基于物理的实时弹塑体形变模拟研究与实现
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摘要
近几年来,弹塑体形变模拟被大量应用于电影特效、游戏的变形场景、医学培训系统,仿生物学的研究及一些三维环境的展示等方面。弹塑体形变模拟目前已成为计算机图形学中比较热门的一个研究领域。而当前现有的弹塑体形变模拟主要分为基于物理的和非物理的模拟两种方式。基于物理的弹塑体形变模拟采用真实世界中的物理学定理可以完美重现虚拟物体在虚拟的空间中真实的运动过程及逼真的形变。这在游戏和医学培训中给人带来很震撼的逼真感,因此大大推动了弹塑体形变模拟的应用。虽然其拥有广泛的应用领域和发展空间,但是目前基于物理的弹塑体形变模拟依然存在诸多的问题需要解决。
在基于物理模拟的基础上,为了解决弹塑体形变模拟的实时性,本文采用传统的质点弹簧模型建模方式,在运动微分方程上使用显示欧拉方程。其计算简单等特点很好的满足其实时计算的要求,为了解决显示欧拉法不稳定的缺陷以及质点弹簧模型所拥有的模拟物体没有整体运动的遗憾,本文采用了基于刚度外核形状匹配的算法对欧拉法计算出来的位置修正,既避免了系统的不稳定又使得弹塑体在模拟时拥有类似刚体的整体运动。由于引入刚度外核的形状匹配思想,使得弹塑体形变模拟变得快速且稳定。同时对基于质点弹簧刚度外核形状匹配算法的结果与性能进行了分析及验证,该算法取得让人比较满意的模拟结果。
本文的创新如下:
(1)提出了一种质点弹簧模型与刚度外核相结合的建模方式。结合显示欧拉法和刚度外核匹配算法的优点,很好解决了弹塑体模拟的实时性问题。
(2)提出一种基于表面网格采样,裂纹动态扩展的建模方法,实现了较快的基于表面的弹簧网格建模的弹塑体断裂。
In recent years, elastoplastic deformation simulation has been used in movie special effects, the deformation scene in the game, the medical training system, bionics research, the exhibition of some three-dimensional environment and so on. Elastoplastic deformation simulation has become rather popular in computer graphics as a research field. Currently the available elastoplastic deformation simulation is divided into physics and non-physics-based simulation in two ways. Physics-based simulation of elastic-plastic deformation using physics theorem in the real world can perfectly reproduce the real movement and realistic deformation of virtual objects in virtual space. It’s used in the game and medical training and brings a shocking sense of realism, and so greatly promotes the application of elastoplastic. Despite its extensive applications and development space, at present physics-based simulation of elastoplastic deformation simulation remains many problems to resolved.
Based on the physics-based simulation, in order to solve the real-time of elastoplastic deformation , this paper adopts the traditional mass-spring modeling methods and uses Euler's equation in the equations of motion. The calculation is simple and so good to meet the requirements of real-time computing. In order to overcome the shortcomings of the instability of Euler method and that the simulacrum not moving as a whole using mass spring model, we adopt shape matching algorithm of stiffness outer core to amend the location which is calculated by using Euler method. This only avoid the system instability but also makes the elastoplastic has the similarity of rigid body overall motion while simulating. Due to the introduction of the shape matching of stiffness, elastoplastic deformation simulation becomes fast and stable. Meanwhile, this paper analyzes and verifies the results and performance of shape matching algorithm of stiffness outer core used in mass spring, and the algorithm makes rather satisfactory simulation results.
The main contributions of this thesis are mainly in the following aspects:
○1 Propose a way based combined with mass-springs and rigid outer core to solution the real-time issues.
○2 Propose a way based surface mesh sampling,dynamic extension to achieve a fast simulation of soft body crack based mass-springs.
