基于物理的真实感流体模拟研究
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摘要
计算机图形学是虚拟现实与数字媒体技术的核心。虚拟现实、电影特效以及电子游戏的强大需求,不仅推动着工业界不断提升图形处理硬件的性能,学术界也积极投身其中。然而在交互式高沉浸感的虚拟环境中,依然存在着诸多基础性的研究问题与挑战,其中逼真的实体运动模拟问题尤为突出。作为计算机图形学的一个分支,计算机动画是计算机图形学和艺术相结合的产物。在构建未来高沉浸感虚拟现实系统中,对计算机动画的研究将具有举足轻重的战略作用。因此,计算机动画始终处在研究的前沿,人们不仅需要静态形象的真实感,也需要运动的真实感。而真实运动的复杂度往往使得人们难以用一些过程表述,这个时候只有借助于真实世界的物理规律才能得以体现。
基于物理的动画已成为计算机动画领域中的一个前沿研究热点。基于物理的动画模拟使得人们摆脱传统僵硬的“固定动画”成为可能,因此具有非常强的前瞻性。基于物理的计算机动画一方面使得本身体现的现象能充分满足人们对真实感的需要;另一方面减轻了程序开发人员和艺术家的劳动强度。
本文以基于物理的计算机动画作为研究目标,对这一课题的研究着重集中在以下三个方面:第一,对基于物理的流体动画模拟算法作出了全面的研究和透彻的分析,在此基础上提炼出了真实感流体模拟的关键问题;第二,针对真实感流体模拟的核心问题,提出了基于物理的真实感流体动画模拟的改进算法;第三,实现了无网格流体动画模拟的算法,对算法的运行结果进行了充分的比较和分析,并就未来的研究热点进行了展望。
本文算法的主要贡献和创新点在于如下工作:
①在涉及流固耦合边界运动的模拟中,提出基于物理采样因子的多分辨率流体模型和真实感流固双向同步耦合模拟方案,解决了传统算法的异步误差问题;
②针对热力学三态相变的模拟,提出基于流固包容模型的平滑相态转变算法,并设计出高适应性的粒子表面重构方法;
③提出多分辨率流体物理模型的概念,针对不同尺度范围的流体动画采用不同的物理模拟方法,构建一个平滑过渡的流体动画模拟系统。
Computer Graphics is the core of the Virtual Reality and Digital Media. Realistic modeling of natural phenomena has been a hotspot and one of the most difficult tasks in Compute Graphics. It has been found wide application in many domains such as computer animation, landscaping, architecture, special effects of movie, computer games, battlefield simulation and virtual reality, etc. Physically based modeling must be applied to attain more realistic results on both shapes and movements, on the other hand, the simplification and acceleration techniques also should be introduced to render the dynamic and whole effects of natural phenomena more quickly. So the physically based modeling aims to seek for a tradeoff between the realistic effects and real time performance, to meet the needs from various applications.
Physically based computer animation is always a hot topic in computer graphics especially in the special effects industry for films and games. Only physics makes the virtual scene more realistic, and takes the easy way out of the complex problems for simulation which gives the developers and artists more and more dream space.
This thesis focuses on the study in three aspects, including research and analysis of physically based fluid simulation algorithms, so as to make sure the key problems in realistic fluid animation; design the advanced methods for fluid simulation, which aim at the immediate problems; implement the meshless fluid simulation algorithms, also
compare the results for conclusion and future works.
The main contributions of this thesis are mainly in the following aspects:
①To make sure stability and nicety in fluid simulation, we attempt on adaptively sampled multi-resolution particle fluid model based on physics and geometry sampling factors, with realistic fluid-solid two way synchronous coupling algorithms in the simulation;
②Use phase transition model with fluid and solid co-exit, with the adaptive surface re-construction method for fluid particles, we can simulation three phases transition realistically;
③Consider the microcosmic physics model for the attachment and penetration of small liquids, we attempt on multi-resolution physics model for large and small scales liquid simulation, with a middle transitional model, so as to build a integrated liquid animation method.
