航海模拟器中缆绳作业的仿真研究
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摘要
船舶在进港靠泊的过程中,最重要的一步就是把第一根缆绳系在缆桩上,具体操作过程为甲板船员把撇缆绳一端的撇缆头投掷到岸上,由带缆工通过撇缆绳把大缆绳的琵琶头拖拽上岸套在缆桩上。其中撇缆是甲板部船员的一项重要基本技能。传统的培训方式是在专门的训练场地,由专业人员演示,然后学员模仿反复练习。这种培训具有占用场地大、易受天气影响、具有一定的危险性等缺点。随着虚拟现实技术和仿真技术的快速发展,开发撇缆作业的模拟器成为可能。如果撇缆作业的培训可以在模拟器上完成,这无疑改善了培训条件,解决了传统培训的弊端。为了达到上述目的本文主要做了如下研究：
1.基于集中质量方法,利用经典的弹簧质点模型对撇缆绳进行了数学建模,实现了撇缆绳的可视化仿真；
2.在弹簧质点模型的基础上,将质点近似为集中质量的球单元,弹簧近似为具有一定质量的杆单元,引入了Kawabata拉伸张力模型,考虑了空气动力的影响,建立了撇缆绳运动的数学模型；
3.利用OpenGL图形库函数编程构建了虚拟手的三维模型,通过控制坐标系转换的函数完成了虚拟手的运动；
4.采用Vhand2.0数据手套作为人机交互的工具,实现了人手到虚拟手的运动映射,完成了撇缆作业的动态仿真。
When the ship is berthing, the most important step is how to tie the first cable been on the bollard. The specific operating processes is that the deck crew throws the heaving line to the shore, and then the dock workers pull the heaving line until the cable also gets on the dock, finally, they put the eye splice on the bollard. Heaving line is an important basic skill for the deck department crew. Traditional training is in the specialized training grounds, students imitate a professional's presentations. There are several drawbacks of such training:occupied large sites; easily affected by weather; fifth, has certain risk. With the rapid development of simulation technology and virtual reality techno-logy, developing the simulator of the heaving line unit is possible. If heaving line training can be done in the simulator, there will undoubtedly improve the training conditions which can solve the shortcomings of traditional training:long cycle, high cost and the risk of training. In order to achieve the above purpose, the main resea-rch contents of this paper are summarized as follows:
1. Based on the lump-mass model, this paper builds the mathematical model for the rope by using spring-mass model, and realizes the visualization of the heaving line.
2. Based on the above model, the paper uses the ball-bar element to build the rope's mathematical model. In this method, Kawabata tensile strain model is adopted to consider the impact of air friction.
3. Author constructs the three-dimensional model of the virtual hand by OpenGL graphics API. The virtual hand's movement is controlled by changing the parameters of the coordinate system conversion.
4. Vhand2.0Data glove is used as the human-computer interaction tools to complete the virtual hand's movement controlling, the dynamic simulation of heaving line operation, implemented after finishing the movement mapping form real hand to virtual hand.
1.基于集中质量方法,利用经典的弹簧质点模型对撇缆绳进行了数学建模,实现了撇缆绳的可视化仿真；
2.在弹簧质点模型的基础上,将质点近似为集中质量的球单元,弹簧近似为具有一定质量的杆单元,引入了Kawabata拉伸张力模型,考虑了空气动力的影响,建立了撇缆绳运动的数学模型；
3.利用OpenGL图形库函数编程构建了虚拟手的三维模型,通过控制坐标系转换的函数完成了虚拟手的运动；
4.采用Vhand2.0数据手套作为人机交互的工具,实现了人手到虚拟手的运动映射,完成了撇缆作业的动态仿真。
When the ship is berthing, the most important step is how to tie the first cable been on the bollard. The specific operating processes is that the deck crew throws the heaving line to the shore, and then the dock workers pull the heaving line until the cable also gets on the dock, finally, they put the eye splice on the bollard. Heaving line is an important basic skill for the deck department crew. Traditional training is in the specialized training grounds, students imitate a professional's presentations. There are several drawbacks of such training:occupied large sites; easily affected by weather; fifth, has certain risk. With the rapid development of simulation technology and virtual reality techno-logy, developing the simulator of the heaving line unit is possible. If heaving line training can be done in the simulator, there will undoubtedly improve the training conditions which can solve the shortcomings of traditional training:long cycle, high cost and the risk of training. In order to achieve the above purpose, the main resea-rch contents of this paper are summarized as follows:
1. Based on the lump-mass model, this paper builds the mathematical model for the rope by using spring-mass model, and realizes the visualization of the heaving line.
