基于质点—弹簧模型的实时三维布料模拟系统
|
摘要
计算机三维图象模拟已经被广泛应用在工程模拟、虚拟现实、影视特效制作和电脑视频游戏等领域。其中,实时三维布料模拟技术由于可以用在人机交互和虚拟现实界面等场合,在应用领域受到了越来越广泛的应用。布料模拟可以增强虚拟人物穿着的衣物,以及旗帜、横幅、窗帘和桌布等虚拟物品的受穿着、悬挂、风吹、摩擦等外力的视觉效果,带来更加真实的虚拟现实体验。
在布料模拟算法中,基于质点-弹簧模型结构,通过计算通过虚拟弹簧联系的布料质点所受的外力和它们之间的相互作用力来模拟布料的受力行为和外观,相比其他布料模拟算法,有模拟真实度高,受力表现更加合理的优势。本文首先系统总结了基于质点-弹簧模型的实时布料模拟的算法,得出了在实时布料模拟中,采用隐式数值积分更为适合的结论。同时,本文也给出了经过实践有效的C++代码实现。
但是,实时的三维布料模拟由于其固有的大时间步长,会导致布料过度拉伸的super-elastic现象。本文针对这个问题,在其于经典质点修正算法的基础上,提出了改进的质点位置修正算法,改进的算法通过选择和每个质点相连的最长拉伸的弹簧,消除了修正抵消效果,从而增强了修正的效果。实验证明这个算法的表现远远优于传统算法的表现,取得了非常好的抑制效果。
本文还探讨了一个布料模拟实验平台的设计和实现。布料模拟平台的设计是根据软件工程的思想,将布料模拟实验中的通用模块抽象出来,形成独立的组件,并在此基础用C++编写了可扩展的布料模拟算法实验平台:在这个平台上,任何用户编写的遵循平台接口的布料模拟算法均可以被平台动态加载,并统计执行结果,从而大大减轻了用C++编写布料模拟算法的工作量。在开发这个平台的过程中,系统经过了仔细的设计以取得其在性能和扩展性之间的平衡,使其成为了一个简单易用,功能强大的布料模拟算法的开发、实验平台。
Three-Dimentional(3D) Computer Graphcis Simulation Technology is widely used inthe fields of engineering, virtual reality, special movie effect making and video game making.
As an important part of 3D Computer Graphics Simulation, 3D Cloth Simulation, espe-cially real-time 3D Cloth Simulation is very useful in real-environment simulation, human-computer interface and virtual reality. It is able to enhance the visual effects of apparels,?ags, banner, curtain, table cloth under external forces like wearing, hanging and blow-ing. Among these algorithms, physical-based cloth simulation algorithm which models the apiece of cloth as a mesh of masses and springs, could achieve more vivid visual effects thanothers by calculating the inter forces on masses and springs with physical laws. In this paper,the implicit integration is proved to be the most suitable algorithm and also present effectiveC++ code implementation.
However, due to the inherent large time-step in real-time simulation, the cloth maybehave super-elastic effect. This paper propose a possible solution of Mass Position Modifi-cation Altered(PMA). This new algorithm eliminates the modification nihilation effect, Thusenhanced the modification effects.
This article illustrate the design and implementation of a cloth simulation experimentalplatform, which is continuously developed when I was working on the algorithm develop-ment, applying the software engineering thoughts, and make a software platform on C++. Avariety of algorithms are able to be tested and benchmarked on this platform. With a lot ofdesign trade-offs to balance the performance and extensibility, It developed into a handy andpowerful platform for developing and testing cloth simulation algorithms.
在布料模拟算法中,基于质点-弹簧模型结构,通过计算通过虚拟弹簧联系的布料质点所受的外力和它们之间的相互作用力来模拟布料的受力行为和外观,相比其他布料模拟算法,有模拟真实度高,受力表现更加合理的优势。本文首先系统总结了基于质点-弹簧模型的实时布料模拟的算法,得出了在实时布料模拟中,采用隐式数值积分更为适合的结论。同时,本文也给出了经过实践有效的C++代码实现。
但是,实时的三维布料模拟由于其固有的大时间步长,会导致布料过度拉伸的super-elastic现象。本文针对这个问题,在其于经典质点修正算法的基础上,提出了改进的质点位置修正算法,改进的算法通过选择和每个质点相连的最长拉伸的弹簧,消除了修正抵消效果,从而增强了修正的效果。实验证明这个算法的表现远远优于传统算法的表现,取得了非常好的抑制效果。
本文还探讨了一个布料模拟实验平台的设计和实现。布料模拟平台的设计是根据软件工程的思想,将布料模拟实验中的通用模块抽象出来,形成独立的组件,并在此基础用C++编写了可扩展的布料模拟算法实验平台:在这个平台上,任何用户编写的遵循平台接口的布料模拟算法均可以被平台动态加载,并统计执行结果,从而大大减轻了用C++编写布料模拟算法的工作量。在开发这个平台的过程中,系统经过了仔细的设计以取得其在性能和扩展性之间的平衡,使其成为了一个简单易用,功能强大的布料模拟算法的开发、实验平台。
Three-Dimentional(3D) Computer Graphcis Simulation Technology is widely used inthe fields of engineering, virtual reality, special movie effect making and video game making.