基于物理的动画已成为计算机动画领域中的一个前沿研究热点。基于物理的动画模拟使得人们摆脱传统僵硬的“固定动画”成为可能,因此具有非常强的前瞻性。基于物理的计算机动画一方面使得本身体现的现象能充分满足人们对真实感的需要;另一方面减轻了程序开发人员和艺术家的劳动强度。
本文以基于物理的计算机动画作为研究目标,对这一课题的研究着重集中在以下三个方面:第一,对基于物理的流体动画模拟算法作出了全面的研究和透彻的分析,在此基础上提炼出了真实感流体模拟的关键问题;第二,针对真实感流体模拟的核心问题,提出了基于物理的真实感流体动画模拟的改进算法;第三,实现了无网格流体动画模拟的算法,对算法的运行结果进行了充分的比较和分析,并就未来的研究热点进行了展望。
本文算法的主要贡献和创新点在于如下工作:
①在涉及流固耦合边界运动的模拟中,提出基于物理采样因子的多分辨率流体模型和真实感流固双向同步耦合模拟方案,解决了传统算法的异步误差问题;
②针对热力学三态相变的模拟,提出基于流固包容模型的平滑相态转变算法,并设计出高适应性的粒子表面重构方法;
③提出多分辨率流体物理模型的概念,针对不同尺度范围的流体动画采用不同的物理模拟方法,构建一个平滑过渡的流体动画模拟系统。
Computer Graphics is the core of the Virtual Reality and Digital Media. Realistic modeling of natural phenomena has been a hotspot and one of the most difficult tasks in Compute Graphics. It has been found wide application in many domains such as computer animation, landscaping, architecture, special effects of movie, computer games, battlefield simulation and virtual reality, etc. Physically based modeling must be applied to attain more realistic results on both shapes and movements, on the other hand, the simplification and acceleration techniques also should be introduced to render the dynamic and whole effects of natural phenomena more quickly. So the physically based modeling aims to seek for a tradeoff between the realistic effects and real time performance, to meet the needs from various applications.
Physically based computer animation is always a hot topic in computer graphics especially in the special effects industry for films and games. Only physics makes the virtual scene more realistic, and takes the easy way out of the complex problems for simulation which gives the developers and artists more and more dream space.
This thesis focuses on the study in three aspects, including research and analysis of physically based fluid simulation algorithms, so as to make sure the key problems in realistic fluid animation; design the advanced methods for fluid simulation, which aim at the immediate problems; implement the meshless fluid simulation algorithms, also
compare the results for conclusion and future works.
The main contributions of this thesis are mainly in the following aspects:
①To make sure stability and nicety in fluid simulation, we attempt on adaptively sampled multi-resolution particle fluid model based on physics and geometry sampling factors, with realistic fluid-solid two way synchronous coupling algorithms in the simulation;
②Use phase transition model with fluid and solid co-exit, with the adaptive surface re-construction method for fluid particles, we can simulation three phases transition realistically;
③Consider the microcosmic physics model for the attachment and penetration of small liquids, we attempt on multi-resolution physics model for large and small scales liquid simulation, with a middle transitional model, so as to build a integrated liquid animation method.
引文
[1] Darwyn R. Peachey. Modeling Waves and Surf. Computer Graphics, 1986, 20(4): 65-74.
