计算机动画中柔软物体变形技术研究
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摘要
近几十年来,由干影视动画、虚拟现实和计算机游戏等领域的不断发展,如何能够更加真实感的模拟仿真物体已经成为人们研究的热点方向。目前对于物体仿真研究主要可以归结为两个方面,一是致力于刚体的研究,另一个就是对柔性物体的研究。对于刚性体的研究,目前已经取得了较为成熟的理论。而对于柔性物体的研究,也仅仅在最近15年。随着柔性材料大量应用的蓬勃发展,柔性物体的计算机仿真逐渐成为计算机图形学的一个重要而又前沿的领域。
目前柔软物体的模拟主要有基于几何模型、物理模型和混合模型三种方法。基于物理模型的柔性物体仿真不但能反映柔性体的外部特征,而且能对软物体的内部结构进行深入的分析,可以得到较真实的模拟效果,因此,基于物理技术已成为近几年来研究的主流方法。
本文主要采用的是基于物理模型方法对柔性物体变形的模拟进行研究,重点考虑到真实感与实时性兼顾等问题。本文的重点主要是在第三章、第四章和第五章。
在第三章中,给出了两种建模方法,一是直接在物体自身建立基于物理的质点-弹簧模型,并简化了质点-弹簧模型。使得计算方便快速,易控制物体变形。二是基于物理的柔软物体自由变形的建模方法,通过将质点-弹簧模型加载到Bezier网格体上,通过变形网格来达到物体的变形。同时给出了质点的动力学方程及其求解的过程。该变形模型方法简单,容易达到全局变形,实时性也达到了预期的效果。
在第四章中,本文对柔软物体变形仿真中的一个重难点——碰撞检测与碰撞响应方法问题进行了研究,运用了点到面模型对物体进行了碰撞检测,同时提出了一种新的碰撞相应处理方法,该方法有效的较少了计算消耗。
最后本文给出了实验的仿真结果,并对实验的结果进行了分析总结。
How to simulate objects more realistic is always a hot topic in computer graphics especially in the special effects industry for films and game. Currently, it has two aspects for the study of the simulation of objects, one is dedicated to the study the rigid body, and the other is the study of soft objects. For the study of the rigid body has been made a more mature theory, but it has only 15 years for the study of the soft objects. With the applications of soft object for multi-purposes and the quick development in the field of virtual reality technique, the study on the simulation of soft objects becomes an important foreland in the research field of Computer Graphic.
Soft object simulation systems are mainly based on geometrical, physical and hybrid methods. The study on the simulation of soft objects becomes an important foreland in the research field of Computer Graphics. Soft objects simulation of physically-based model not only shows the appearance of flexible objects, but also well analyzes the internal structure of it. Therefore, the simulation method becomes the main trend in the research field gradually. In this paper, it uses the physical model that based on the method of simulation of the deformation of soft objects for research. The main focus of this paper is in chapter three, chapter four and chapter five.
In chapter three, it gives two modeling methods, one is to establish the physically mass-spring model on soft object itself, and simplify mass-spring model, makes the calculation more quickly and easily, and real-time has reached the desired results. Secondly, this paper uses a new modeling method that simulation based on physically soft-object free-form deformation. and it will let mass-spring model load into Bezier mesh, through deform the grid to achieve the deformation of object. At the same time, this paper gives the particle’s kinetic equation and its solution process. The deformation modeling method is simple, and easy to achieve the globe deformation.
In chapter four, a study on the difficulty of the simulation, such as collision detection and collision response, is carried out and it uses Point to Plane model for collision detection. A new approach for the collision response is proposed and this new approach greatly reduces the calculation consumption.
The last work in this paper is to leave the experimental simulation results and analysis and summarize the experimental results.
