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Issue No.01 - January/February (2006 vol.26)
pp: 64-74
Christoph F?nfzig , Braunschweig University of Technology, Germany
Torsten Ullrich , Graz University of Technology, Austria
Dieter W. Fellner , Graz University of Technology, Austria
ABSTRACT
This article presents a fast collision detection technique for all types of rigid bodies demonstrated with polygon soups. During the preprocessing step, a spherical sampling of the model is performed and then stored in a wavelet-like representation. This representation is space-efficient and allows the on-the-fly generation of spherical shell bounding volumes. In contrast to the commonly used filter banks, this construction uses the max-plus algebra. This guarantees that each low-resolution version of a bounding volume encloses all versions of higher resolution. The technique is scalable in the information it gives in collision determination. If it reports a single triangle per spherical shell then the collision time only depends on the sampling density and the extent of spherical shells, used as bounding volumes, but not on the primitives' count of the model. Due to this fact, it's possible to estimate the time bounds for the collision test tightly. For bounding volume hierarchies known worst-case time bounds are not tight, as the bounding volumes can overlap in space. As an intermediate approach it's possible to report a single triangle per layer of each model. For surface models this information together with surface neighborhood is often sufficient for collision response. If we check all triangle pairs inside a spherical shell for intersection, then the approach is most general and works well in situations with few collisions, which are the most relevant in practice.
INDEX TERMS
spherical distance field, collision detection, filter banks, max-plus algebra
CITATION
Christoph F?nfzig, Torsten Ullrich, Dieter W. Fellner, "Hierarchical Spherical Distance Fields for Collision Detection", IEEE Computer Graphics and Applications, vol.26, no. 1, pp. 64-74, January/February 2006, doi:10.1109/MCG.2006.17
REFERENCES
1. L. Lin and D. Manocha, "Collision and Proximity Queries," Handbook of Discrete and Computational Geometry, 2nd ed., J.E. Goodman and J. O'Rourke, eds., CRC Press, 2004.
2. E. Praun and H. Hoppe, "Spherical Parametrization and Remeshing," ACM Trans. Graphics, vol. 22, no. 3, 2003, pp. 340-349.
3. S. Krishnan et al., "Spherical Shells: A Higher-Order Bounding Volume for Fast Proximity Queries," Proc. IEEE 3rd Int'l Workshop Algorithmic Foundations of Robotics, P.K. Agrawal, L.E. Kavraki, and M. Mason, eds., A K Peters, 1998, pp. 177-190.
4. S. Krishnan et al., "Rapid and Accurate Contact Determination between Spline Models Using ShellTrees," Computer Graphics Forum, vol. 17, no. 3, 1998, pp. 315-326.
5. G. Hamlin, R. Kelley, and J. Tornero, "Efficient Distance Calculation Using the Spherically-Extended Polytope (s-tope) Model," Proc. IEEE Int'l Conf. Robotics and Automation, IEEE CS Press, 1992, pp. 2502-2507.
6. E.J. Stollnitz, T.D. DeRose, and D.H. Salesin, Wavelets for Computer Graphics: Theory and Applications, Morgan Kaufmann, 1996.
7. M. Akian et al., "Linear Systems in (max,+) Algebra," Proc. 29th Conf. Decision and Control, IEEE CS Press, 1990, pp. 151-156.
8. K. Bühler, "Taylor Models and Affine Arithmetics— Towards a More Sophisticated Use of Reliable Arithmetics in Computer Graphics," Proc. 17th Spring Conf. Computer Graphics (SCCG), IEEE CS Press, 2001, pp. 40-48.
9. S. Morigi and G. Casciola, "Inverse Spherical Surfaces," J. Computational and Applied Mathematics, vol. 176, no. 2, 2005, pp. 411-424.
10. G. Zachmann, "Rapid Collision Detection by Dynamically Aligned DOP-Trees," Proc. Virtual Reality Ann. Int'l Symp., IEEE CS Press, 1998, p. 90.
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