[2] Alain Fournier, William T. Reeves. A Simple Model of Ocean Waves. Computer Graphics, 1986, 20(4): 75-84
[3] Jerry Tessendorf. Simulating Ocean Waves. SIGGRAPH '99 Course Notes & SIGGRAPH 2000: Course Notes 25: Simulating Nature: From Theory to Practice, Pages: 3.1-3.18
[4] Jos Stam. Stable Fluids. SIGGRAPH 1999, 121-128
[5]周永霞,石教英,郁佳荣.基于物理的烟雾动画.计算机辅助设计与图形学学报, 2006, 18(9): 1367-1371
[6] Ronald Fedkiw, Henrik Wann Jensen, Jos Stam. Visual Simulation of Smoke. SIGGRAPH 2001, 15-22
[7] Nick Foster, Ronald Fedkiw. Practical Animations of Liquids. SIGGRAPH 2001, 23-30
[8] Douglas P. Enright, Steve Marschner, Ronald Fedkiw. Animation and Rendering of Complex Water Surfaces. ACM Transactions on Graphics, 2002, 21(3): 736-744
[9] Tolga Goktekin, Adam W. Bargteil, James F. O'Brien. A Method for Animating Viscoelastic Fluids. ACM Transactions on Graphics, 2004, 23(3): 463-468
[10] Mark Carlson, Peter J. Mucha, Greg Turk. Rigid Fluid: Animating the Interplay Between Rigid Bodies and Fluid. ACM Transactions on Graphics, 2004, 23(3): 377-384
[11] Frank Losasso, Frederic Gibou, Ronald Fedkiw. Simulating Water and Smoke with an Octree Data Structure. ACM Transactions on Graphics, 2004, 23(3): 457-462
[12] ByungMoon Kim, Yingjie Liu, Ignacio Llamas, et al. Simulation of Bubbles in Foam With Volume Control. ACM Transactions on Graphics, 2007, 26(3)
[13] Duc Nguyen, Ronald Fedkiw, Henrik Wann Jensen. Physically Based Modeling and Animation of Fire. ACM Transactions on Graphics, 2002, 21(3): 721-728
[14] Jos Stam, Eugene Fiume. Turbulent Wind Fields for Gaseous Phenomena. SIGGRAPH 1993, 369-376
[15] Andrew Selle, Nick Rasmussen, Ron Fedkiw. A Vortex Particle Method for Smoke, Fire, and Explosions. ACM Transactions on Graphics, 2005, 24(3): 910-914
[16] Jeong-Mo Hong, Chang-Hun Kim. Discontinuous Fluids. ACM Transactions on Graphics, 2005, 24(3): 915-920
[17] Huamin Wang, Peter J. Mucha, Greg Turk. Water Drops on Surfaces. ACM Transactions on Graphics, 2005, 24(3): 921-929
[18] Wen Zheng, Jun-Hai Yong(雍俊海), Jean-Claude Paul. Simulation of Bubbles. Eruographics / ACM SIGGRAPH Symposium on Computer Animation. 2006, 325-333
[19] Paul Cleary, Soon Hyoung Pyo, Mahesh Prakash, et al. Bubbling and Frothing Liquids. ACM Transactions on Graphics, 2007, 26(3)
[20] Adrien Treuille, Antoine McNamara, Zoran Popovi?, et al. Keyframe Control of Smoke Simulations. ACM Transactions on Graphics, 2003, 22(3): 716-723
[21] Arnauld Lamorlette, Nick Foster. Structural Modeling of Flames for a Production Environment. ACM Transactions on Graphics, 2002, 21(3): 729-735
[22] Raanan Fattal, Dani Lischinski. Target-Driven Smoke Animation. ACM Transactions on Graphics, 2004, 23(3): 441-448
[23] Antoine McNamara, Adrien Treuille, Zoran Popovi?, et al. Fluid Control Using the Adjoint Method. ACM Transactions on Graphics, 2004, 23(3): 449-456
[24] Geoffrey Irving, Eran Guendelman, Frank Losasso, et al. Efficient Simulation of Large Bodies of Water by Coupling Two- and Three-Dimensional Techniques. ACM Transactions on Graphics, 2006, 25(3): 805-811
[25] Nick Rasmussen, Duc Nguyen, Willi Geiger, et al. Smoke Simulation For Large Scale Phenomena. ACM Transactions on Graphics, 2003, 22(3): 703-707