在基于物理模拟的基础上,为了解决弹塑体形变模拟的实时性,本文采用传统的质点弹簧模型建模方式,在运动微分方程上使用显示欧拉方程。其计算简单等特点很好的满足其实时计算的要求,为了解决显示欧拉法不稳定的缺陷以及质点弹簧模型所拥有的模拟物体没有整体运动的遗憾,本文采用了基于刚度外核形状匹配的算法对欧拉法计算出来的位置修正,既避免了系统的不稳定又使得弹塑体在模拟时拥有类似刚体的整体运动。由于引入刚度外核的形状匹配思想,使得弹塑体形变模拟变得快速且稳定。同时对基于质点弹簧刚度外核形状匹配算法的结果与性能进行了分析及验证,该算法取得让人比较满意的模拟结果。
本文的创新如下:
(1)提出了一种质点弹簧模型与刚度外核相结合的建模方式。结合显示欧拉法和刚度外核匹配算法的优点,很好解决了弹塑体模拟的实时性问题。
(2)提出一种基于表面网格采样,裂纹动态扩展的建模方法,实现了较快的基于表面的弹簧网格建模的弹塑体断裂。
In recent years, elastoplastic deformation simulation has been used in movie special effects, the deformation scene in the game, the medical training system, bionics research, the exhibition of some three-dimensional environment and so on. Elastoplastic deformation simulation has become rather popular in computer graphics as a research field. Currently the available elastoplastic deformation simulation is divided into physics and non-physics-based simulation in two ways. Physics-based simulation of elastic-plastic deformation using physics theorem in the real world can perfectly reproduce the real movement and realistic deformation of virtual objects in virtual space. It’s used in the game and medical training and brings a shocking sense of realism, and so greatly promotes the application of elastoplastic. Despite its extensive applications and development space, at present physics-based simulation of elastoplastic deformation simulation remains many problems to resolved.
Based on the physics-based simulation, in order to solve the real-time of elastoplastic deformation , this paper adopts the traditional mass-spring modeling methods and uses Euler's equation in the equations of motion. The calculation is simple and so good to meet the requirements of real-time computing. In order to overcome the shortcomings of the instability of Euler method and that the simulacrum not moving as a whole using mass spring model, we adopt shape matching algorithm of stiffness outer core to amend the location which is calculated by using Euler method. This only avoid the system instability but also makes the elastoplastic has the similarity of rigid body overall motion while simulating. Due to the introduction of the shape matching of stiffness, elastoplastic deformation simulation becomes fast and stable. Meanwhile, this paper analyzes and verifies the results and performance of shape matching algorithm of stiffness outer core used in mass spring, and the algorithm makes rather satisfactory simulation results.
The main contributions of this thesis are mainly in the following aspects:
○1 Propose a way based combined with mass-springs and rigid outer core to solution the real-time issues.
○2 Propose a way based surface mesh sampling,dynamic extension to achieve a fast simulation of soft body crack based mass-springs.
引文
[1] TERZOPOULOS D., FLEISCHER K.:Modeling inelastic deformation: viscolelasticity,plasticity,fracture. In SIGGRAPH‘88(1988),pp.269-278.
[2] GRINSPUN E., HIRANI A.N.,DESBRUN M., SCHRODER P.:Discrete shells. In Proceedings of the 2003 ACM SIGGRAPH/Eurographics Symposium on Computer animation(2003),pp.62-67.
[3] BHAT K.,TWIGG C,.HODGINS J. K., KHOSLA P., POPOVIC Z., SEITZS.:Estimating cloth simulation parameters from wideo. In ACM SIGGRAPH/Eurographics Symposium on Computer Animation(July 2003).
[4] BIANCHI G., SOLENTHALER. B., SZEKELY G.,HARDERS M.:Simultaneous topology and stiffness identification for mass-spring models based on fem reference deformations. In MICCAI(2)(2004) ,pp.293-301.
[5] M ULLER, M., HEIDELBERGER, B., TESCHNER, M., AND GROSS, M. 2005. Meshless Deformations Based on Shape Matching. ACM Trans. on Graphics 24, 3 (Aug.), 471–478.
[6] M ULLER, M., HEIDELBERGER, B., HENNIX, M., AND RAT-CLIFF, J. 2006. Position Based Dynamics. In Proc. of Virtual Reality Interactions and Physical Simulations (VRIPhys), 71–80.
[7] Alec R. Rivers, Doug L. James: Fast LSM: Fast Lattice Shape Matching for Robust Real-Time Deformation ACM Transactions on Graphics (SIGGRAPH 2007)
[8] R Keiser, B Adams , D Gasser et al. A Unified Largangian Approach to Solid-Fluid Animation[C]. Proc of the 2006 conference on Graphics interface,2006:125-133.
[9] M Pauly, R Keiser,B Adams et al. Meshless animation of fracturing solids[J].ACM Transactions on Graphics,2005,24(3):957-964.
[10] M Wicke, D Steinemann, M Gross. Efficient Animation of Point-Sampled Thin Shells[J]. Computer Graphics Forum,2005,24(3):667-676.
[11] DL James, DK Pai. Real time simulation of multizone elastokinematic models[C].Proc of the ICRA '02.2002:927-932.
[12] M Pauly, R Keiser, B Adams et al. Meshless animation of fracturing solids[J].ACM Transactions on Graphics,2005,24(3):957-964.
[13] JAMES D.L.,PAI D.K.: ArtDefo: accurate real time deformable objects. In SIGGRAPH’99 (1999),pp.65-72.