As an important part of 3D Computer Graphics Simulation, 3D Cloth Simulation, espe-cially real-time 3D Cloth Simulation is very useful in real-environment simulation, human-computer interface and virtual reality. It is able to enhance the visual effects of apparels,?ags, banner, curtain, table cloth under external forces like wearing, hanging and blow-ing. Among these algorithms, physical-based cloth simulation algorithm which models the apiece of cloth as a mesh of masses and springs, could achieve more vivid visual effects thanothers by calculating the inter forces on masses and springs with physical laws. In this paper,the implicit integration is proved to be the most suitable algorithm and also present effectiveC++ code implementation.
However, due to the inherent large time-step in real-time simulation, the cloth maybehave super-elastic effect. This paper propose a possible solution of Mass Position Modifi-cation Altered(PMA). This new algorithm eliminates the modification nihilation effect, Thusenhanced the modification effects.
This article illustrate the design and implementation of a cloth simulation experimentalplatform, which is continuously developed when I was working on the algorithm develop-ment, applying the software engineering thoughts, and make a software platform on C++. Avariety of algorithms are able to be tested and benchmarked on this platform. With a lot ofdesign trade-offs to balance the performance and extensibility, It developed into a handy andpowerful platform for developing and testing cloth simulation algorithms.
引文
[1] 朱淮冰, 金小刚, 冯结青等布料动画模拟综述. 计算机辅助设计与图形学学报,5, 2004.
[2] 柳有权, 刘学慧, 朱红斌等基于物理的流体模拟动画综述. 计算机辅助设计与图形学学报,12,2005.
[3] 李政仪, 张伟鹏, 赵龙基于物理的图形建模研究. 计算机仿真,7, 2005.
[4] 周永霞, 郁佳荣, 石教英. 基于物理的实时人体动画. 浙江大学学报(工学版),12, 2006.
[5] 宁松, 林木华, 刘郊一种快速的基于物理模型的织物模拟. 计算机仿真,12, 2006.
[6] 朱刚, 郝正同, 陈擘威运用java3d实现三维实时物理模拟动画. 阜阳师范学院学报(自然科学版),4, 2006.
[7] 杨铭民. 从物理学角度研究计算机动画的运动规律. 现代电视技术,8, 2005.
[8] 田海山, 何援军, 邝旻织物动画模拟的实时数值解法. 上海交通大学学报,3, 2006.
[9] M. Aono. A wrinkle propagation model for cloth. pages 95–115, 1990.
[10] Masaki Aono, Paolo Denti, David E. Breen, and Michael J. Wozny. Fitting A woven cloth modelto a curved surface: Dart insertion. IEEE Computer Graphics and Applications, 16(5):60–70, 19961996.
[11] David Baraff. Fast contact force computation for nonpenetrating rigid bodies. pages 23–34, 1994.
[12] David Baraff and Andrew P. Witkin. Large steps in cloth simulation. pages 43–54, July 1998.
[13] Ronen Barzel and Alan H. Barr. A modeling system based on dynamic constraints. In SIGGRAPH’88: Proceedings of the 15th annual conference on Computer graphics and interactive techniques,pages 179–188, New York, NY, USA, 1988. ACM.
[14] Therese Bonte, Andrea Galimberti, and Caterina Rizzi. A 3d graphic environment for garmentsdesign. pages 137–150, 2002.
[15] D. Breen, D. House, and P. Getto. A particle-based model for simulating the draping behavior ofwoven cloth, 1994.
[16] David E. Breen, Donald H. House, and Michael J. Wozny. Predicting the drape of woven cloth usinginteracting particles. pages 365–372, 1994.
