Abstract
Given is a set S of n points, each colored with one of k≥3 colours. We say that a triangle defined by three points of S is 3-colored if its vertices have distinct colours. We prove in this paper that the problem of constructing the boundary of the union T(S) of all such 3-colored triangles can be done in optimal O(n log n) time.
This work was done while this author was visiting INRIA.
This work has been supported in part by the ESPRIT Basic Research Action Nr. 3075 (ALCOM), by the French Ministry of Research, and by NSF Grant CCR-89-06419.
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References
J.D. Boissonnat and O. Devillers. Motion Planning of Legged Robots. Technical Report, Institut National de Recherche en Informatique et Automatique, (France), 1991. In preparation.
F.P. Preparata and M.I. Shamos. Computational Geometry: an Introduction. Springer-Verlag, 1985.
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© 1992 International Federation for Information Processing
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Boissonnat, JD., Devillers, O., Preparata, F.P. (1992). Computing the union of 3-colored triangles. In: Davisson, L.D., et al. System Modelling and Optimization. Lecture Notes in Control and Information Sciences, vol 180. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0113275
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DOI: https://doi.org/10.1007/BFb0113275
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