隨著電腦硬體的進步，虛擬實境已成為越來越普遍的技術，並廣泛應用於娛樂，訓練，醫學等方面。為了增加與虛擬環境的互動性與真實度,虛擬實境中觸覺方面的回饋於近幾年發展快速。本論文綜合整理了一些碰撞偵測演算法、虛擬牆力模式和摩擦力模式，以遊戲用的力回饋搖桿作為虛擬實境中的力回饋裝置，和微軟公司發展的DirectX作為3D電腦繪圖的軟體工具，建立了具有力回饋的虛擬環境介面。本研究比較三種虛擬牆力模式，並設計四個操作性質的實驗，探討力回饋對於虛擬實境中操作任務的影響。

As the progress of computer, virtual reality has become a more and more widespread technology and is applied extensively in entertainment, training, or medical science. To increase the interaction and reality of the virtual technology, the development of haptic feedback improves rapidly in recent years. This paper focuses on judgment existing collision detection algorithms, virtual wall models, and friction models from the view point of man-machine interface. A virtual environment interface with force feedback by using a joystick for computer game as a haptic device is established. A virtual environment is also built by employing the DirectX, a 3D computer graphic software developed by Microsoft Corp. Three virtual wall models are compared and four operational experiments are conducted to explore the influence of force feedback on operation task in virtual environment.

第一章　緒論...............................1
　1.1　研究動機與目的......................1
　1.2　文獻回顧............................2
　1.3　論文架構............................3
第二章　虛擬實境...........................4
　2.1　虛擬實境............................4
　2.2　DirectX.............................8
　　2.2.1　DirectX介紹.....................8
　　2.2.2　電腦繪圖－DirectGraphics.......11
　　2.2.3 　力回饋－DirectInput............14
　2.3　力回饋裝置.........................16
第三章　碰撞偵測..........................21
　3.1　各種碰撞偵測演算法.................22
　　3.1.1　球.............................22
　　3.1.2　中間軸.........................23
　　3.1.3　AABB...........................24
　　3.1.4　OBB............................25
　　3.1.5　k-DOPs.........................25
　　3.1.6　Q-Collide......................26
　　3.1.7　H-Collide......................26
　3.2　兩階段計算.........................28
第四章　動態與力模式......................33
　4.1 動量守恆...........................33
　4.2　虛擬牆.............................38
　　4.2.1　零階保持與取樣估計保持.........38
　　4.2.2　彈簧與阻尼模式.................40
　　4.2.3　剎車衝量模式...................41
　　4.2.4　磁滯曲線模式...................41
　4.3　摩擦力.............................44
　　4.3.1　古典摩擦.......................44
　　4.3.2　Dahl模式.......................45
　　4.3.3　Karnopp模式....................46
　　4.3.4　Bristle模式....................46
　　4.3.5　Reset Integrator模式...........47
第五章　模擬實驗與結果....................49
　5.1　自由落體...........................49
　5.2　虛擬牆碰撞感受.....................52
　5.3　一維運動推物體.....................53
　5.4　倒單擺.............................55
　5.5　具摩擦力之旋轉鈕...................57
　5.6　具摩擦力之斜面循圓.................62
　5.7　實驗討論...........................66
第六章　結論與未來方向....................68
參考文獻..................................70
附錄A　實驗數據...........................74
附錄B　倒單擺動態推導.....................80

[1]　A. Gregory, M. Lin, S. Gottschalk, and R. Taylor, “H- collide: A framework for fast and accurate collision
detection for haptic interaction”, In the Proceedings
of IEEE Virtual Reality Conference, 1999

[2]　A. M. Osama, S.Horiguchi, "Tele-Handshake:Cooperative
haptic shared virtual environment", Proceedings of
Eurohaptics 2001. Birmingham, UK 1-4 pages 60-64, July
2001

[3]　A. M. Osama, S. Horiguchi and S. Kunifuji, "An
Experimental Study on the Effects of Network Delay in
Cooperative Shared Haptic Virtual Environment",
Computers & Graphics, Elsevier Publisher, Vol. 27,
No.2, pages 205-213, 2003

[4] B. Mirtich, “V-Clip:Fast and Robust polyhedral
collision detection”, ACM TOG, Vol. 17, No.3,
pages177-208, July 1998

[5] Colgate J.E., Grafing P.E., Stanely, M.C., and
Schenkel G., “Implementation of stiff virtual walls
in force-reflecting interfaces”, in IEEE Virtual
Reality Annual International Symposium, pages.202-208,
1993

[6]　Cruz-Neira, C, "Computational humanities: the new
challenge for VR", Computer Graphics and applications,
IEEE , Vol.23 , Issue:3 , pages 10-13, 2003

[7]　D. A. Jr. Haessig and B. Friedland, “On the Modeling
and Simulation of Friction”, Journal of Dynamic
Systems, Measurement, and Control, DSC-113:354-362,
1991

[8]　D. Constantinescu, I. Chau, S. P. DiMaio, L.
Filipozzi, S. E. Salcudean, and F. Ghassemi, “Haptic
Rendering of Planar Rigid-Body Motion using a
Redundant Parallel Mechanism”, In Proc. IEEE
International Conference on Robotics & Automation
Vol.3 , pages 24-28, 2000

[9]　G. C. Burdea, “Invited review:The Synergy between
virtual reality and robotics”, IEEE Trans. On
Robotics and Automation, Vol.15, no.3, pages 400-410,
1999