[17] David E. Breen, Donald H. House, and Michael J. Wozny. Predicting the drape of woven cloth usinginteracting particles. Computer Graphics, 28(Annual Conference Series):365–372, 1994.
[18] David E. Breen, Donald H. House, and Michael J. Wozny. Predicting the drape of woven cloth usinginteracting particles. pages 365–372, 1994.
[19] David E. Breen, Donald H. House, and Michael J. Wozny. Predicting the drape of woven cloth usinginteracting particles. pages 365–372, 1994.
[20] R. Bridson, S. Marino, and R. Fedkiw. Simulation of clothing with folds and wrinkles. pages 28–36,2003.
[21] Michel Carignan, Ying Yang, Nadia Magnenat Thalmann, and Daniel Thalmann. Dressing animatedsynthetic actors with complex deformable clothes. pages 99–104, 1992.
[22] K. Choi and H. Ko. Stable but responsive cloth.
[23] Masaki Aono David. Modeling methods for the design of 3d broadcloth composite parts.
[24] Mathieu Desbrun, Peter Schro¨der, and Alan Barr. Interactive animation of structured deformableobjects. pages 1–8, 1999.
[25] Bernhard Eberhardt, Andreas Weber, and Wolfgang Strasser. A fast, ?exible, particle-system modelfor cloth draping. IEEE Comput. Graph. Appl., 16(5):52–59, 1996.
[26] Jeffrey W. Eischen, Shigan Deng, and Timothy G. Clapp. Finite-element modeling and control of?exible fabric parts. IEEE Comput. Graph. Appl., 16(5):71–80, 1996.
[27] M. Fontana, C. Rizzi, and U. Cugini. Physics-based modelling and simulation of functional clothfor virtual prototyping applications. pages 267–272, 2004.
[28] Allen Van Gelder. Approximate simulation of elastic membranes by triangulated spring meshes. J.Graph. Tools, 3(2):21–42, 1998.
[29] Donald H. House and David E. Breen, editors. Cloth modeling and animation. A. K. Peters, Ltd.,Natick, MA, USA, 2000.
[30] Young-Min Kang and Hwan-Gue Cho. Complex deformable objects in virtual reality. pages 49–56,2002.
[31] Young-Min Kang and Hwan-Gue Cho. Real-time animation of complex virtual cloth with physicalplausibility and numerical stability. Presence: Teleoper. Virtual Environ., 13(6):668–680, 2004.
[32] Michael Kass and Gavin Miller. Rapid, stable ?uid dynamics for computer graphics. pages 49–57,1990.
[33] Hing N. Ng and Richard L. Grimsdale. Computer graphics techniques for modeling cloth. IEEEComput. Graph. Appl., 16(5):28–41, 1996.
[34] Hidehiko Okabe, Haruki Imaoka, Takako Tomiha, and Haruo Niwaya. Three dimensional apparelcad system. SIGGRAPH Comput. Graph., 26(2):105–110, 1992.
[35] John C. Platt and Alan H. Barr. Constraints methods for ?exible models. SIGGRAPH Comput.Graph., 22(4):279–288, 1988.
[36] Xavier Provot. Deformation constraints in a mass-spring model to describe rigid cloth behavior.pages 147–154, 1995.
[37] Jonathan R Shewchuk. An introduction to the conjugate gradient method without the agonizingpain. Technical report, Pittsburgh, PA, USA, 1994.
[38] Demetri Terzopoulos and Kurt Fleischer. Modeling inelastic deformation: viscolelasticity, plasticity,fracture. pages 269–278, 1988.
[39] Demetri Terzopoulos and Kurt Fleischer. Modeling inelastic deformation: viscolelasticity, plasticity,fracture. In SIGGRAPH ’88: Proceedings of the 15th annual conference on Computer graphics andinteractive techniques, pages 269–278, New York, NY, USA, 1988. ACM.
[40] Demetri Terzopoulos, John Platt, Alan Barr, and Kurt Fleischer. Elastically deformable models.pages 205–214, 1987.
[41] Demetri Terzopoulos, John Platt, Alan Barr, and Kurt Fleischer. Elastically deformable models. InSIGGRAPH ’87: Proceedings of the 14th annual conference on Computer graphics and interactivetechniques, pages 205–214, New York, NY, USA, 1987. ACM.
[42] Demetri Terzopoulos and Hong Qin. Dynamic nurbs with geometric constraints for interactivesculpting. ACM Trans. Graph., 13(2):103–136, 1994.