目前柔软物体的模拟主要有基于几何模型、物理模型和混合模型三种方法。基于物理模型的柔性物体仿真不但能反映柔性体的外部特征,而且能对软物体的内部结构进行深入的分析,可以得到较真实的模拟效果,因此,基于物理技术已成为近几年来研究的主流方法。
本文主要采用的是基于物理模型方法对柔性物体变形的模拟进行研究,重点考虑到真实感与实时性兼顾等问题。本文的重点主要是在第三章、第四章和第五章。
在第三章中,给出了两种建模方法,一是直接在物体自身建立基于物理的质点-弹簧模型,并简化了质点-弹簧模型。使得计算方便快速,易控制物体变形。二是基于物理的柔软物体自由变形的建模方法,通过将质点-弹簧模型加载到Bezier网格体上,通过变形网格来达到物体的变形。同时给出了质点的动力学方程及其求解的过程。该变形模型方法简单,容易达到全局变形,实时性也达到了预期的效果。
在第四章中,本文对柔软物体变形仿真中的一个重难点——碰撞检测与碰撞响应方法问题进行了研究,运用了点到面模型对物体进行了碰撞检测,同时提出了一种新的碰撞相应处理方法,该方法有效的较少了计算消耗。
最后本文给出了实验的仿真结果,并对实验的结果进行了分析总结。
How to simulate objects more realistic is always a hot topic in computer graphics especially in the special effects industry for films and game. Currently, it has two aspects for the study of the simulation of objects, one is dedicated to the study the rigid body, and the other is the study of soft objects. For the study of the rigid body has been made a more mature theory, but it has only 15 years for the study of the soft objects. With the applications of soft object for multi-purposes and the quick development in the field of virtual reality technique, the study on the simulation of soft objects becomes an important foreland in the research field of Computer Graphic.
Soft object simulation systems are mainly based on geometrical, physical and hybrid methods. The study on the simulation of soft objects becomes an important foreland in the research field of Computer Graphics. Soft objects simulation of physically-based model not only shows the appearance of flexible objects, but also well analyzes the internal structure of it. Therefore, the simulation method becomes the main trend in the research field gradually. In this paper, it uses the physical model that based on the method of simulation of the deformation of soft objects for research. The main focus of this paper is in chapter three, chapter four and chapter five.
In chapter three, it gives two modeling methods, one is to establish the physically mass-spring model on soft object itself, and simplify mass-spring model, makes the calculation more quickly and easily, and real-time has reached the desired results. Secondly, this paper uses a new modeling method that simulation based on physically soft-object free-form deformation. and it will let mass-spring model load into Bezier mesh, through deform the grid to achieve the deformation of object. At the same time, this paper gives the particle’s kinetic equation and its solution process. The deformation modeling method is simple, and easy to achieve the globe deformation.
In chapter four, a study on the difficulty of the simulation, such as collision detection and collision response, is carried out and it uses Point to Plane model for collision detection. A new approach for the collision response is proposed and this new approach greatly reduces the calculation consumption.
The last work in this paper is to leave the experimental simulation results and analysis and summarize the experimental results.
引文
1.奇东旭,马华东,黄心渊,徐迎庆,李华山.计算机动画原理与应用[M].北京:科学出版社,1998.
2. Knowlton K.A computer technique for producing animated movies.proc,AFIPS,1964,25:67-87
3. Knowlton K.Computer-produced movies.Science,1965,150(3700):1116-1120
4.金小刚,鲍虎军,彭群生.计算机动画综述[J].软件学报,1997 (8)241-251.
5.鲍虎军,金小刚,彭群生.计算机动画的算法基础[M].杭州:浙江大学出版社,2000.310-367
6. Barr A H. Global and local deformation of solid primitives, Computer Graphics,1984,18(3):21-30
7. Sederberg T W,Parry S R.Free-Form Deformation of Solid Geometric Models.Computer Graphics,1992,26(2):151-160
8. Hsu W M,Hughes J F,Kaufman H. Direct manipulation of Free-Form Deformation.Computer graphics,1992,26(2):177-184
