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.
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© 1993 Springer-Verlag Berlin Heidelberg
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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
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DOI: https://doi.org/10.1007/3-540-57155-8_234
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