[43] Xiaoyuan Tu. Artificial animals for computer animation: biomechanics, locomotion, perception,and behavior. PhD thesis, Toronto, Ont., Canada, Canada, 1996. Adviser-Demetri Terzopoulos andAdviser-Eugene Fiume.
[44] Greg Turk and Marc Levoy. Zippered polygon meshes from range images. In SIGGRAPH ’94:Proceedings of the 21st annual conference on Computer graphics and interactive techniques, pages311–318, New York, NY, USA, 1994. ACM.
[45] Julien Villard and Houman Borouchaki. Adaptive meshing for cloth animation. pages 243–252,15–18 September 2002.
[46] Jerry Weil. The synthesis of cloth objects. SIGGRAPH Comput. Graph., 20(4):49–54, 1986.
[47] Ying Yang, Nadia Magnenat Thalmann, and Daniel Thalmann. 3d garment design and animation -a new design tool for the garment industry.
[48] Young-MinKang, Jeong-HyeonChoi, Hwan-Gue Cho, and Do-Hoon Lee. An efficient animation ofwrinkled cloth with approximate implicit integration. The Visual Computer, pages 147–157, 2001.
[2] 柳有权, 刘学慧, 朱红斌等基于物理的流体模拟动画综述. 计算机辅助设计与图形学学报,12,2005.
[3] 李政仪, 张伟鹏, 赵龙基于物理的图形建模研究. 计算机仿真,7, 2005.
[4] 周永霞, 郁佳荣, 石教英. 基于物理的实时人体动画. 浙江大学学报(工学版),12, 2006.
[5] 宁松, 林木华, 刘郊一种快速的基于物理模型的织物模拟. 计算机仿真,12, 2006.
[6] 朱刚, 郝正同, 陈擘威运用java3d实现三维实时物理模拟动画. 阜阳师范学院学报(自然科学版),4, 2006.
[7] 杨铭民. 从物理学角度研究计算机动画的运动规律. 现代电视技术,8, 2005.
[8] 田海山, 何援军, 邝旻织物动画模拟的实时数值解法. 上海交通大学学报,3, 2006.
[9] M. Aono. A wrinkle propagation model for cloth. pages 95–115, 1990.
[10] Masaki Aono, Paolo Denti, David E. Breen, and Michael J. Wozny. Fitting A woven cloth modelto a curved surface: Dart insertion. IEEE Computer Graphics and Applications, 16(5):60–70, 19961996.
[11] David Baraff. Fast contact force computation for nonpenetrating rigid bodies. pages 23–34, 1994.
[12] David Baraff and Andrew P. Witkin. Large steps in cloth simulation. pages 43–54, July 1998.
[13] Ronen Barzel and Alan H. Barr. A modeling system based on dynamic constraints. In SIGGRAPH’88: Proceedings of the 15th annual conference on Computer graphics and interactive techniques,pages 179–188, New York, NY, USA, 1988. ACM.
[14] Therese Bonte, Andrea Galimberti, and Caterina Rizzi. A 3d graphic environment for garmentsdesign. pages 137–150, 2002.
[15] D. Breen, D. House, and P. Getto. A particle-based model for simulating the draping behavior ofwoven cloth, 1994.
[16] David E. Breen, Donald H. House, and Michael J. Wozny. Predicting the drape of woven cloth usinginteracting particles. pages 365–372, 1994.
[17] David E. Breen, Donald H. House, and Michael J. Wozny. Predicting the drape of woven cloth usinginteracting particles. Computer Graphics, 28(Annual Conference Series):365–372, 1994.
[18] David E. Breen, Donald H. House, and Michael J. Wozny. Predicting the drape of woven cloth usinginteracting particles. pages 365–372, 1994.
[19] David E. Breen, Donald H. House, and Michael J. Wozny. Predicting the drape of woven cloth usinginteracting particles. pages 365–372, 1994.
[20] R. Bridson, S. Marino, and R. Fedkiw. Simulation of clothing with folds and wrinkles. pages 28–36,2003.
[21] Michel Carignan, Ying Yang, Nadia Magnenat Thalmann, and Daniel Thalmann. Dressing animatedsynthetic actors with complex deformable clothes. pages 99–104, 1992.
[22] K. Choi and H. Ko. Stable but responsive cloth.
[23] Masaki Aono David. Modeling methods for the design of 3d broadcloth composite parts.
[24] Mathieu Desbrun, Peter Schro¨der, and Alan Barr. Interactive animation of structured deformableobjects. pages 1–8, 1999.
