research-article

Efficient Collision Detection Using Bounding Volume Hierarchies of k-DOPs

Authors:

James T. Klosowski,

Joseph S. B. Mitchell,

Henry Sowizral,

Karel ZikanAuthors Info & Claims

IEEE Transactions on Visualization and Computer Graphics, Volume 4, Issue 1

Pages 21 - 36

https://doi.org/10.1109/2945.675649

Published: 01 January 1998 Publication History

Abstract

Collision detection is of paramount importance for many applications in computer graphics and visualization. Typically, the input to a collision detection algorithm is a large number of geometric objects comprising an environment, together with a set of objects moving within the environment. In addition to determining accurately the contacts that occur between pairs of objects, one needs also to do so at real-time rates. Applications such as haptic force-feedback can require over 1,000 collision queries per second.In this paper, we develop and analyze a method, based on bounding-volume hierarchies, for efficient collision detection for objects moving within highly complex environments. Our choice of bounding volume is to use a "discrete orientation polytope" ("k-dop"), a convex polytope whose facets are determined by halfspaces whose outward normals come from a small fixed set of k orientations. We compare a variety of methods for constructing hierarchies ("BV-trees") of bounding k-dops. Further, we propose algorithms for maintaining an effective BV-tree of k-dops for moving objects, as they rotate, and for performing fast collision detection using BV-trees of the moving objects and of the environment.Our algorithms have been implemented and tested. We provide experimental evidence showing that our approach yields substantially faster collision detection than previous methods.

References

[1]

J. Arvo and D. Kirk, "A Survey of Ray Tracing Acceleration Techniques," An Introduction to Ray Tracing, A.S. Glassner, ed., pp. 201-262. Academic Press, 1990.

Digital Library

[2]

D.H. Ballard, "Strip Trees: A Hierarchical Representation for Curves," Comm. ACM, vol. 24, no. 5, pp. 310-321, May 1981.

Digital Library

[3]

D. Baraff, "Curved Surfaces and Coherence for Non-Penetrating Rigid Body Simulation," Computer Graphics (SIGGRAPH '90 Proc.), vol. 24, pp. 19-28, Dallas, Tex., Aug. 1990.

Digital Library

[4]

D. Baraff, "Fast Contact Force Computation for Nonpenetrating Rigid Bodies," Computer Graphics (SIGGRAPH '94 Proc.), vol. 28, pp. 23-34, Orlando, Fla., July 1994.

Digital Library

[5]

D. Baraff, "Interactive Simulation of Solid Rigid Bodies," Computer Graphics Applications, vol. 15, no. 3, pp. 63-75, May 1995.

Digital Library

[6]

G. Barequet B. Chazelle L.J. Guibas J.S.B. Mitchell and A. Tal, "BOXTREE: A Hierarchical Representation for Surfaces in 3D," EuroGraphics '96, J. Rossignac and F. Sillion, eds., vol. 15, no. 3, pp. C-387-C-484. Blackwell Publishers, Eurographics Assoc., 1996.

[7]

N. Beckmann H.-P. Kriegel R. Schneider and B. Seeger, "The R*-Tree: An Efficient and Robust Access Method for Points and Rectangles," Proc. ACM SIGMOD Int'l Conf. Management of Data, pp. 322-331, 1990.

Digital Library

[8]

W. Bouma and G. Vanecek, Jr., "Collision Detection and Analysis in a Physical Based Simulation," Eurographics Workshop on Animation and Simulation, pp. 191-203, Vienna, Sept. 19, 1991.

[9]

S. Cameron, "Collision Detection by Four-Dimensional Intersection Testing," IEEE Trans. Robotics and Automation, vol. 6, no. 3, pp. 291-302, 1990.

[10]

J. Canny, "Collision Detection for Moving Polyhedra," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 8, no. 2, pp. 200-209, Mar. 1986.

Digital Library

[11]

J.D. Cohen M.C. Lin D. Manocha and M.K. Ponamgi, "I-COLLIDE: An Interactive and Exact Collision Detection System for Large-Scale Environments," Proc. ACM Interactive 3D Graphics Conf., pp. 189-196, 1995.