[14] JAMES D.L.,PAI D. K.: Multiresolution Green’s function methods for interactive simulation of large-scale elastostatic objects. ACM Transactions on Graphics22,1(2003),47-82.
[15] 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.
[16] TERAN J.,BLEMKER S., HING V. N. T.,FEDKIW R.: Finite volume methods for the simulation of skeletal muscle. In Eurographics/SIGGRAPH Symposium on Computer Animation(2003).
[17] TU X., TERZOPOULOS D.: Artificial fishes: physics locomotion ,perception , behavior , In SIGGRAPH‘94(1994),pp.43-50.
[18] M.Hauth, O. EtzmuB,W.StraBer.Analysis of numerical methods for the simulation of deformable models.The Visual Computer.2003,19(7-8):581-600.
[19] CRYTEK GMBH,2009.http://www.crytek.com/technology/cryengine-3/specifications/
[20] Wilhelms J,Gelder A V.Anatomically based modeling.In Proceedings of SIGGRAPH97,1997:173-180.
[21] Molino. N, Bao, Z asnd Fedkiw,R., a virtual node algorithm for changing mesh topology during simulation, SIGGRAPH 2004,ACM TOG23,385-392(2004).
[22] MULLER, M., DORSEY, J., MCMILLAN, L., JAGNOW, R., AND CUTLER, B. 2002. Stable Real-Time Deformations. In ACM SIGGRAPH Symposium on Computer Animation, 49–54.
[23] Irving, G., Schroeder, C., and Fedkiw, R. "Volume Conserving Finite Element Simulations of Deformable Models". SIGGRAPH 2007, ACM TOG 26, 13, 2007.
[24] IRVING G., TERAN J., FEDKIW R.: Invertible finite elements for robust simulation of large deformation. In Proceedings of the 2004 ACM SIGRAPH/Eurographics symposium on Computer animation (2004),pp.131-140.
[25] TESCHNER M., HEIDELBERGER B., MULLER M.,GROSS M.:A versatile and robust model for geometrically complex deformable solids. In Proceeding of Computer Graphics International(CGI)(Jun 2004),pp.312-319.
[26] MOLINO N.,BAO Z., FEDKIW R.: A virtual node algorithm for changing mesh topology during simulation. ACM Trans. Graph.23,3(2004),385-392.
[27] TERZOPOULOS D., WATERS K.:Physically-based facial modeling ,analysis,and animation.Journal of Visualization and Computer Animation I,(1990),73-80.
[28] O’BRIEN J.F.,BARGTEIL A. W., HODGINS J.K.:Graphical modeling and animation of ductile fracture. In Proceedings of SIGGRAPH 2002 (2002),pp.291-294.
[29] BIANCHI G., SOLENTHALER. B., SZEKELY G.,HARDERS M.:Simultaneous topology and stiffness identification for mass-spring models based on fem reference deformations. In MICCAI(2)(2004) ,pp.293-301.
[30] M Pauly, R Keiser,B Adams et al. Meshless animation of fracturing solids[J].ACM Transactions on Graphics,2005,24(3):957-964.
[31] Y OON,S.,AND KIM,M.2006.Sweep-based freeform deformations, In Eurographics,vol.25,Eurographics Assoc.,487-96.
[32] Sarah F.F. Gibson,Brian Mirtich,A surgery of Deformable Modeling in Computer Graphics,MERL,TR-97,1997:1-33.
[2] GRINSPUN E., HIRANI A.N.,DESBRUN M., SCHRODER P.:Discrete shells. In Proceedings of the 2003 ACM SIGGRAPH/Eurographics Symposium on Computer animation(2003),pp.62-67.
[3] BHAT K.,TWIGG C,.HODGINS J. K., KHOSLA P., POPOVIC Z., SEITZS.:Estimating cloth simulation parameters from wideo. In ACM SIGGRAPH/Eurographics Symposium on Computer Animation(July 2003).
[4] BIANCHI G., SOLENTHALER. B., SZEKELY G.,HARDERS M.:Simultaneous topology and stiffness identification for mass-spring models based on fem reference deformations. In MICCAI(2)(2004) ,pp.293-301.
[5] M ULLER, M., HEIDELBERGER, B., TESCHNER, M., AND GROSS, M. 2005. Meshless Deformations Based on Shape Matching. ACM Trans. on Graphics 24, 3 (Aug.), 471–478.
[6] M ULLER, M., HEIDELBERGER, B., HENNIX, M., AND RAT-CLIFF, J. 2006. Position Based Dynamics. In Proc. of Virtual Reality Interactions and Physical Simulations (VRIPhys), 71–80.