[10]　Gino Van Den Bergen,“Efficient collision detection
of complex deformable models using AABB trees”,
Journal of Graphics Tools, vol.2, Issue 4, pages 1-
13, 1998

[11] Hubbard, P.M. ”Approximating Polyhedra with Spheres
for Time-Critical Collision Detection”, ACM
Transactions on Graphics, Vol. 15, No. 3, pages 179-
210, 1996

[12]　I. Han and B.J. Gilmore. “Impact Analysis for
Multiple-Body Systems with Friction and Sliding
Contact”, In D.P. Sathyadev, editor, Flex. Assembly
Systems, pages 99-108. New York, 1989

[13]　James T. Klosowski, Martin Held, Joseph S.B.
Mitchell, Henry Sowizral, and Karel Zikan,
“Efficient Collision Detection Using Bounding Volume
Hierarchies of k-DOPs”, IEEE Transactions on
visualization and computer graphics, vol. 4,
NO.1 ,pages 21-36, 1998

[14]　J. B. Keller, “Impact with friction”, Journal of
Applied Mechanics, vol.53, pages 1-4, 1986

[15]　J. Cohen, M. Lin, Manocha, and M.Ponamgi, “I-
collide: An interactive and exact collision detection
system for large-scale environments”, In Proc. Of
ACM Interactive 3D Graphics Conference, pages 189-
196, 1995

[16]　J.L. Meriam, L.G. Kraige, Engineering Mechanics
Dynamics Fourth Edition, 1997

[17]　Jungwon Yoon and Jeha Ryu, “Design, Fabrication, and
Evaluation of a New Haptic Device Using a Parallel
Mechanism”, IEEE Transactions on mechatronics,
vol.6, no.3, pages:221 – 233, 2001

[18]　Karnopp, D., “Computer Simulation of Stick-Slip
Friction in Mechanical Dynamic Systems”, ASME
Journal of Dynamic Systems, Measurement, and Control,
Vol.107, pages 100-103, 1985

[19]　Matthew Moore and Jane Wihlelms,“Collision Detection
and Response for Computer Animation”, ACM SIGGRAPH,
Vol.22, No.4, pages289-298, August 1988

[20]　M. Goldfarb and J. Wang, “Passive Stiffness
Simulation with Rate-Independent Hysteresis”, In
Proc. ASME,Dynamic Systems and Control Division,
volume DSC-67, pages 345-350, Nashville, TN,1999

[21]　Minsky, M. , M. Ouh-young, O. Steele, F. P. Brooks,
Jr., M. Behensky, “Feeling and seeing: Issues in
Force Display.”, Computer Graphics, vol.24, no.2,
pages 235-243, 1990

[22]　O’Sullivan, C. Dingliana, J.,”Real-Time Collision
Detection and Response Using Sphere-Trees”, Image
Synthesis Group, Trinity College Dublin, 1999

[23]　Raymond M. Brach, “Rigid Body Collisions”, Journal
of Applied Mechanics,vol. 56, pages.133-138, 1989

[24]　R.E. Ellis, N. Sarkar, and M.A. Jenkins. “Numerical
Methods for the Haptic Presentation of Contact:
Theory, Simulations, and Experiments”, In Proc.
ASME, Dynamic Systems and Control Division, volume
DSC-58, pages 413-420, New York, NY,1996

[25]　S.E. Salcudean and T.D. Vlaar, “On the Emulation of
Stiff Walls and Static Friction with a Magnetically
Levitated Input/Output Device”, Journal of Dynamic
Systems, Measurement, and Control, Vol. 119, pages
127-132, 1997

[26]　S. Gottschalk, M.C. Lin, D. Manocha, “OBBTree: A
hierarchical structure for rapid interference
detection”, In Proc. SIGGRAPH ‘96, pages 171-180,
1996

[27]　Stephen A. Ehmann and Ming. C. Lin, “Accurate Fast
Proximity Queries Between Polyhedra Using Convex
Surface Decomposition”, EUROGRAPHICS, vol.20, no.3,
2001

[28]　T. Yoshikawa and K. Henmi, “Human Skill Transfer
Using Haptic Virtual Reality Technology”, In P.
Corke and J. Trevelyan, editors, Experimental
Robotics VI, pages 351-360, 2000

[29]　http://users.volja.net/fajrvehr/

[30]　林瑋慶 , ”模擬系統之兩軸力回饋搖桿設計與控制” , 碩士
論文，國立交通大學電機與控制工程學系，2002

[31]　林敬涵 , “力回饋操縱桿與虛擬實境之整合研究” , 碩士論
文，國立台灣大學造船及海洋工程研究所，1998

[32]　陳正義 , “具摩擦及不確定性傳動系統之運動控制” , 博士
論文，國立中山大學機械與機電工程研究所，1999

[33]　謝馥圭 , “PC虛擬實境” , 儒林圖書公司 , 1996

[34]　汪成為 , "人類認識世界的好幫手" , 牛頓出版公司 , 2001

[35]　DirectX說明文件

[36]　藤田伸二著,陳寬裕,鍾正雄譯,”DirectX電玩遊戲設計for
Visual Basic”,知城數位科技公司,2001

[37]　Mason McCuskey著,黃聖峰譯,”DirectX特效遊戲程式設計”,
博碩文化,2002

[38]　Jim Adams著,張世敏譯,”2D/3D RPG角色扮演遊戲程式設計-
使用DirectX”,博碩文化,2003

[39]　張碩,”自動控制系統”,鼎茂圖書公司,2001