[26]柳有权,刘学惠,吴恩华.基于GPU带有复杂边界的三维实时流体模拟.软件学报, 2006, 17(3): 568-576
[27] Jens Kruger, Rudiger Westermann. Linear Algebra Operators for GPU Implementation of Numerical Algorithms. ACM Transactions on Graphics, 2003, 22(3): 908-916
[28]周世哲,满家巨.基于多重网格法的实时流体模拟.计算机辅助设计与图形学学报, 2007, 19(7):935-940
[29] Adrien Treuille, Andrew Lewis, Zoran Popovi?. Model Reduction for Real-Time Fluids. ACM Transactions on Graphics, 2006, 25(3): 826-834
[30] Yoshinori Dobashi, Tsuyoshi Yamamoto, Tomoyuki Nishita. Real-Time Rendering of Aerodynamic Sound Using Sound Textures Based on Computational Fluid Dynamics. ACM Transactions on Graphics, 2003, 22(3): 732-740
[31] Matthias Müller, David Charypar, Markus Gross. Particle-Based Fluid Simulation for Interactive Applications. Eurographics / ACM SIGGRAPH Symposium on Computer Animation 2003. 154-159
[32] Simon Premo?e, Tolga Tasdizen, James Bigler, et al. Whitaker. Particle-Based Simulation of Fluids. Computer Graphics Forum, 2003, 22(3): 401-410
[33]朱红斌,刘学惠,柳有权,等.基于Lattice Boltzmann模型的液-液混合流模型.计算机学报, 2006, 29(12): 2071-2079
[34] Kevin Steele, David Cline, Parris K.Egbert, et al. Modeling and rendering viscous liquids. Journal of Computer Animation and Virtual World, 2004, 15(3-4): 183-192
[35] Simon Premo?e, Tolga Tasdizen, James Bigler, et al. Whitaker. Particle-Based Simulation of Fluids. Computer Graphics Forum, 2003, 22(3): 401-410
[36] Bart Adams, Mark Pauly, Richard Keiser, et al. Adaptively Sampled Particle Fluids. ACM Transactions on Graphics, 2007, 26(3)
[37] Markus Becker, Matthias Teschner. Weakly compressible SPH for free surface flows. Eurographics/ACM SIGGRAPH Symposium on Computer Animation 2007. 209-217
[38] Peter Kipfer, Rüdiger Westermann. Realistic and Interactive Simulation of Rivers. Proceedngs of the 2006 Conference on Graphics Interface, 2006. 41-48
[39] Hai Mao, Yee-Hong Yang. Fluid-Fluid Collision for Particle-Based Immiscible Fluid Animation. Proceedngs of the 2006 Conference on Graphics Interface, 2006. 49-55
[40] Matthias Müller, Barbara Solenthaler, Richard Keiser, et al. Particle-Based Fluid-Fluid Interaction. Eurographics / ACM SIGGRAPH Symposium on Computer Animation 2005. 237-244
[41] Simon Clavet, Philippe Beaudoin, Pierre Poulin. Particle-based Viscoelastic Fluid Simulation. Eurographics / ACM SIGGRAPH Symposium on Computer Animation 2005. 219-228
[42] Ryoichi Mizuno, Yoshinori Dobashi, Bing-Yu Chen, et al. Physics Motivated Modeling of Volcanic Clouds as a Two Fluids Model. In: Proceedings of Pacific Graphics, Canmore, 2003.440-444
[43] Bryan E. Feldman, James F. O'Brien, Okan Arikan. Animating Suspended Particle Explosions. ACM Transactions on Graphics, 2003, 22(3): 708-715
[44] Frank Losasso, Tamar Shinar, Andrew Selle, et al. Multiple Interacting Liquids. ACM Transactions on Graphics, 2006, 25(3): 812-819
[45] Christopher Batty, Florence Bertails, Robert Bridson. A Fast Variational Framework for Accurate Solid-Fluid Coupling. ACM Transactions on Graphics, 2007, 26(3)
[46] D Terzopoulos, J Platt, A Barr et al. Elastically deformable models. ACM SIGGRAPH Computer Graphics,1987,21(4):205-214
[47] D Terzopoulos, J Platt, K Fleischer. Heating and melting deformable models.Proc of Graphics Interface,London,Ontario,1989:219-226