2. Based on the above model, the paper uses the ball-bar element to build the rope's mathematical model. In this method, Kawabata tensile strain model is adopted to consider the impact of air friction.
3. Author constructs the three-dimensional model of the virtual hand by OpenGL graphics API. The virtual hand's movement is controlled by changing the parameters of the coordinate system conversion.
4. Vhand2.0Data glove is used as the human-computer interaction tools to complete the virtual hand's movement controlling, the dynamic simulation of heaving line operation, implemented after finishing the movement mapping form real hand to virtual hand.
引文
[1]中华人民共和国海事局.<1978年海员培训、发证和值班标准国际公约>2010年马尼拉修正案[M].大连：大连海事大学出版社,2010.12.
[2]中华人民共和国交通部.中华人民共和国船员培训管理规则,中华人民共和国交通部令1997年第13号.
[3]方泉根.计算机仿真技术在21世纪航海教育中的发展与应用[J].上海海运学院学报,2001,22(2)：24-28.
[4]DNV. Standard for Certification of Maritime Simulators Systems No.2.14[S]. Norway,2011.1.
[5]刘斯云.航海模拟器视景系统中自主拖轮运动规划算法及实现的研究[D].大连：大连海事大学,2001.
[6]方泉根.航海模拟器的现状及展望[J].中国航海,1996,38(1)：38-43.
[7]包雄关.航海模拟器的功能[J].大连海事大学学报,2003,15(1)：23-26.
[8]邓健,刘克中.港口工程通航评估中船舶操纵模拟器的应用[J].航海技术,2008,(6)：6-8.
[9]L H Ronald, E K James. A Representation of Fluid Forces in Finite Segment Cable Models. AD Report, AD-A090181,1980.
[10]Baraff D, Witkin A.Large Stepsin Cloth simulation. IN:SIGGRAPH98, Orlando,1998:19-24
[11]Ablow C.M, S. Schechter Numerical Simulation of Undersea Cable Dynamics. SRI Intern-ational, Menlo Park, CA 94025, USA.
[12]Yang Sun, John W. Leonard. Dynamics of Ocean Cables with Local Low-Tension Regions [J].Ocean Engineering,1998,25(6):443-463.
[13]Milinazzo Fawnlike M,Latchman SA. An Efficient Algorithm For Simulating The Dynamics for Towed Cale Systems [J].Ocean Engineering,1987,14(6) 513-526.
[14]向溢,谭家华.码头系泊缆绳张力的蒙特卡洛算法[J].上海交通大学学报,2001,35(4)：548-551.
[15]靳明君,张志国.悬链线柔索索长的计算[J].铁道标准设计,2004,(5)：9-11.
[16]王飞.规则波作用下拖缆数值分析研究[J].海洋工程,2006,24(1)：92-97.
[17]李万超.船舶操纵模拟器中拖轮子系统的研究[D].大连：大连海事大学,2004.
[18]刘鑫.航海模拟器视景中缆绳的绘制[D].大连：大连海事大学,2011.
[19]王尔光.中层拖网的水层控制[J].大连水产学院学报,1992,6(2)：21-28.
[20]F.Hu, K. Matuda etal.Dynamic analysis of midwater trawl system by a two dimensional lumped mass method [J].Fisheries Science,1995,61:229-233.
