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Using Linked Volumes to Model Object Collisions, Deformation, Cutting, Carving, and Joining
October-December 1999 (vol. 5 no. 4)
pp. 333-348

Abstract—In volume graphics, objects are represented by arrays or clusters of sampled 3D data. A volumetric object representation is necessary in computer modeling whenever interior structure affects an object's behavior or appearance. However, existing volumetric representations are not sufficient for modeling the behaviors expected in applications such as surgical simulation, where interactions between both rigid and deformable objects and the cutting, tearing, and repairing of soft tissues must be modeled in real time. Three-dimensional voxel arrays lack the sense of connectivity needed for complex object deformation, while finite element models and mass-spring systems require substantially reduced geometric resolution for interactivity and they can not be easily cut or carved interactively. This paper discusses a linked volume representation that enables physically realistic modeling of object interactions such as: collision detection, collision response, 3D object deformation, and interactive object modification by carving, cutting, tearing, and joining. The paper presents a set of algorithms that allow interactive manipulation of linked volumes that have more than an order of magnitude more elements and considerably more flexibility than existing methods. Implementation details, results from timing tests, and measurements of material behavior are presented.

[1] D. Baraff, “Analytical Methods for Dynamic Simulation of Non-Penetrating Rigid Bodies,” Computer Graphics Proc., Ann. Conf. Series, pp. 19-28, 1989.
[2] B. Mirtich and J. Canny, "Impulse-Based Simulation of Rigid Bodies," Proc. ACM Symp. Interactive 3D Graphics, pp. 181-188, 1995.
[3] M.C. Lin, "Efficient Collision Detection for Animation and Robotics," PhD thesis, Dept. of Electrical Eng. and Computer Science, Univ. of California, Berkeley, Dec. 1993.
[4] T. Galyean and J. Hughes, "Sculpting: An Interactive Volumetric Modeling Technique," Computer Graphics, Vol. 25, No. 4, July 1991.
[5] W. Wang and A.F. Kaufman, “Volume Sculpting,” Proc. Symp. Interactive 3D Graphics Proceedings, pp. 151-156, Apr. 1995.
[6] R. Avila and L. Sobierajski, "A Haptic Interaction Method for Volume Visualization," Proc. Visualization 96, IEEE Computer Society Press, Los Alamitos, Calif., Oct. 1996, pp. 197-204.
[7] S. Gibson, “Beyond Volume Rendering: Visualization, Haptic Exploration, and Physical Modeling of Voxel-Based Objects,” Visualization in Scientific Computing, R. Scateni, J. van Wijk, and P. Zanarini, eds., pp. 10-24, Springer-Verlag, 1995.
[8] T. He and A. Kaufman, “Collision Detection for Volumetric Models,” Proc. IEEE Visualization '97, pp. 27-34, Oct. 1997.
[9] Y. Kurzion and R. Yagel, “Space Deformation Using Ray Deflectors,” Proc. Sixth Eurographics Workshop Rendering, pp. 21-32, Dublin, Ireland, 1995.
[10] M. Desbrun and M.-P. Gascuel, “Animating Soft Substances with Implicit Surfaces,” Proc. SIGGRAPH '95, pp. 287-290, 1995.
[11] S. Gibson and B. Mirtich, “A Survey of Deformable Modeling in Computer Graphics,” Technical Report TR97-19, MERL-A Mitsubishi Electric Research Lab, 1997.
[12] S. Cotin, H. Delingette, N. Ayache, J.M. Clement, V. Tassetti, and J. Marescaux, “Geometrical and Physical Representations for a Simulator of Hepatic Surgery,” Medicine Meets Virtual Reality IV, 1996.
[13] S. Cotin, “Modeles Anatomiques Deformables en Temps-Reel,” PhD thesis, INRIA Sophia Antipolis/Univ. de Nice, 1997.
[14] S. Cotin, H. Delingette, and N. Ayache, Real-Time Elastic Deformations of Soft Tissues for Surgery Simulation IEEE Trans. Visualization and Computer Graphics, vol. 5, no. 1, pp. 62-73, 1999.
[15] M. Bro-Nielsen, “Fast Finite Elements for Surgery Simulation,” Medicine Meets Virtual Reality V, 1997.
[16] D. Terzopoulos and K. Fleischer, "Modeling Inelastic Deformation: Viscoelasticity, Plasticity, Fracture," Computer Graphics (SIGGRAPH '88 Proc.), J. Dill, ed., vol. 22, pp. 269-278, Aug. 1988.
[17] M. Bro-Nielsen, “Modelling Elasticity in Solids Using Active Cubes—Application to Simulated Operations,” Computer Vision, Virtual Reality in Medicine, pp. 535-541, 1995.
[18] R. Osborne, H. Pfister, H. Lauer, N. McKenzie, S. Gibson, W. Hiatt, and T. Ohkami, “EM-Cube: An Architecture for Low-Cost Real-Time Volume Rendering,” Proc. 1997 SIGGRAPH/EUROGRAPHICS Workshop Graphics Hardware, pp. 131-138, 1997.