[48] DE Breen, DH House, MJ Wozny. Predicting the drape of woven cloth using interacting particles. Proc of SIGGRAPH. New York: ACM Press,1994:365-372
[49] JF O'Brien, AW Bargteil, JK Hodgins. Graphical modeling and animation of ductile fracture. Proc of SIGGRAPH. New York: ACM Press,2002:291-294
[50] N Molino, Z Bao, R Fedkiw. A virtual node algorithm for changing mesh topology during simulation. ACM Transactions on Graphics, 2004, 23(3):385-392
[51] M Müller, R Keiser, A Nealen, et al. Point based animation of elastic, plastic and melting objects.Proc of the 2004 ACM SIGGRAPH / Eurographics symposium on Computer animation. Grenoble, France, 2004: 141-151
[52] R Keiser, B Adams, D Gasser, et al. A Unified Lagrangian Approach to Solid-Fluid Animation. Proc of the 2006 conference on Graphics interface, 2006:125-133
[53] M Pauly, R Keiser, B Adams, et al. Meshless animation of fracturing solids. ACM Transactions on Graphics, 2005, 24(3):957-964
[54] M Wicke, D Steinemann, M Gross. Efficient Animation of Point-Sampled Thin Shells. Computer Graphics Forum, 2005, 24(3):667-676
[55] Tsunemi Takahashi, Heihachi Ueki, Atsushi Kunimatsu, et al. The simulation of fluid-rigid body interaction. ACM SIGGRAPH 2002 conference abstracts and applications. 266-266
[56] Eran Guendelman, Andrew Selle, Frank Losasso, et al. Coupling water and smoke to thin deformable and rigid shells. ACM Transactions on Graphics, 2005, 24(3):973-981
[57] Bryan M. Klingner, Bryan E. Feldman, Nuttapong Chentanez, et al. Fluid animation with dynamic meshes. ACM Transactions on Graphics, 2006, 25(3):820-825
[2] Alain Fournier, William T. Reeves. A Simple Model of Ocean Waves. Computer Graphics, 1986, 20(4): 75-84
[3] Jerry Tessendorf. Simulating Ocean Waves. SIGGRAPH '99 Course Notes & SIGGRAPH 2000: Course Notes 25: Simulating Nature: From Theory to Practice, Pages: 3.1-3.18
[4] Jos Stam. Stable Fluids. SIGGRAPH 1999, 121-128
[5]周永霞,石教英,郁佳荣.基于物理的烟雾动画.计算机辅助设计与图形学学报, 2006, 18(9): 1367-1371
[6] Ronald Fedkiw, Henrik Wann Jensen, Jos Stam. Visual Simulation of Smoke. SIGGRAPH 2001, 15-22
[7] Nick Foster, Ronald Fedkiw. Practical Animations of Liquids. SIGGRAPH 2001, 23-30
[8] Douglas P. Enright, Steve Marschner, Ronald Fedkiw. Animation and Rendering of Complex Water Surfaces. ACM Transactions on Graphics, 2002, 21(3): 736-744
[9] Tolga Goktekin, Adam W. Bargteil, James F. O'Brien. A Method for Animating Viscoelastic Fluids. ACM Transactions on Graphics, 2004, 23(3): 463-468
[10] Mark Carlson, Peter J. Mucha, Greg Turk. Rigid Fluid: Animating the Interplay Between Rigid Bodies and Fluid. ACM Transactions on Graphics, 2004, 23(3): 377-384
[11] Frank Losasso, Frederic Gibou, Ronald Fedkiw. Simulating Water and Smoke with an Octree Data Structure. ACM Transactions on Graphics, 2004, 23(3): 457-462
[12] ByungMoon Kim, Yingjie Liu, Ignacio Llamas, et al. Simulation of Bubbles in Foam With Volume Control. ACM Transactions on Graphics, 2007, 26(3)
[13] Duc Nguyen, Ronald Fedkiw, Henrik Wann Jensen. Physically Based Modeling and Animation of Fire. ACM Transactions on Graphics, 2002, 21(3): 721-728
[14] Jos Stam, Eugene Fiume. Turbulent Wind Fields for Gaseous Phenomena. SIGGRAPH 1993, 369-376