[21]Bessonneau J S, Marichal D.Study of the dynamics of submerged supple nets (applications to trawls)[J].Ocean Engineering,1998,25(7):563-583.
[22]Katsuya Suzuki, Tsutomu Takagi, Takashi Shimizu Etal. Validity and Visualization of a Numerical Model Used to Determine Dynamic Configuration of Fishing Nets [J].Fisheries Science.2003,69:695-705.
[23]Walton T S, Polachech H.Calculation of Transient Motion of Submerged Cables. Mathematics of Computation,1960,14:27-46.
[24]赵国伟,熊会宾,黄海,闫泽红.柔性绳索体展开过程数值模拟及实验[J].航空学报,2009,30(8)：1429-1434.
[25]孙霄峰.单船中拖网系统的建模与仿真[D].大连：大连海事大学,2008.
[26]高帅.渔网的动态仿真及可视化研究[D].大连：大连海事大学,2011.
[27]宋庆文,周源华.一类柔软物体悬垂的实时模拟技术[J].上海交通大学学报,2002,36(2)：1846-1850.
[28]罗文龙,王德才,孙玉萍等.柔性物体实时可视化仿真[J].重庆邮电学院学报,2006,18(2)：251-254.
[29]武继银.基于OSG的实时布料仿真[D].济南：山东大学,2009.
[30]X.Provot. Deformation Constraints in a Mass-Spring Model to Describe Rigid Cloth Behavior. Proc. Graphics Interface,1995:147-154.
[31]刘鹏远,李瑞华,胡昌林.虚拟环境下柔性线缆建模方法[J].军械工程学院学报,2008,20(3)：63-65.
[32]胡晓楠,张建斌,赵国伟.柔性绳索在空气阻力作用下的动力学仿真研究[J].机械科学与技术,2010,29(10)：1334-1337.
[33]http://baike.baidu.com/view/600151.htm.
[34]Keni Bernardin, Koichi Ogawara, Katsushi Ikecuchi et al.Sensor Fusion Approach for Recognizing Continuous Human Grasping Sequenees Using Hidden Markov Models. IEEE Transactions on Robotics,2005,21(1):47-57.
[35]Iberall T.Human prehension and dexterous robot hands.The Internationa Journal of Robotics Research,1997,16(3):285-299.
[36]Iberall T. The nature of human prehension:three dexterous hands in one.IEEE Internationa Conference Robotics and Atuomation,1987:396-401.
[37]R.G..0 Hagan, A.Zelinsky, S.Rougeaux.Virtual hands and virtual reality multimodal platform to design safer industrial system.Computers in Idustriy,2007,58 (1):47-57.
[38]Mamy Pouliquen, Alain Bernard, Jaeques Marsot ET al.Visual gesture interfaces for virtual environments.Interacting with Computers,2002,14(3):231-250.
[39]李琪,白英彩,曾芬芳.一个虚拟手原型的实现[J].上海交通大学学报,1999,33(1 1)：1377-1380.
[40]李志华,钟毅芳.虚拟手模型及其抓取技术[J].小型微型计算机系统,2003,24(6)：1071-1074.
[41]曾芬芳,梁柏林,刘镇等.基于数据手套的人机交互环境设计[J].中国图象图形学报,2000,5(2)：153-157.
[42]熊友军,李世其,王文涛.基于数据手套驱动的虚拟机器人操作技术[J].机械科学与技术,2004,23(12)：1433-1436.
[43]田艺.基于数据手套的双手手势交互[D].杭州：浙江大学,2006.
[44]罗刚.基于数据手套的虚拟手实时交互平台的研究与设计[D].杭州：浙江大学,2006.
[45]梅继红,雷小永,戴树岭.基于数据手套的虚拟操作技术研究[J].系统仿真学报,2002,14(3)：330-332.
[46]张俊杰.基于数据手套的机械手控制系统开发研究[D].武汉：华中科技大学,2005.