Digital Library

[12]

International Business Machines Corporation, User's Guide, IBM 3D Interaction Accelerator<sup>TM</sup>, version 1, release 2.0. IBM T.J. Watson Research Center, Yorktown Heights, N.Y., Sept. 1995.

[13]

A. Crosnier and J. Rossignac, "T-BOX: The Intersection of Three Mini-Max Boxes," internal report, IBM T.J. Watson Research Center, Yorktown Heights, N.Y., 1995.

[14]

D. Dobkin J. Hershberger D. Kirkpatrick and S. Suri, "Computing the Intersection-Depth of Polyhedra," Algorithmica, vol. 9, pp. 518-533, 1993.

[15]

D. Dobkin and D. Kirkpatrick, "Fast Detection of Polyhedral Intersection," Theoretical Computer Science, vol. 27, pp. 241-253, 1983.

[16]

D. Dobkin and D. Kirkpatrick, "A Linear Algorithm for Determining the Separation of Convex Polyhedra," J. Algorithms, vol. 6, pp. 381-392, 1985.

[17]

D. Dobkin and D. Kirkpatrick, "Determining the Separation of Preprocessed Polyhedra—A Unified Approach," Proc. 17th Int'l Colloquium Automata, Languages, and Programming, Lecture Notes in Computer Science, vol. 443, pp. 400-413. Springer-Verlag, 1990.

Digital Library

[18]

K. Dobrindt K. Mehlhorn and M. Yvinec, "A Complete and Efficient Algorithm for the Intersection of a General and a Convex Polyhedron," Proc. Third Workshop Algorithms Data Structures, Lecture Notes in Computer Science, vol. 709, pp. 314-324. Springer Verlag, 1993.

Digital Library

[19]

A. Garcia-Alonso N. Serrano and J. Flaquer, "Solving the Collision Detection Problem," IEEE Computer Graphics and Applications, vol. 14, pp. 36-43, May 1994.

Digital Library

[20]

J. Goldsmith and J. Salmon, "Automatic Creation of Object Hierarchies for Ray Tracing," IEEE Computer Graphics and Applications, vol. 7, pp. 14-20, 1987.

Digital Library

[21]

S. Gottschalk M.C. Lin and D. Manocha, "OBBTree: A Hierarchical Structure for Rapid Interference Detection," Computer Graphics (SIGGRAPH '96 Proc.), vol. 30, pp. 171-180, New Orleans, Aug. 1996.

Digital Library

[22]

N. Greene, "Detecting Intersection of a Rectangular Solid and a Convex Polyhedron," Graphics Gems IV, P.S. Heckbert, ed., pp. 74-82. Academic Press, 1994.

Digital Library

[23]

M. Held, "A Library of Efficient and Reliable Intersection Routines," technical report, Dept. of Applied Mathematics and Statistics, State Univ. of New York at Stony Brook, 1997. http://www.ams.sunysb.edu/~held/

[24]

M. Held J.T. Klosowski and J.S.B. Mitchell, "Evaluation of Collision Detection Methods for Virtual Reality Fly-Throughs," Proc. Seventh Canadian Conf. Computer Geometry, pp. 205-210, 1995.

[25]

M. Held J.T. Klosowski and J.S.B. Mitchell, "Speed Comparison of Generalized Bounding Box Hierarchies," technical report, Dept. of Applied Math, State Univ. of New York at Stony Brook, 1995.

[26]

M. Held J.T. Klosowski and J.S.B. Mitchell, "Real-Time Collision Detection for Motion Simulation Within Complex Environments," SIGGRAPH '96 Visual Proc., p. 151, New Orleans, Aug. 1996

Digital Library

[27]

P.M. Hubbard, "Collision Detection for Interactive Graphics Applications," IEEE Trans. Visualization and Computer Graphics, vol. 1, no. 3, pp. 218-230, Sept. 1995.

Digital Library

[28]

P.M. Hubbard, "Approximating Polyhedra With Spheres for Time-Critical Collision Detection," ACM Trans. Graphics, vol. 15, no. 3, pp. 179-210, July 1996.

Digital Library

[29]

T.L. Kay and J.T. Kajiya, "Ray Tracing Complex Scenes," Computer Graphics (SIGGRAPH '86 Proc.), vol. 20, pp. 269-278, Aug. 1986.