[15] Andrew Selle, Nick Rasmussen, Ron Fedkiw. A Vortex Particle Method for Smoke, Fire, and Explosions. ACM Transactions on Graphics, 2005, 24(3): 910-914
[16] Jeong-Mo Hong, Chang-Hun Kim. Discontinuous Fluids. ACM Transactions on Graphics, 2005, 24(3): 915-920
[17] Huamin Wang, Peter J. Mucha, Greg Turk. Water Drops on Surfaces. ACM Transactions on Graphics, 2005, 24(3): 921-929
[18] Wen Zheng, Jun-Hai Yong(雍俊海), Jean-Claude Paul. Simulation of Bubbles. Eruographics / ACM SIGGRAPH Symposium on Computer Animation. 2006, 325-333
[19] Paul Cleary, Soon Hyoung Pyo, Mahesh Prakash, et al. Bubbling and Frothing Liquids. ACM Transactions on Graphics, 2007, 26(3)
[20] Adrien Treuille, Antoine McNamara, Zoran Popovi?, et al. Keyframe Control of Smoke Simulations. ACM Transactions on Graphics, 2003, 22(3): 716-723
[21] Arnauld Lamorlette, Nick Foster. Structural Modeling of Flames for a Production Environment. ACM Transactions on Graphics, 2002, 21(3): 729-735
[22] Raanan Fattal, Dani Lischinski. Target-Driven Smoke Animation. ACM Transactions on Graphics, 2004, 23(3): 441-448
[23] Antoine McNamara, Adrien Treuille, Zoran Popovi?, et al. Fluid Control Using the Adjoint Method. ACM Transactions on Graphics, 2004, 23(3): 449-456
[24] Geoffrey Irving, Eran Guendelman, Frank Losasso, et al. Efficient Simulation of Large Bodies of Water by Coupling Two- and Three-Dimensional Techniques. ACM Transactions on Graphics, 2006, 25(3): 805-811
[25] Nick Rasmussen, Duc Nguyen, Willi Geiger, et al. Smoke Simulation For Large Scale Phenomena. ACM Transactions on Graphics, 2003, 22(3): 703-707
[26]柳有权,刘学惠,吴恩华.基于GPU带有复杂边界的三维实时流体模拟.软件学报, 2006, 17(3): 568-576
[27] Jens Kruger, Rudiger Westermann. Linear Algebra Operators for GPU Implementation of Numerical Algorithms. ACM Transactions on Graphics, 2003, 22(3): 908-916
[28]周世哲,满家巨.基于多重网格法的实时流体模拟.计算机辅助设计与图形学学报, 2007, 19(7):935-940
[29] Adrien Treuille, Andrew Lewis, Zoran Popovi?. Model Reduction for Real-Time Fluids. ACM Transactions on Graphics, 2006, 25(3): 826-834
[30] Yoshinori Dobashi, Tsuyoshi Yamamoto, Tomoyuki Nishita. Real-Time Rendering of Aerodynamic Sound Using Sound Textures Based on Computational Fluid Dynamics. ACM Transactions on Graphics, 2003, 22(3): 732-740
[31] Matthias Müller, David Charypar, Markus Gross. Particle-Based Fluid Simulation for Interactive Applications. Eurographics / ACM SIGGRAPH Symposium on Computer Animation 2003. 154-159
[32] Simon Premo?e, Tolga Tasdizen, James Bigler, et al. Whitaker. Particle-Based Simulation of Fluids. Computer Graphics Forum, 2003, 22(3): 401-410
[33]朱红斌,刘学惠,柳有权,等.基于Lattice Boltzmann模型的液-液混合流模型.计算机学报, 2006, 29(12): 2071-2079
[34] Kevin Steele, David Cline, Parris K.Egbert, et al. Modeling and rendering viscous liquids. Journal of Computer Animation and Virtual World, 2004, 15(3-4): 183-192
[35] Simon Premo?e, Tolga Tasdizen, James Bigler, et al. Whitaker. Particle-Based Simulation of Fluids. Computer Graphics Forum, 2003, 22(3): 401-410
[36] Bart Adams, Mark Pauly, Richard Keiser, et al. Adaptively Sampled Particle Fluids. ACM Transactions on Graphics, 2007, 26(3)
[37] Markus Becker, Matthias Teschner. Weakly compressible SPH for free surface flows. Eurographics/ACM SIGGRAPH Symposium on Computer Animation 2007. 209-217
