Abstract
Efficient data structures are given for the following two query problems: (i) Preprocess a set P of simple polygons with a total of n edges, so that all polygons of P intersected by a query segment can be reported efficiently, and (ii) Preprocess a set S of n segments, so that the connected components of the arrangement of S intersected by a query segment can be reported quickly. In both cases the data structure should return the labels of the intersected polygons or components, not their complete description. Efficient data structures are presented for the static case, the dynamic case, and an efficient on-line construction algorithm for the connected components is given.
Part of this work was done while the second author was visiting the first author at Duke University on a grant of the Dutch Organization for Scientific Research (N.W.O.). The research of the second author was also supported by the ESPRIT Basic Research Action No. 3075 (project ALCOM) and an NSERC International Fellowship. The research of the first author was supported by National Science Foundation Grant CCR-91-06514.
This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Agarwal, P. K., Partitioning Arrangements of Lines: II. Applications, Discr. & Comp. Geom. 5 (1991), pp. 533–573.
Agarwal, P. K., Ray Shooting and other Applications of Spanning Trees with Low-Stabbing Number, SIAM J. Computing 21 (1992), 540–570.
Agarwal, P. K., and M. Sharir, Applications of a New Space Partitioning Technique, Discrete & Computational Geometry 9 (1993), 11–38.
Cormen, T. H., C. E. Leiserson, and R. L. Rivest, Introduction to Algorithms, MIT Press, Cambridge, 1990.
Dillencourt M., H. Samet, and M. Tammiuen, A general approach to connected component labeling for arbitrary image representation, JACM 39 (1992), pp. 253–280.
Dobkin, D. P., and H. Edelsbrunner, Space Searching for Intersecting Objects, J. Algorithms 8 (1987), pp. 348–361.
Imai, H., and T. Asano, Finding the Connected Components and a Maximum Clique of an Intersection Graph of Rectangles in the Plane, J. Algorithms 4 (1984), pp. 310–323.
Janardan, R., and M. Lopez, Generalized Intersection Searching Problems, Int. J. Comp. Geom. & Appl. 3 (1993), 39–70.
Matoušek, J., Efficient Partition Trees, 8 (1992), pp. 315–334.
Mehlhorn, K., Data Structures and Algorithms 3: Multi-dimensional Searching and Computational Geometry, Springer-Verlag, Heidelberg, 1984.
Preparata, F.P., An optimal real time algorithm for planar convex hulls, CACM 22 (1979), pp. 402–405.
Scholten, H. W., and M. H. Overmars, General Methods for Adding Range Restrictions to Decomposable Searching Problems, J. Symb. Comp. 7 (1989), pp. 1–10.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1993 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Agarwal, P.K., van Kreveld, M. (1993). Connected component and simple polygon intersection searching. In: Dehne, F., Sack, JR., Santoro, N., Whitesides, S. (eds) Algorithms and Data Structures. WADS 1993. Lecture Notes in Computer Science, vol 709. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-57155-8_234
Download citation
DOI: https://doi.org/10.1007/3-540-57155-8_234
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-57155-1
Online ISBN: 978-3-540-47918-5
eBook Packages: Springer Book Archive