Abstract
We extend the kinetic data structure for collision detection between moving simple polygons introduced in [14] to incorporate a hierarchical representation of convex chains. This permits us to define and maintain an adaptive hierarchical outer approximation for convex polygons. This representation can be exploited to give separation sensitive complexity bounds for kinetic collision detection comparable to those of Erickson et al. [11] who deal with pairs of convex polygons. More importantly, it forms the bases of a more general representation, developed in a companion paper, that applied to collections of general (not necessarily convex) polygonal objects.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
P. K. Agarwal, J. Basch, M. de Berg, L. J. Guibas, and J. Hershberger. Lower bounds for kinetic planar subdivisions. In Proc. 15th ACM Sympos. Comp. Geom., pages 247–254, 1999.
P. K. Agarwal, J. Basch, L. J. Guibas, J. Hershberger, and L. Zhang. Deformable free space tilings for kinetic collision detection. In Proc. 5th Workshop Algorithmic Found. Robotics, 2000.
J. Basch, J. Erickson, L. J. Guibas, J. Hershberger, and L. Zhang. Kinetic collision detection for two simple polygons. In Proc. 10th ACM-SIAM Sympos. Discrete Algorithms, pages 102–111, 1999.
J. Basch, L. Guibas, and J. Hershberger. Data structures for mobile data. In Proc. 8th ACM-SIAM Sympos. Discrete Algorithms, pages 747–756, 1997.
B. Chazelle and D. P. Dobkin. Intersection of convex objects in two and three dimensions. J. ACM, 34(1):1–27, Jan. 1987.
T. H. Cormen, C. E. Leiserson, and R. L. Rivest. Introduction to Algorithms. MIT Press, Cambridge, MA, 1990.
D. Dobkin, J. Hershberger, D. Kirkpatrick, and S. Suri. Implicitly searching convolutions and computing depth of collision. In Proc. 1st Annu. SIGAL Internat. Sympos. Algorithms, volume 450 of Lecture Notes Comput. Sci., pages 165–180. Springer-Verlag, 1990.
D. P. Dobkin and D. G. Kirkpatrick. Fast detection of polyhedral intersection. Theoret. Comput. Sci., 27(3):241–253, Dec. 1983.
D. P. Dobkin and D. G. Kirkpatrick. A linear algorithm for determining the separation of convex polyhedra. J. Algorithms, 6:381–392, 1985.
D. P. Dobkin and D. G. Kirkpatrick. Determining the separation of preprocessed polyhedra–A unified approach. In M. S. Paterson, editor, Automata, Languages and Programming, 17th International Colloquium, volume 443 of Lecture Notes in Computer Science, pages 400–413, Warwick University, England, 16–20 July 1990. Springer-Verlag.
J. Erickson, L. Guibas, J. Stolfi, and L. Zhang. Separation-sensitive collision detection for convex objects. In Proc. 10th ACM-SIAM Sympos, Discrete Algorithms, pages 327–336, 1999.
L. Guibas, J. Snoeyink, and L. Zhang. Compact voronoi diagrams for moving convex polygons. In To appear Proc. 7th Scandinavian Workshop on Algorithm Theory, 2000.
L. J. Guibas. Kinetic data structures: A state of the art report. In Proc. 3rd Workshop Algorithmic Found. Robotics, pages 191–209, 1998.
D. Kirkpatrick, J. Snoeyink, and B. Speckmann. Kinetic collision detection for simple polygons. In Proc. 16th ACM Sympos. on Comp. Geom., pages 322–330, 2000.
D. Kirkpatrick and B. Speckmann. Separation sensitive kinetic collision detection for simple polygons. In preparation.
M. McAllister, D. Kirkpatrick, and J. Snoeyink. A compact piecewise-linear voronoi diagram for convex sites in the plane. Discrete Comp. Geom., 15:73–105, 1996.
D. M. Mount. Intersection detection and separators for simple polygons. In Proc. 8th Annu. ACM Sympos. Comput. Geom., pages 303–311, 1992.
S. Suri. Minimum link paths in polygons and related problems. PhD thesis, Dept. Comp. Sci., Johns Hopkins Univ., 1987.
G. T. Toussaint. Shortest path solves translation separability of polygons. Technical Report SOCS-85.27, School Comput. Sci., McGill Univ., 1985.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2001 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Kirkpatrick, D., Speckmann, B. (2001). Separation Sensitive Kinetic Separation Structures for Convex Polygons. In: Akiyama, J., Kano, M., Urabe, M. (eds) Discrete and Computational Geometry. JCDCG 2000. Lecture Notes in Computer Science, vol 2098. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-47738-1_21
Download citation
DOI: https://doi.org/10.1007/3-540-47738-1_21
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-42306-5
Online ISBN: 978-3-540-47738-9
eBook Packages: Springer Book Archive