[47]王文涛.基于虚拟手的人机交互技术研究[D].武汉：华中科技大学,2005.
[48]刘江省,姚英学,李建广等.虚拟装配中基于数据手套的虚拟操作研究[J].系统仿真学报,2004,16(8)：1744-1747.
[49]于红敏.基于VTree平台的数据手套交互模块的研究[D].大连：大连海事大学,2008.
[50]李娜.集装箱装卸仿真系统中虚拟交互的研究与实现[D].大连：大连海事大学,2009.
[51]丁俐.集装箱装卸模拟器中虚拟交互方式的实用化研究[D].大连：大连海事大学,2011.
[52]http://wenku.baidu.com/view/bflde10879563clec5da71ad.html
[53]陆熊,宋爱国.力_触觉再现中柔性物体可视化物理形变模型研究进展[J].计算机辅助设计与图形学学报,2008,20(11)：1389-1395.
[54]Larrabee J R W F, Sutton D.A finite element model of skin deformation.II.An experimental model of skin deformation [J].Laryngoscope,1986,96(4):406-412.
[55]Chen D T, Zeltzer D. Pump it up:Computer animation of biomechanically based model of muscle using the finite element method [C].Computer Graphics Proceedings, Annual Conference Series,ACM SIGGRAPH.Chicago,1992:89-98
[56]Pieper S D,Laub D R,Rosen J,A finite-element Facial model for simulating plastic surgery [J]. Plastic Reconstructive Surgery,1995,96(5):1100-1105.
[57]Gladilin E,Zachow.S,Deuflhard P,et al.A biomechanical model for soft tissue simulation in craniofacial surgery[C]//Proceeding of the International Workshop on Medical Imaging and Augmented RealityJHong Kong,2001:137-141
[58]KeeveQGirod. Craniofacial surgery simulation [M].Lecture Notes in Computer Science. Heid-elberg:Springer,1996,1131:541-546.
[59]Picinbono G, Lombardo J C, Delingette H, etal. Anisotropic elasticity and force extrapolation to improve realism of surgery simulation [C].Proceedings of the 2000 IEEE International Conferrence on Robotics & Automation,San Francisco,2000:596-602.
[60]程楠.集中质量法在深海系泊冲击张力计算中的应用研究[D].天津：天津大学建筑工程学院,2008.5.
[61]Taibi E H, Hammouche A. Model of the tensile stressstrain behavior of fabrics [J]. Textile Research Journal,2002,71 (7):582-586.
[62]Bathe K J.In Finite Element Procedures in Engineering Analysis [M]. Prentice-Hall,1982.
[63]http://baike.baidu.com/view/149100.htm.
[64]Rouse H. Elementary mechanics of fluids [M]. New York:Dover,1978:232-270.
[65]Michael T. Heath(张威,贺华,冷爱萍译).科学计算导论[M].北京：清华大学出版社,2005.
[66]威尔逊.结构静力与动力分析—强调地震工程学的物理方法[M].北京：中国建筑工业出版社,2006.
[67]黄志英,万红.船用撇缆的转体式投掷方法理论研究[J]交通信息与安全(增刊),2010,28(1)：116-119.
[68]Dave Shreiner, The Khronos OpenGL ARB Working Group李军,徐波等译OpenGL编程指南(原书第七版)[M].机械工业出版社,2010.1.
[69]刘博,张玉茹,任大伟等.人手食指运动学建模[J].机器人,2007,29(3)：214-218.
[70]焦圣品,白英彩,曾芬芳.虚拟现实中手的建模[J].上海交通大学学报,1998,32(10)：134-136.
[71]潘振宽,崔树娟,张继萍等.基于层次包围盒的碰撞检测方法[J].青岛大学学报：自然科学版,2005,18(1)：71-76.
[72]邹益胜,丁国富等.实时碰撞检测算法综述[J].计算机应用研究,2008,25(1)：8-12.