9. Gressmair J,Purgatofer W.Deformation of Solids with Trivariate B-Splines.Proc.Eurographics’89.1989,21:137-148
10. Lamousin H J,Waggenspack W N.NURBS-based Free-From Deformation.IEEE Computer Graphics and Application,1994,14(6)59-65
11. Kalra P,Mangjli A,Thalmann N.Simulation of Facial Muscle Actions Based on Rational Free-Form Deformation.Computer Graphics Forum,1992,2(3):59-69
12. Coquillart S.Extended Free-Form Deformation:A Sculpturing Tool for 3D Geometric Modeling.Computer Graphics,1990,24(4):187-193
13. MacCracken R,Jay K I.Free-Form Deformation with Lattices of Arbitrary Topology.Computer Graphics,1996,30:181-189
14. Kenneth L.Joy and Ron Mac Cracken.The refinement rules for Catmull-Clark solids.Technical Report CSE-96-1,Department of Computer Science,University of California,Davis,January 1996
15. Bechmann D,Bertrand Y,Thery S.Continuous free form deformation.Computer Networks and ISDN System,1997,29:1715-1725
16. Lazarus F,Coquillart S,Jancene P.Axial Deformations:An Intuitive Deformation Technique.Computer-Aided Design,1994,26(8):608-612
17. Chang Y.K,Rockwood A P.A Generalized de Casteljau Approach to 3D Free-formDeformation,1994,28:257-260
18.冯结青,马利庄,彭群生.基于弧长参数的轴变形心方法[J].计算机学报,1996,19:161-170
19. Borrel P, Bechmann D. Deformation of N-dimensional objects. International Journal of Computational Geometry & Applications, 1991,1(4):427-453
20. L,E,Sutherland.The ultimate display. In Proceedings of the IFIP Congress 65.Volume2,1 965,506-583
21. Weil J.The synthesis of cloth object. Computer Garphics,1986,20 (4):49-54
22. B K Hinds, J McCartney. Interactive garment design.Visual Computer.1990,6(l):53-61
23. Delingette H,Subsol G,Cotin S,Pignon J.A craniofacial surgery simulation testbed. Proceedings of Visualization in Biomedical Computing,Rochester.NY.1994.607-618
24.成迟薏,石教英,徐迎庆,沈向洋.基于物理模型的窗帘运动实时动画[J].软件学报,2000,11(9):1228-1236
25. Chen D T,Zeltzer D.Pump it up:Computer animation of a biom- echanically based model of muscle using finite element method. Proceedings of Computer Graphics,1992,26:89-98
26. James D L,Pai D K.Accurate real time deformable objects.Proceedings of SIGGRA PH’99 Conference,Los Angeles,CA,1999,65-72
27. JI Feng. Research on Simulation of Soft Tissue Deformation in Virtual Orthodontics.IEEE Computer society,2006, 318-322
28. Cui Tong,Aiguo Song,Wu Juan.A Mass-Spring Model for Haptic Display of Flexble Object Global Deformation.International Conference on Mechatronics and Automation,2007,2753-2756
29.冯结青,彭群生.基于差值的Bernstein多项式复合及曲面应用[J].软件学报,2002,10
30.鲍春波,王博亮,刘卓,程明.一种用于软组织变形仿真的动态质点弹簧模型[J].系统仿真学报,2006,18(4):847-852
31. JI Feng. Research on Simulation of Soft Tissue Deformation in Virtual Orthodontics. In: IEEE Computer society,2006, 318-322
32.陈旿,徐乃平.真实感布仿真中布与刚体的碰撞检测及修正[J].软件学报,2001,12(12): 1874-1880
33.张建英.针织物动态模拟方法的研究[D].杭州:浙江大学,2004
34.高春波,刘玉树.碰撞检测技术综述[J].计算机工程与应用,2002,38(5):9-11
35.靳碧鹏.基于物理的计算机实时动画研究[D].合肥:电子科技大学,2007
36. David Baraff, Andrew Witkin. Dynamic simulation of non-penetrating flexible bodies.Computer Graphics: Proceedings of SIGGRAPH,1992,303-308
37.鲍虎军,金小刚,彭群生.计算机动画的算法基础[M].杭州:浙江大学出版社,2000.431-451
38. Dave Shreiner;Mason Woo;Jackie Neider;Tom Davis .OpenGL编程指南[M].北京.机械工业出版社,2008.2-32
39.刘涛.基于VC++的OpenGL编程讲座之概述[EB/OL]. http://dev.yesky.com/424/2080424.shtml, 2005—08—22
2. Knowlton K.A computer technique for producing animated movies.proc,AFIPS,1964,25:67-87
3. Knowlton K.Computer-produced movies.Science,1965,150(3700):1116-1120
4.金小刚,鲍虎军,彭群生.计算机动画综述[J].软件学报,1997 (8)241-251.
