在本論文的研究中，我們提出了混合式的物理變形模塑(hybrid physical-based deformation modeling)技術應用於我們所發展的內視鏡手術模擬系統中。混合式的物理變形模塑包括下列三部份：(i) 近似連續性的自由框架模塑
、(ii) 非剛體的碰撞偵測、及(iii) 彈簧模式的力回饋模組。有三種常見的物理變形模塑：彈簧模塑、近似連續
模塑、及有限元素法，被應用在手術模擬系統中。這三種方法在變形的真實度及計算的效率上都有各自的優
缺點。我們提出的混合式物理變形模塑比單純的彈簧模式具有更真實的物理變形特性；比單純的近似連續變
形模塑更有效率，且允許拓樸結構的改變。

In this paper, we develop a hybrid physical-based deformation modeling (HPDM) technique for the proposed laparoscopic surgery simulation system. The proposed technique consists of three components: (i) approximate continuum free-form deformation modeling, (ii) efficient collision detection for non-rigid objects, and (iii) mass-spring modeling for force feedback implementation. Three physical-based deformation modeling techniques have been applied on the surgical simulation which are mass-spring model, approximate continuum model, and finite element model. All these models have disadvantages of less realism or time consuming. Here, we propose the HPDM to achieve the realistic deformation of organs in a computationally efficient framework. The proposed HPDM exhibits more physical accuracy and realism than the mass-spring modeling exhibits and exposes more advantages of more efficient computation, allowing topology change, and satisfying arbitrary geometric meshes than the approximate continuum model exposes.

Abstractii
Contentsiii
List of Figuresv
List of Tablesvi
Chapter 1 Introduction1
1.1 Motivation1
1.2 System overview3
1.2.1 Physical-based deformation modeling 3
1.2.2 Collision detection3
1.2.3 Haptic interface4
1.3 Thesis organization4
Chapter 2 Related Works6
2.1 Requirements for surgical simulation 6
2.1.1 Real-time deformation6
2.1.2 Geometric representation7
2.1.3 Change of topological structures8
2.2 Deformation modeling techniques8
2.2.1 Geometric-based techniques 8
2.2.2 Physical-based techniques9
2.2.3 Hybrid techniques10
2.3 Studies on surgical simulation systems 11
Chapter 3 Hybrid Physical-based Deformation Modeling 15
3.1 Hybrid physical-based deformation modeling framework 15
3.2 Free form deformation15
3.3 Direct manipulation of free form17
3.4 Approximate continuum modeling19
3.4.1 Kinematics and dynamics19
3.4.2 Internal energy of deformation20
3.4.3 Discretization23
3.5 Mass-spring deformation modeling26
3.6 Hybrid physical-based deformation modeling approach28
Chapter 4 Integrated Environment for Surgical simulation 32
4.1 Surgical simulation environment32
4.1.1 The complexity of abdominal model32
4.1.2 Realistic virtual environment33
4.1.3 Realistic position of virtual laparosocpe and
virtual surgical instruments 33
4.1.4 Virtual surgical instrument control 36
4.2 Efficient collision detection 36
4.2.1 Building an AABB tree37
4.2.2 Intersection testing37
4.2.3 Updating an AABB tree after a deformation38
Chapter 5 Experiments and Discussions40
5.1 Experiments40
5.1.1 Comparison of different approaches 41
5.1.2 Comparison of different-resolution models42
5.1.3 Comparison of different computer platforms 47
5.2 Discussions48
Chapter 6 Conclusions49
References51