[73]LIN MC, GOTTSCHALK S.Collision detection between geometric models:a survey [C].Proc of IMA Conference on Mathematics of Sur-faces,1998:37-56.
[74]Van den Bergen G.Efficient collision detection of complex deformable models using AABB trees [J]. Journal of Graphics Tools,1997,2(4):1-13.
[75]JIM NEZ P, THOMAS F, TORRAS C.3D collision detection:a survey [J].Computers and Graphics,2001,25(2):269-285.
[76]GOTTACHALK S, LIN MC, MANOCHA D.OBB-Tree:A Hierarchical Structure for Rapid Interference Detection [J]. The Proceedings of ACM SIGGRAPH'96,1996:171-180.
[2]中华人民共和国交通部.中华人民共和国船员培训管理规则,中华人民共和国交通部令1997年第13号.
[3]方泉根.计算机仿真技术在21世纪航海教育中的发展与应用[J].上海海运学院学报,2001,22(2)：24-28.
[4]DNV. Standard for Certification of Maritime Simulators Systems No.2.14[S]. Norway,2011.1.
[5]刘斯云.航海模拟器视景系统中自主拖轮运动规划算法及实现的研究[D].大连：大连海事大学,2001.
[6]方泉根.航海模拟器的现状及展望[J].中国航海,1996,38(1)：38-43.
[7]包雄关.航海模拟器的功能[J].大连海事大学学报,2003,15(1)：23-26.
[8]邓健,刘克中.港口工程通航评估中船舶操纵模拟器的应用[J].航海技术,2008,(6)：6-8.
[9]L H Ronald, E K James. A Representation of Fluid Forces in Finite Segment Cable Models. AD Report, AD-A090181,1980.
[10]Baraff D, Witkin A.Large Stepsin Cloth simulation. IN:SIGGRAPH98, Orlando,1998:19-24
[11]Ablow C.M, S. Schechter Numerical Simulation of Undersea Cable Dynamics. SRI Intern-ational, Menlo Park, CA 94025, USA.
[12]Yang Sun, John W. Leonard. Dynamics of Ocean Cables with Local Low-Tension Regions [J].Ocean Engineering,1998,25(6):443-463.
[13]Milinazzo Fawnlike M,Latchman SA. An Efficient Algorithm For Simulating The Dynamics for Towed Cale Systems [J].Ocean Engineering,1987,14(6) 513-526.
[14]向溢,谭家华.码头系泊缆绳张力的蒙特卡洛算法[J].上海交通大学学报,2001,35(4)：548-551.
[15]靳明君,张志国.悬链线柔索索长的计算[J].铁道标准设计,2004,(5)：9-11.
[16]王飞.规则波作用下拖缆数值分析研究[J].海洋工程,2006,24(1)：92-97.
[17]李万超.船舶操纵模拟器中拖轮子系统的研究[D].大连：大连海事大学,2004.
[18]刘鑫.航海模拟器视景中缆绳的绘制[D].大连：大连海事大学,2011.
[19]王尔光.中层拖网的水层控制[J].大连水产学院学报,1992,6(2)：21-28.
[20]F.Hu, K. Matuda etal.Dynamic analysis of midwater trawl system by a two dimensional lumped mass method [J].Fisheries Science,1995,61:229-233.
[21]Bessonneau J S, Marichal D.Study of the dynamics of submerged supple nets (applications to trawls)[J].Ocean Engineering,1998,25(7):563-583.
[22]Katsuya Suzuki, Tsutomu Takagi, Takashi Shimizu Etal. Validity and Visualization of a Numerical Model Used to Determine Dynamic Configuration of Fishing Nets [J].Fisheries Science.2003,69:695-705.
[23]Walton T S, Polachech H.Calculation of Transient Motion of Submerged Cables. Mathematics of Computation,1960,14:27-46.
[24]赵国伟,熊会宾,黄海,闫泽红.柔性绳索体展开过程数值模拟及实验[J].航空学报,2009,30(8)：1429-1434.
