Abstract
Much attention has been given to triangulating sets of points and polygons (see [1] for a survey) but the problem of triangulating line segments has not been previously explored. It is well known that a polygon can always be triangulated and a simple proof of this can be found in [2]. Furthermore, efficient algorithms exist for carrying out this task [3,4]. Thus at first glance one may wonder why not just construct a simple polygon through the set of line segments and subsequently apply the algorithms of [3] or [4]. Unfortunately a set of line segments does not necessarily admit a simple circuit [5]. The reader can easily construct such an example with three parallel line segments. In the following section we provide optimal O(nlogn) algorithm for triangulating a set of n line segments. Optimality follows from the fact that Ω(nlogn) time is a lower bound for triangulating a set of points [6, p. 187] which is a set of line segments of zero length. Section 3 is devoted to presenting algorithms for inserting and deleting edges from triangulations.
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References
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© 1987 Plenum Press, New York
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ElGindy, H.A., Toussaint, G.T. (1987). On Computing and Updating Triangulations. In: Ghosh, S.P., Kambayashi, Y., Tanaka, K. (eds) Foundations of Data Organization. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-1881-1_21
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DOI: https://doi.org/10.1007/978-1-4613-1881-1_21
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