations using space and time adaptive sampling," in Proc. ACM SIGGRAPH’01, Los Angeles, Aug.12-17, 2001, pp.31-36.
[5] Fries T. P., and H. G. Matthies, Classification and Overview of Meshfree Methods, Technical report, Mathematics and Computer Science Dept., Univ. of Braunschweig, Brunswick, Germany, July 2004.
[6] Glenn F., Game Physics Articles, http://www.gaffer.org/articles/
[7] Grinspun E., Krysl P., and Schröder P., " A simple framework for adaptive simulation," in Proc. 29th Anal. Conf. on Computer graphics and interactive techniques, San Antonia, Texas, July 23-26, 2002, pp.281-290.
[8] Guo X. and Q. Hong, "Collision detection and deformable objects: real-time meshless deformation," Computer Animation and Virtual Worlds, vol.16, no. 3-4, pp.189-200, 2005.
[9] Hirota G., R. Maheshwari, and M. C. Lin, " Fast volume-preserving free form deformation using multi-level optimization," in Proc. fifth ACM symp. on Solid modeling and applications, Ann Arbor, Michigan, June 08-11, 1999, pp.234 -245.
[10] Hecker C., "Physics Part3: Collision Response," Game Developer Magazine, pp.11-18, Mar. 1997.
[11] James D. and D. Pai, "BD-tree: output-sensitive collision detection for reduced deformable models," ACM Transactions on Graphics, vol.23, no.3, 2004.
[12] James D. and D. Pai, "Accurate real time deformable objects," in Proc. 26th Anal. Conf. on Computer graphics and interactive techniques, Los Angeles, Aug.8-13, 1999, pp.65-72.
[13] Kircher S. and M. Garland. "Progressive multiresolution meshes for deforming surfaces," in Proc. ACM SIGGRAPH symp. on Computer Animation, Los Angeles, CA, July 29-31, 2005, pp.191-200.
[14] Lau W. H., O. Chan, M. Luk, and W. B. Li, "A collision detection framework for deformable objects," in Proc. ACM symp. on Virtual Reality Software and Technology, Hong-King, Nov. 11-13, 2002, pp.113-120.
[15] Linden N., H. Reynolds, and C. Sullivan, Real Time Implicit Bulging and Volume Preservation, Technical report, Computer Science Dept., Univ. of Trinity College, Dublin, Ireland, 1999.
[16] Müller M., R. Keiser, A. Nealen, M. Pauly, M. Gross, and M. Alexa, "Point based animation of elastic, plastic and melting objects," in Proc. ACM SIGGRAPH Symp. on Computer Animation, Grenoble, France, Aug. 27-29, 2004, pp.142.
[17] Müller M., B. Heidelberger, M. Teschner, and M. Gross, "Meshless Deformations Based on Shape Matching," ACM Trans. on Graphics, vol. 24, no. 3, pp. 471-478, 2005.
[18] Müller M, J. Dorsey, L. McMillan, R. Jagnow, and B. Cutler, "Stable real-time deformations," in Proc. 2002 ACM SIGGRAPH/Eurographics symp. on Computer Animation, San Antonio, Texas, July 21-22, 2002, pp.49-54.
[19] Teran J., S. Blemker, V. Hing, and R. Fedkiw, "Finite volume methods for the simulation of skeletal muscle," in Proc. ACM SIGGRAPH symp. on Computer Animation, San Diego, CA, July 26-27, 2003, pp.68-74.
[20] Yoshizawa S., A. G. Belyaev, and H. P. Seidel, "Free-form skeleton-driven mesh deformations," in Proc. 8th ACM symp. on Solid Modeling and Applications, Seattle, Washington, June 16-20, 2003, pp.247-253.