[25] Bernhard Eberhardt, Andreas Weber, and Wolfgang Strasser. A fast, ?exible, particle-system modelfor cloth draping. IEEE Comput. Graph. Appl., 16(5):52–59, 1996.
[26] Jeffrey W. Eischen, Shigan Deng, and Timothy G. Clapp. Finite-element modeling and control of?exible fabric parts. IEEE Comput. Graph. Appl., 16(5):71–80, 1996.
[27] M. Fontana, C. Rizzi, and U. Cugini. Physics-based modelling and simulation of functional clothfor virtual prototyping applications. pages 267–272, 2004.
[28] Allen Van Gelder. Approximate simulation of elastic membranes by triangulated spring meshes. J.Graph. Tools, 3(2):21–42, 1998.
[29] Donald H. House and David E. Breen, editors. Cloth modeling and animation. A. K. Peters, Ltd.,Natick, MA, USA, 2000.
[30] Young-Min Kang and Hwan-Gue Cho. Complex deformable objects in virtual reality. pages 49–56,2002.
[31] Young-Min Kang and Hwan-Gue Cho. Real-time animation of complex virtual cloth with physicalplausibility and numerical stability. Presence: Teleoper. Virtual Environ., 13(6):668–680, 2004.
[32] Michael Kass and Gavin Miller. Rapid, stable ?uid dynamics for computer graphics. pages 49–57,1990.
[33] Hing N. Ng and Richard L. Grimsdale. Computer graphics techniques for modeling cloth. IEEEComput. Graph. Appl., 16(5):28–41, 1996.
[34] Hidehiko Okabe, Haruki Imaoka, Takako Tomiha, and Haruo Niwaya. Three dimensional apparelcad system. SIGGRAPH Comput. Graph., 26(2):105–110, 1992.
[35] John C. Platt and Alan H. Barr. Constraints methods for ?exible models. SIGGRAPH Comput.Graph., 22(4):279–288, 1988.
[36] Xavier Provot. Deformation constraints in a mass-spring model to describe rigid cloth behavior.pages 147–154, 1995.
[37] Jonathan R Shewchuk. An introduction to the conjugate gradient method without the agonizingpain. Technical report, Pittsburgh, PA, USA, 1994.
[38] Demetri Terzopoulos and Kurt Fleischer. Modeling inelastic deformation: viscolelasticity, plasticity,fracture. pages 269–278, 1988.
[39] Demetri Terzopoulos and Kurt Fleischer. Modeling inelastic deformation: viscolelasticity, plasticity,fracture. In SIGGRAPH ’88: Proceedings of the 15th annual conference on Computer graphics andinteractive techniques, pages 269–278, New York, NY, USA, 1988. ACM.
[40] Demetri Terzopoulos, John Platt, Alan Barr, and Kurt Fleischer. Elastically deformable models.pages 205–214, 1987.
[41] Demetri Terzopoulos, John Platt, Alan Barr, and Kurt Fleischer. Elastically deformable models. InSIGGRAPH ’87: Proceedings of the 14th annual conference on Computer graphics and interactivetechniques, pages 205–214, New York, NY, USA, 1987. ACM.
[42] Demetri Terzopoulos and Hong Qin. Dynamic nurbs with geometric constraints for interactivesculpting. ACM Trans. Graph., 13(2):103–136, 1994.
[43] Xiaoyuan Tu. Artificial animals for computer animation: biomechanics, locomotion, perception,and behavior. PhD thesis, Toronto, Ont., Canada, Canada, 1996. Adviser-Demetri Terzopoulos andAdviser-Eugene Fiume.
[44] Greg Turk and Marc Levoy. Zippered polygon meshes from range images. In SIGGRAPH ’94:Proceedings of the 21st annual conference on Computer graphics and interactive techniques, pages311–318, New York, NY, USA, 1994. ACM.
[45] Julien Villard and Houman Borouchaki. Adaptive meshing for cloth animation. pages 243–252,15–18 September 2002.
[46] Jerry Weil. The synthesis of cloth objects. SIGGRAPH Comput. Graph., 20(4):49–54, 1986.
[47] Ying Yang, Nadia Magnenat Thalmann, and Daniel Thalmann. 3d garment design and animation -a new design tool for the garment industry.
[48] Young-MinKang, Jeong-HyeonChoi, Hwan-Gue Cho, and Do-Hoon Lee. An efficient animation ofwrinkled cloth with approximate implicit integration. The Visual Computer, pages 147–157, 2001.