Digital Library

[30]

M. Lin, "Efficient Collision Detection for Animation and Robotics," PhD thesis, Dept. of Electrical Eng. and Computer Science, Univ. of California, Berkeley, 1993.

Digital Library

[31]

M. Lin and J. Canny, "Efficient Algorithms for Incremental Distance Computation," Proc. IEEE Int'l Conf. Robotics and Automation, vol. 2, pp. 1,008-1,014, 1991.

[32]

M. Lin and D. Manocha, "Fast Interference Detection Between Geometric Models," Visual Computing, vol. 11, no. 10, pp. 542-561, 1995.

[33]

M. Moore and J. Wilhelms, "Collision Detection and Response for Computer Animation," Computer Graphics (SIGGRAPH '88 Proc.), vol. 22, pp. 289-298, Aug. 1988.

Digital Library

[34]

B. Naylor J.A. Amatodes and W. Thibault, "Merging BSP Trees Yields Polyhedral Set Operations," Computer Graphics (SIGGRAPH '90 Proc.), vol. 24, pp. 115-124, Dallas, Tex., Aug. 1990.

Digital Library

[35]

H. Noborio S. Fukuda and S. Arimoto, "Fast Interference Check Method Using Octree Representation," Advanced Robotics, vol. 3, no. 3, pp. 193-212, 1989.

[36]

J. O'Rourke, Computational Geometry in C. New York: Cambridge Univ. Press, 1994.

Digital Library

[37]

I. Palmer and R. Grimsdale, "Collision Detection for Animation Using Sphere-Trees," Computer Graphics Forum, vol. 14, no. 2, pp. 105-116, June 1995.

[38]

M. Ponamgi D. Manocha and M. Lin, "Incremental Algorithms for Collision Detection Between General Solid Models," Proc. ACM SIGGRAPH Symp. Solid Modeling, pp. 293-304, 1995.

Digital Library

[39]

F.P. Preparata and M.I. Shamos, Computational Geometry—An Introduction. New York: Springer-Verlag, 1985.

Digital Library

[40]

E. Schömer, "Interaktive Montagesimulation mit Kollisionserkennung," PhD thesis, Universität des Saarlandes, Germany, 1994.

[41]

E. Schömer and C. Thiel, "Subquadratic Algorithms for the General Collision Detection Problem," Abstracts 12th European Workshop Computational Geometry (CG '96), pp. 95-101, 1996.

[42]

G. Vanecek, Jr., "Brep-Index: A Multidimensional Space Partitioning Tree," Int'l J. Computational Geometry and Applications, vol. 1, no. 3, pp. 243-261, 1991.

[43]

S. Suri P.M. Hubbard and J.F. Hughes, "Collision Detection in Aspect and Scale Bounded Polyhedra," Proc. Ninth ACM-SIAM Symp. Discrete Algorithms, to appear, Jan. 1998.

Digital Library

[44]

H. Weghorst G. Hooper and D.P. Greenberg, "Improved Computational Methods for Ray Tracing," ACM Trans. Graphics, vol. 3, no. 1, pp. 52-69, Jan. 1984.

Digital Library

[45]

G. Zachmann, "Exact and Fast Collision Detection," Diploma thesis, Fraunhofer Inst. for Computer Graphics, Technische Hochschule Darmstadt, Fachbereich Informatik, Germany, 1994.

[46]

G. Zachmann and W. Felger, "The BoxTree: Enabling Real-Time and Exact Collision Detection of Arbitrary Polyhedra," Proc. SIVE '95, pp. 104-113, 1995.

[47]

K. Zikan and P. Konecny, "Lower Bound of Distance in 3D," Proc. Winter School of Computer Graphics (WSCG '97), vol. 3, pp. 640-649, 1997. Available as Technical Report FIMU-RS-97-01, Faculty of Informatics, Masaryk Univ., Czech Republic, Jan. 1997. (http://www.fi.muni.cz/informatics/reports/)

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cover image IEEE Transactions on Visualization and Computer Graphics

IEEE Transactions on Visualization and Computer Graphics Volume 4, Issue 1

January 1998

93 pages

ISSN:1077-2626

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Copyright © Copyright © 1997 IEEE. All Rights Reserved.

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IEEE Educational Activities Department

United States

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Published: 01 January 1998

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