5.鲍虎军,金小刚,彭群生.计算机动画的算法基础[M].杭州:浙江大学出版社,2000.310-367
6. Barr A H. Global and local deformation of solid primitives, Computer Graphics,1984,18(3):21-30
7. Sederberg T W,Parry S R.Free-Form Deformation of Solid Geometric Models.Computer Graphics,1992,26(2):151-160
8. Hsu W M,Hughes J F,Kaufman H. Direct manipulation of Free-Form Deformation.Computer graphics,1992,26(2):177-184
9. Gressmair J,Purgatofer W.Deformation of Solids with Trivariate B-Splines.Proc.Eurographics’89.1989,21:137-148
10. Lamousin H J,Waggenspack W N.NURBS-based Free-From Deformation.IEEE Computer Graphics and Application,1994,14(6)59-65
11. Kalra P,Mangjli A,Thalmann N.Simulation of Facial Muscle Actions Based on Rational Free-Form Deformation.Computer Graphics Forum,1992,2(3):59-69
12. Coquillart S.Extended Free-Form Deformation:A Sculpturing Tool for 3D Geometric Modeling.Computer Graphics,1990,24(4):187-193
13. MacCracken R,Jay K I.Free-Form Deformation with Lattices of Arbitrary Topology.Computer Graphics,1996,30:181-189
14. Kenneth L.Joy and Ron Mac Cracken.The refinement rules for Catmull-Clark solids.Technical Report CSE-96-1,Department of Computer Science,University of California,Davis,January 1996
15. Bechmann D,Bertrand Y,Thery S.Continuous free form deformation.Computer Networks and ISDN System,1997,29:1715-1725
16. Lazarus F,Coquillart S,Jancene P.Axial Deformations:An Intuitive Deformation Technique.Computer-Aided Design,1994,26(8):608-612
17. Chang Y.K,Rockwood A P.A Generalized de Casteljau Approach to 3D Free-formDeformation,1994,28:257-260
18.冯结青,马利庄,彭群生.基于弧长参数的轴变形心方法[J].计算机学报,1996,19:161-170
19. Borrel P, Bechmann D. Deformation of N-dimensional objects. International Journal of Computational Geometry & Applications, 1991,1(4):427-453
20. L,E,Sutherland.The ultimate display. In Proceedings of the IFIP Congress 65.Volume2,1 965,506-583
21. Weil J.The synthesis of cloth object. Computer Garphics,1986,20 (4):49-54
22. B K Hinds, J McCartney. Interactive garment design.Visual Computer.1990,6(l):53-61
23. Delingette H,Subsol G,Cotin S,Pignon J.A craniofacial surgery simulation testbed. Proceedings of Visualization in Biomedical Computing,Rochester.NY.1994.607-618
24.成迟薏,石教英,徐迎庆,沈向洋.基于物理模型的窗帘运动实时动画[J].软件学报,2000,11(9):1228-1236
25. Chen D T,Zeltzer D.Pump it up:Computer animation of a biom- echanically based model of muscle using finite element method. Proceedings of Computer Graphics,1992,26:89-98
26. James D L,Pai D K.Accurate real time deformable objects.Proceedings of SIGGRA PH’99 Conference,Los Angeles,CA,1999,65-72
27. JI Feng. Research on Simulation of Soft Tissue Deformation in Virtual Orthodontics.IEEE Computer society,2006, 318-322
28. Cui Tong,Aiguo Song,Wu Juan.A Mass-Spring Model for Haptic Display of Flexble Object Global Deformation.International Conference on Mechatronics and Automation,2007,2753-2756
29.冯结青,彭群生.基于差值的Bernstein多项式复合及曲面应用[J].软件学报,2002,10
30.鲍春波,王博亮,刘卓,程明.一种用于软组织变形仿真的动态质点弹簧模型[J].系统仿真学报,2006,18(4):847-852
31. JI Feng. Research on Simulation of Soft Tissue Deformation in Virtual Orthodontics. In: IEEE Computer society,2006, 318-322
32.陈旿,徐乃平.真实感布仿真中布与刚体的碰撞检测及修正[J].软件学报,2001,12(12): 1874-1880
33.张建英.针织物动态模拟方法的研究[D].杭州:浙江大学,2004
34.高春波,刘玉树.碰撞检测技术综述[J].计算机工程与应用,2002,38(5):9-11
35.靳碧鹏.基于物理的计算机实时动画研究[D].合肥:电子科技大学,2007
36. David Baraff, Andrew Witkin. Dynamic simulation of non-penetrating flexible bodies.Computer Graphics: Proceedings of SIGGRAPH,1992,303-308
37.鲍虎军,金小刚,彭群生.计算机动画的算法基础[M].杭州:浙江大学出版社,2000.431-451
38. Dave Shreiner;Mason Woo;Jackie Neider;Tom Davis .OpenGL编程指南[M].北京.机械工业出版社,2008.2-32
39.刘涛.基于VC++的OpenGL编程讲座之概述[EB/OL]. http://dev.yesky.com/424/2080424.shtml, 2005—08—22