[1] Basdogan, C., C.-H. Ho, M. A. Srinivasan, S. D. Small, and S. L. Dawson, "Force interactions in laparoscopic simulations: haptic rendering of soft tissues," in Proc. of the medicine meets virtual reality conference, San Diego, CA, Jan.19-22, 1998, pp.385-391.
[2] Bechmann, D., "Space deformation models survery," Computer & Graphics, Vol.18, No.4, pp.571-586, 1994.
[3] Bro-Nielsen, M., "Finite element modeling in surgery simulation," Proc. IEEE, Vol.86, No.3, pp.490-503, 1998.
[4] Chen, Y., Q.-H. Zhu, and K. Arie, "Physically based animation of volumetric objects," in Proc. IEEE Computer Animation, Philadelphia, Jun.8-10, 1998, pp.154-160.
[5] Coquillart, S., "Extended free-form deformation: a sculpturing tool for 3D geometric modeling," in Proc. Siggraph'90, Vol.24, No.4, Dallas, TX, Aug.6-10, 1990, pp.187-196.
[6] Cotin, S., H. Delingette, and N. Ayache, Efficient Linear Elastic Models of Soft Tissues for Real-time Surgery Simulation, Technique Report TR-98-3510, Institut National de Recherche en Informatique et en Automatique (INRIA), 1998.
[7] Cover, S. A., N. F. Ezquerra, J. F. O'Brien, R. Rowe, J. Gadacz, and E. Palm, "Interactively deformable models for surgery simulation," IEEE Computer Graphics & Applications, Vol.13, No.6, pp.68-75, 1993.
[8] Delingette, H., "Toward realistic soft-tissue modeling in medical simulation," Proc. IEEE, Vol.86, No.3, pp.512-523, 1998.
[9] Gibson, S. F. F. and B. Mirtich, A Survery of Deformable Modeling in Computer Graphics, Technique Report TR-97-19, Mitsubishi Electric Research Laboratory, 1997.
[10] Guan, Z., J. Ling, N. Tao, X. Ping, and T. Rongxi, "Study and application of physics-based deformable curves and surfaces," Computer & Graphics, Vol.21, No.4, pp.305-313, 1997.
[11] Gudukbay, U., B. Ozguc, and Y. Tokad, "A spring force formulation for elastically deformable models," Computer & Graphics, Vol.21, No.3, pp.335-346, 1997.
[12] Hsu, W. M., J. F. Hughes, and H. Kaufman, "Direct manipulation of free-form deformations," in Proc. Siggraph'92, Vol.26, No.2, Chicago, IL, Jul.26-31, 1992, pp.177-184.
[13] Kuhn, C., U. Kuhnapfel, H.-G. Krumm, and B. Neisius, "A 'virtual reality' based training system for minimally invasive surgery," in Proc. Computer Assisted Radiology (CAR'96), Paris, Jun., 1996, pp.764-769.
[14] Kuhnapfel, U. G. and B. Neisius, "CAD-based graphical computer simulation in endoscopic surgery," Endoscopic Surgery and Allied Technologies, Vol.1, No.2, pp.181-184, 1993.
[15] Louchet, J., X. Provot, and D. Crochemore, "Evolutionary identification of cloth animation models," in Proc. Eurographics Working Group on Computer Animation and Simulation (EGCAS'95), pp.44-54, 1995.
[16] Meseure, P. and C. Chaillou, "Deformable body simulation with adaptive subdivision and cuttings," in Proc. WSCG'97, Plzen, Feb.10-14, 1997, pp.361-370.
[17] Ng, H. N. and R. L. Grimsdate., "Computer graphics techniques for modeling cloth," IEEE Computer Graphics & Applications, Vol.16, No.5, pp.28-41, 1996.
[18] Provot, X., "Deformation constraints in a mass-spring model to describe rigid cloth behavior," in Proc. Graphics Interface, Quebec City, Canada, May17-19, 1995, pp.147-154.
[19] Qin, H. and D. Terzopoulos, "Dynamic NURBS swung surfaces for physics-based shape design," Computer-Aided Design, Vol.27, No.2, pp.111-127, 1995.
[20] Sederberg, T. W. and S. R. Parry, "Free-form deformation of solid geometric models," in Proc. Siggraph'86, Vol.20, No.4, Dallas, TX, Aug.18-22, 1986, pp.151-160.
[21] Terzopoulos, D. and H. Qin, "Dynamic NURBS with geometric constraints for interactive sculpting," ACM Trans. on Graphics, Vol.13, No.2, pp.103-136, 1994.
[22] Terzopoulos, D., J. Platt, A. Barr, and K. Fleischer, "Elastically deformable models," in Proc. Siggraph'87, Vol.21, No.4, Anaheim, CA, Jul.27-31, 1987, pp.205-214.