[19] A. Kaufman, D. Cohen, and R. Yagel, "Volume Graphics," Computer, Vol. 26, No. 7, July 1993, pp. 51-64.
[20] A. Kaufman, “Efficient Algorithms for 3-D Scan Conversion of Parametric Curves, Surfaces, and Volumes,” Computer Graphics, vol. 21, pp. 171-179, 1987.
[21] A.F. Kaufman, Volume Visualization. IEEE CS Press, 1990.
[22] L.M. Sobierajski and A.E. Kaufman, “Volumetric Ray Tracing,” Proc. 1994 Symp. Volume Visualization, IEEE Computer Society Press, Los Alamitos, Calif., 1994, pp. 11-18.
[23] L. Sobierajski and A. Kaufman, “Volumetric Radiosity,” Technical Report 94.01.05, Dept. of Computer Science, State Univ. of New York, Stony Brook, 1994.
[24] A. Mor, S. Gibson, and J. Samosky, “Interacting with 3-Dimensional Medical Data: Haptic Feedback for Surgical Simulation,” Proc. Phantom Usergroup Workshop, 1996.
[25] S. Gibson, "3D ChainMail: A Fast Algorithm for Deforming 3D Objects," Proc. Symp. on Interactive 3D Graphics, ACM Press, New York, April 1997, pp. 149-154.
[26] S. Gibson, C. Fyock, E. Grimson, T. Kanade, R. Kikinis, H. Lauer, N. McKenzie, A. Mor, S. Nakajima, T. Ohkami, R. Osborne, J. Samosky, and A. Sawada, “Volumetric Object Modeling for Surgical Simulation,” Medical Image Analysis, vol. 2, no. 2, 1998.
[27] J. Cohen, M. Lin, D. Manocha, and M. Ponamgi, "I-Collide: An Interactive and Exact Collision Detection System for Large-Scale Environments," Proc. ACM Interactive 3D Graphics Conf., pp. 189-196, 1995.
[28] ? Shinya and ? Forgue, “Interference Detection through Rasterization,” J. Visualization and Computer Animation, vol. 4, no. 2, pp. 132-134, 1991.
[29] T. Uchiki, T. Ohashi, and M. Tokoro, “Collision Detection in Motion Simulation,” Computers and Graphics, vol. 7, pp. 285-293, 1983.
[30] N. Greene, "Voxel Space Automata: Modeling with Stochastic Growth Processes in Voxel Space," Computer Graphics, vol. 23, no. 3, July 1989, pp. 175-184.
[31] J. Lengyel, M. Reichert, B. Donald, and D. Greenberg, “Real-Time Robot Motion Planning Using Rasterization Computer Graphics Hardware,” Computer Graphics Proc., Ann. Conf. Series, pp. 327-335, 1990.
[32] D. Terzopoulos, J. Platt, A. Barr, and K. Fleischer, “Elastically Deformable Models,” Proc. ACM SIGGRAPH, pp. 205-214, 1987.
[33] D. Baraff and A. Witkin, "Dynamic Simulation of Nonpenetrating Flexible Bodies," Proc. ACM SIGGRAPH: Computer Graphics, vol. 26, no. 2, pp. 303-308, July 1992.
[34] S. Gibson, “Using Distance Maps for Accurate Surface Representation in Sampled Volumes,” Proc. 1998 Symp. Volume Visualization, pp. 23-30, Oct. 1998.
[35] D. Terzopoulos and K. Waters, “Physically-Based Facial Modeling, Analysis, and Animation,” J. Visualization and Computer Animation, vol. 1, pp. 73-80, 1990.
[36] K. Waters, “A Muscle Model for Animating Three-Dimensional Facial Expression,” Computer Graphics, vol. 21, no. 4, pp. 17-24, 1987.
[37] Y. Lee, D. Terzopoulos, and K. Waters, “Realistic Modeling for Facial Animation,” Proc. Ann. Conf. Series, SIGGRAPH 1995, pp. 55-62, 1995.
[38] R.M. Koch, M.H. Gross, F.R. Carls, D.F. von Büren, G. Fankhauser, and Y. Parish, "Simulating Facial Surgery Using Finite Element Methods," SIGGRAPH 96 Conf. Proc., Holly Rushmeier, ed., pp. 421-428, Aug. 1996.
[39] X. Tu and D. Terzopoulos, "Artificial Fishes: Physics, Locomotion, Perception, Behavior," Proc. Siggraph 94, ACM, New York, July 1994, pp. 43-50.
[40] J. Christensen, J. Marks, and T. Ngo, “Automatic Motion Synthesis for 3D Mass-Spring Models,” The Visual Computer, vol. 13, pp. 20-28, 1987.
[41] M. Carignan et al., "Dressing Animated Synthetic Actors with Complex Deformable Clothes," Proc. Siggraph 92, ACM, New York, July 1992, Vol. 26, pp. 99-104.