[25]孙霄峰.单船中拖网系统的建模与仿真[D].大连：大连海事大学,2008.
[26]高帅.渔网的动态仿真及可视化研究[D].大连：大连海事大学,2011.
[27]宋庆文,周源华.一类柔软物体悬垂的实时模拟技术[J].上海交通大学学报,2002,36(2)：1846-1850.
[28]罗文龙,王德才,孙玉萍等.柔性物体实时可视化仿真[J].重庆邮电学院学报,2006,18(2)：251-254.
[29]武继银.基于OSG的实时布料仿真[D].济南：山东大学,2009.
[30]X.Provot. Deformation Constraints in a Mass-Spring Model to Describe Rigid Cloth Behavior. Proc. Graphics Interface,1995:147-154.
[31]刘鹏远,李瑞华,胡昌林.虚拟环境下柔性线缆建模方法[J].军械工程学院学报,2008,20(3)：63-65.
[32]胡晓楠,张建斌,赵国伟.柔性绳索在空气阻力作用下的动力学仿真研究[J].机械科学与技术,2010,29(10)：1334-1337.
[33]http://baike.baidu.com/view/600151.htm.
[34]Keni Bernardin, Koichi Ogawara, Katsushi Ikecuchi et al.Sensor Fusion Approach for Recognizing Continuous Human Grasping Sequenees Using Hidden Markov Models. IEEE Transactions on Robotics,2005,21(1):47-57.
[35]Iberall T.Human prehension and dexterous robot hands.The Internationa Journal of Robotics Research,1997,16(3):285-299.
[36]Iberall T. The nature of human prehension:three dexterous hands in one.IEEE Internationa Conference Robotics and Atuomation,1987:396-401.
[37]R.G..0 Hagan, A.Zelinsky, S.Rougeaux.Virtual hands and virtual reality multimodal platform to design safer industrial system.Computers in Idustriy,2007,58 (1):47-57.
[38]Mamy Pouliquen, Alain Bernard, Jaeques Marsot ET al.Visual gesture interfaces for virtual environments.Interacting with Computers,2002,14(3):231-250.
[39]李琪,白英彩,曾芬芳.一个虚拟手原型的实现[J].上海交通大学学报,1999,33(1 1)：1377-1380.
[40]李志华,钟毅芳.虚拟手模型及其抓取技术[J].小型微型计算机系统,2003,24(6)：1071-1074.
[41]曾芬芳,梁柏林,刘镇等.基于数据手套的人机交互环境设计[J].中国图象图形学报,2000,5(2)：153-157.
[42]熊友军,李世其,王文涛.基于数据手套驱动的虚拟机器人操作技术[J].机械科学与技术,2004,23(12)：1433-1436.
[43]田艺.基于数据手套的双手手势交互[D].杭州：浙江大学,2006.
[44]罗刚.基于数据手套的虚拟手实时交互平台的研究与设计[D].杭州：浙江大学,2006.
[45]梅继红,雷小永,戴树岭.基于数据手套的虚拟操作技术研究[J].系统仿真学报,2002,14(3)：330-332.
[46]张俊杰.基于数据手套的机械手控制系统开发研究[D].武汉：华中科技大学,2005.
[47]王文涛.基于虚拟手的人机交互技术研究[D].武汉：华中科技大学,2005.
[48]刘江省,姚英学,李建广等.虚拟装配中基于数据手套的虚拟操作研究[J].系统仿真学报,2004,16(8)：1744-1747.
[49]于红敏.基于VTree平台的数据手套交互模块的研究[D].大连：大连海事大学,2008.
[50]李娜.集装箱装卸仿真系统中虚拟交互的研究与实现[D].大连：大连海事大学,2009.
[51]丁俐.集装箱装卸模拟器中虚拟交互方式的实用化研究[D].大连：大连海事大学,2011.