[38] Peter Kipfer, Rüdiger Westermann. Realistic and Interactive Simulation of Rivers. Proceedngs of the 2006 Conference on Graphics Interface, 2006. 41-48
[39] Hai Mao, Yee-Hong Yang. Fluid-Fluid Collision for Particle-Based Immiscible Fluid Animation. Proceedngs of the 2006 Conference on Graphics Interface, 2006. 49-55
[40] Matthias Müller, Barbara Solenthaler, Richard Keiser, et al. Particle-Based Fluid-Fluid Interaction. Eurographics / ACM SIGGRAPH Symposium on Computer Animation 2005. 237-244
[41] Simon Clavet, Philippe Beaudoin, Pierre Poulin. Particle-based Viscoelastic Fluid Simulation. Eurographics / ACM SIGGRAPH Symposium on Computer Animation 2005. 219-228
[42] Ryoichi Mizuno, Yoshinori Dobashi, Bing-Yu Chen, et al. Physics Motivated Modeling of Volcanic Clouds as a Two Fluids Model. In: Proceedings of Pacific Graphics, Canmore, 2003.440-444
[43] Bryan E. Feldman, James F. O'Brien, Okan Arikan. Animating Suspended Particle Explosions. ACM Transactions on Graphics, 2003, 22(3): 708-715
[44] Frank Losasso, Tamar Shinar, Andrew Selle, et al. Multiple Interacting Liquids. ACM Transactions on Graphics, 2006, 25(3): 812-819
[45] Christopher Batty, Florence Bertails, Robert Bridson. A Fast Variational Framework for Accurate Solid-Fluid Coupling. ACM Transactions on Graphics, 2007, 26(3)
[46] D Terzopoulos, J Platt, A Barr et al. Elastically deformable models. ACM SIGGRAPH Computer Graphics,1987,21(4):205-214
[47] D Terzopoulos, J Platt, K Fleischer. Heating and melting deformable models.Proc of Graphics Interface,London,Ontario,1989:219-226
[48] DE Breen, DH House, MJ Wozny. Predicting the drape of woven cloth using interacting particles. Proc of SIGGRAPH. New York: ACM Press,1994:365-372
[49] JF O'Brien, AW Bargteil, JK Hodgins. Graphical modeling and animation of ductile fracture. Proc of SIGGRAPH. New York: ACM Press,2002:291-294
[50] N Molino, Z Bao, R Fedkiw. A virtual node algorithm for changing mesh topology during simulation. ACM Transactions on Graphics, 2004, 23(3):385-392
[51] M Müller, R Keiser, A Nealen, et al. Point based animation of elastic, plastic and melting objects.Proc of the 2004 ACM SIGGRAPH / Eurographics symposium on Computer animation. Grenoble, France, 2004: 141-151
[52] R Keiser, B Adams, D Gasser, et al. A Unified Lagrangian Approach to Solid-Fluid Animation. Proc of the 2006 conference on Graphics interface, 2006:125-133
[53] M Pauly, R Keiser, B Adams, et al. Meshless animation of fracturing solids. ACM Transactions on Graphics, 2005, 24(3):957-964
[54] M Wicke, D Steinemann, M Gross. Efficient Animation of Point-Sampled Thin Shells. Computer Graphics Forum, 2005, 24(3):667-676
[55] Tsunemi Takahashi, Heihachi Ueki, Atsushi Kunimatsu, et al. The simulation of fluid-rigid body interaction. ACM SIGGRAPH 2002 conference abstracts and applications. 266-266
[56] Eran Guendelman, Andrew Selle, Frank Losasso, et al. Coupling water and smoke to thin deformable and rigid shells. ACM Transactions on Graphics, 2005, 24(3):973-981
[57] Bryan M. Klingner, Bryan E. Feldman, Nuttapong Chentanez, et al. Fluid animation with dynamic meshes. ACM Transactions on Graphics, 2006, 25(3):820-825