[42] D. Baraff and A. Witkin, "Large Steps in Cloth Simulation," Proc. Siggraph 98, Annual Conference Series, ACM, New York, July 1998, pp. 43-54.
[43] J. Collier, B. Collier, G. O'Toole, and S. Sargand, “Drape Prediction by Means of Finite Element Analysis,” J. Textile Inst., vol. 82, pp. 96-107, 1991.
[44] D. Chen, “Pump It Up: Computer Animation of a Biomechanically Based Model of Muscle Using the Finite Element Method,” PhD thesis, Media Arts and Sciences, Massachusetts Inst. of Tech nology, 1991.
[45] I. Essa, S. Scarloff, and A. Pentland, “A Unified Approach for Physical and Geometric Modeling for Graphics and Animation,” Proc. Eurographics '92, vol. 11, pp. 129-138, 1992.
[46] I. Hunter, T. Doukoglou, S. Lafontaine, and P. Charette, “A Teleoperated Microsurgical Robot and Associated Virtual Environment for Eye Surgery,” Presence, vol. 2, pp. 265-280, 1993.
[47] E. Keeve, S. Girod, P. Pfeifle, and B. Girod, “Anatomy-Based Facial Tissue Modeling Using the Finite Element Method,” Proc. IEEE Visualization '96, pp. 21-28, 1996.
[48] A. Pentland and J. Williams, “Good Vibrations: Modal Dynamics for Graphics and Animation,” Proc. ACM SIGGRAPH, pp. 215-222, 1989.
[49] M. Bro-Nielsen and S. Cotin, “Real-Time Volumetric Deformable Models for Surgery Simulation Using Finite Elements and Condensation,” Proc. Eurographics '96, vol. 15, pp. 57-66, 1996.
[50] Y. Fung, Biomechanics: Mechanical Properties of Living Tissues. New York: Springer-Verlag, 1993.
[51] M. Schill and S. Gibson, “Biomechanical Simulation of the Vitreous Humor in the Eye Using an Enhanced Chainmail Algorithm,” Proc. Medical Image Computation and Computer Integrated Surgery (MICAI '98), Oct. 1998.
[52] P.-G. Maillot, “Three-Dimensional Homogeneous Clipping of Triangle Strips,” Graphics Gems, J. Arvo, ed. New York: AP Professional, 1991.
[53] M. Bro-Nielsen, D. Helfrick, B. Glass, X. Zeng, and H. Connacher, “VR Simulation of Abdominal Trauma Surgery,” Medicine Meets Virtual Reality VI, 1998.
[54] G. Kriezis, N. Patrikalakis, and F. Wolter, “Topological and Differential Equation Methods for Surface Intersections,” Computer-Aided Design, vol. 24, pp. 41-55, 1990.
[55] S. Krishnan and D. Manocha, "An Efficient Surface Intersection Algorithm based on Lower Dimensional Formulation," ACM Trans. Computer Graphics, vol. 16, no. 1, pp. 74-106, 1997.
[56] W.E. Lorensen and H.E. Cline, “Marching Cubes: A High Resolution 3D Surface Construction Algorithm,” Computer Graphics (SIGGRAPH '87 Proc.), vol. 21, pp. 163-169, 1987.
[57] T. van Hook, “Real-Time Shaded Milling Display,” Computer Graphics Proc., Ann. Conf. Series, pp. 15-20, 1986.
[58] Y. Huang and J. Oliver, “NC Milling Error Assessment and Tool Path Correction,” Computer Graphics Proc., Ann. Conf. Series, pp. 287-294, 1994.
[59] B. Naylor, “Sculpt: An Interactive Solid Modeling Tool,” Proc. Graphics Interface '90, pp. 138-148, 1990.
[60] D. Terzopoulos, J. Platt, and K. Fleischer, “Heating and Melting Deformable Models (from Goop to Glop),” Proc. Graphics Interface '89, pp. 219-226, 1989.
[61] S.W. Wang and A.E. Kaufman, “Volume Sampled Voxelization of Geometric Primitives,” Visualization 93 Proc., IEEE Computer Society Press, Los Alamitos, Calif., 1993, pp. 78-84.
[62] P. Lacroute and M. Levoy, "Fast Volume Rendering Using a Shear-Warp Factorization of the Viewing Transformation," Proc. Siggraph 94, ACM Press, New York, pp. 451-458.
[63] S. Cotin, H. Delingette, and N. Ayache, “Efficient Linear Elastic Models of Soft Tissues for Surgery Simulation,” Technical Report 3510 INRIA, 1998.

Index Terms:
Volume graphics, volume modeling, physics-based graphics.
Citation:
Sarah F. Frisken-Gibson, "Using Linked Volumes to Model Object Collisions, Deformation, Cutting, Carving, and Joining," IEEE Transactions on Visualization and Computer Graphics, vol. 5, no. 4, pp. 333-348, Oct.-Dec. 1999, doi:10.1109/2945.817350
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