[52]http://wenku.baidu.com/view/bflde10879563clec5da71ad.html
[53]陆熊,宋爱国.力_触觉再现中柔性物体可视化物理形变模型研究进展[J].计算机辅助设计与图形学学报,2008,20(11)：1389-1395.
[54]Larrabee J R W F, Sutton D.A finite element model of skin deformation.II.An experimental model of skin deformation [J].Laryngoscope,1986,96(4):406-412.
[55]Chen D T, Zeltzer D. Pump it up:Computer animation of biomechanically based model of muscle using the finite element method [C].Computer Graphics Proceedings, Annual Conference Series,ACM SIGGRAPH.Chicago,1992:89-98
[56]Pieper S D,Laub D R,Rosen J,A finite-element Facial model for simulating plastic surgery [J]. Plastic Reconstructive Surgery,1995,96(5):1100-1105.
[57]Gladilin E,Zachow.S,Deuflhard P,et al.A biomechanical model for soft tissue simulation in craniofacial surgery[C]//Proceeding of the International Workshop on Medical Imaging and Augmented RealityJHong Kong,2001:137-141
[58]KeeveQGirod. Craniofacial surgery simulation [M].Lecture Notes in Computer Science. Heid-elberg:Springer,1996,1131:541-546.
[59]Picinbono G, Lombardo J C, Delingette H, etal. Anisotropic elasticity and force extrapolation to improve realism of surgery simulation [C].Proceedings of the 2000 IEEE International Conferrence on Robotics & Automation,San Francisco,2000:596-602.
[60]程楠.集中质量法在深海系泊冲击张力计算中的应用研究[D].天津：天津大学建筑工程学院,2008.5.
[61]Taibi E H, Hammouche A. Model of the tensile stressstrain behavior of fabrics [J]. Textile Research Journal,2002,71 (7):582-586.
[62]Bathe K J.In Finite Element Procedures in Engineering Analysis [M]. Prentice-Hall,1982.
[63]http://baike.baidu.com/view/149100.htm.
[64]Rouse H. Elementary mechanics of fluids [M]. New York:Dover,1978:232-270.
[65]Michael T. Heath(张威,贺华,冷爱萍译).科学计算导论[M].北京：清华大学出版社,2005.
[66]威尔逊.结构静力与动力分析—强调地震工程学的物理方法[M].北京：中国建筑工业出版社,2006.
[67]黄志英,万红.船用撇缆的转体式投掷方法理论研究[J]交通信息与安全(增刊),2010,28(1)：116-119.
[68]Dave Shreiner, The Khronos OpenGL ARB Working Group李军,徐波等译OpenGL编程指南(原书第七版)[M].机械工业出版社,2010.1.
[69]刘博,张玉茹,任大伟等.人手食指运动学建模[J].机器人,2007,29(3)：214-218.
[70]焦圣品,白英彩,曾芬芳.虚拟现实中手的建模[J].上海交通大学学报,1998,32(10)：134-136.
[71]潘振宽,崔树娟,张继萍等.基于层次包围盒的碰撞检测方法[J].青岛大学学报：自然科学版,2005,18(1)：71-76.
[72]邹益胜,丁国富等.实时碰撞检测算法综述[J].计算机应用研究,2008,25(1)：8-12.
[73]LIN MC, GOTTSCHALK S.Collision detection between geometric models:a survey [C].Proc of IMA Conference on Mathematics of Sur-faces,1998:37-56.
[74]Van den Bergen G.Efficient collision detection of complex deformable models using AABB trees [J]. Journal of Graphics Tools,1997,2(4):1-13.
[75]JIM NEZ P, THOMAS F, TORRAS C.3D collision detection:a survey [J].Computers and Graphics,2001,25(2):269-285.
[76]GOTTACHALK S, LIN MC, MANOCHA D.OBB-Tree:A Hierarchical Structure for Rapid Interference Detection [J]. The Proceedings of ACM SIGGRAPH'96,1996:171-180.