[7] Alec R. Rivers, Doug L. James: Fast LSM: Fast Lattice Shape Matching for Robust Real-Time Deformation ACM Transactions on Graphics (SIGGRAPH 2007)
[8] R Keiser, B Adams , D Gasser et al. A Unified Largangian Approach to Solid-Fluid Animation[C]. Proc of the 2006 conference on Graphics interface,2006:125-133.
[9] M Pauly, R Keiser,B Adams et al. Meshless animation of fracturing solids[J].ACM Transactions on Graphics,2005,24(3):957-964.
[10] M Wicke, D Steinemann, M Gross. Efficient Animation of Point-Sampled Thin Shells[J]. Computer Graphics Forum,2005,24(3):667-676.
[11] DL James, DK Pai. Real time simulation of multizone elastokinematic models[C].Proc of the ICRA '02.2002:927-932.
[12] M Pauly, R Keiser, B Adams et al. Meshless animation of fracturing solids[J].ACM Transactions on Graphics,2005,24(3):957-964.
[13] JAMES D.L.,PAI D.K.: ArtDefo: accurate real time deformable objects. In SIGGRAPH’99 (1999),pp.65-72.
[14] JAMES D.L.,PAI D. K.: Multiresolution Green’s function methods for interactive simulation of large-scale elastostatic objects. ACM Transactions on Graphics22,1(2003),47-82.
[15] 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.
[16] TERAN J.,BLEMKER S., HING V. N. T.,FEDKIW R.: Finite volume methods for the simulation of skeletal muscle. In Eurographics/SIGGRAPH Symposium on Computer Animation(2003).
[17] TU X., TERZOPOULOS D.: Artificial fishes: physics locomotion ,perception , behavior , In SIGGRAPH‘94(1994),pp.43-50.
[18] M.Hauth, O. EtzmuB,W.StraBer.Analysis of numerical methods for the simulation of deformable models.The Visual Computer.2003,19(7-8):581-600.
[19] CRYTEK GMBH,2009.http://www.crytek.com/technology/cryengine-3/specifications/
[20] Wilhelms J,Gelder A V.Anatomically based modeling.In Proceedings of SIGGRAPH97,1997:173-180.
[21] Molino. N, Bao, Z asnd Fedkiw,R., a virtual node algorithm for changing mesh topology during simulation, SIGGRAPH 2004,ACM TOG23,385-392(2004).
[22] MULLER, M., DORSEY, J., MCMILLAN, L., JAGNOW, R., AND CUTLER, B. 2002. Stable Real-Time Deformations. In ACM SIGGRAPH Symposium on Computer Animation, 49–54.
[23] Irving, G., Schroeder, C., and Fedkiw, R. "Volume Conserving Finite Element Simulations of Deformable Models". SIGGRAPH 2007, ACM TOG 26, 13, 2007.
[24] IRVING G., TERAN J., FEDKIW R.: Invertible finite elements for robust simulation of large deformation. In Proceedings of the 2004 ACM SIGRAPH/Eurographics symposium on Computer animation (2004),pp.131-140.
[25] TESCHNER M., HEIDELBERGER B., MULLER M.,GROSS M.:A versatile and robust model for geometrically complex deformable solids. In Proceeding of Computer Graphics International(CGI)(Jun 2004),pp.312-319.
[26] MOLINO N.,BAO Z., FEDKIW R.: A virtual node algorithm for changing mesh topology during simulation. ACM Trans. Graph.23,3(2004),385-392.
[27] TERZOPOULOS D., WATERS K.:Physically-based facial modeling ,analysis,and animation.Journal of Visualization and Computer Animation I,(1990),73-80.
[28] O’BRIEN J.F.,BARGTEIL A. W., HODGINS J.K.:Graphical modeling and animation of ductile fracture. In Proceedings of SIGGRAPH 2002 (2002),pp.291-294.
[29] BIANCHI G., SOLENTHALER. B., SZEKELY G.,HARDERS M.:Simultaneous topology and stiffness identification for mass-spring models based on fem reference deformations. In MICCAI(2)(2004) ,pp.293-301.
[30] M Pauly, R Keiser,B Adams et al. Meshless animation of fracturing solids[J].ACM Transactions on Graphics,2005,24(3):957-964.
[31] Y OON,S.,AND KIM,M.2006.Sweep-based freeform deformations, In Eurographics,vol.25,Eurographics Assoc.,487-96.
[32] Sarah F.F. Gibson,Brian Mirtich,A surgery of Deformable Modeling in Computer Graphics,MERL,TR-97,1997:1-33.