Abstract
We study the C-oriented line simplification problem: Given a polygonal chain P represented by an ordered set of vertices p 1,...,p n in the plane, a set of orientations C, and a constant ∈, we search for a “C-oriented” polygonal chain Q consisting of the minimum number of line segments that has distance at most ε to P in the Fréechet metric. A polygonal chain is C-oriented if the line segments are parallel to orientations in C. We restrict our attention to the version of the problem where two circles of radius ∈ formed around adjacent vertices of the polygonal chain do not intersect. We solve the C-oriented line simplification problem constructively by using dynamic programming together with a nice data structure. For usual cases of C our algorithm solves the problem in time O(kn 2log(n)) where k is the minimum number of line segments of Q and uses O(kn 2) space.
This work was partially supported by grants from the Swiss Federal Office for Education and Science (Projects ESPRIT IV LTR No. 21957 CGAL and N0. 28155 GALIA), and by the Swiss National Science Foundation (grant “Combinatorics and Geometry”).
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Neyer, G. (1999). Line Simplification with Restricted Orientations. In: Dehne, F., Sack, JR., Gupta, A., Tamassia, R. (eds) Algorithms and Data Structures. WADS 1999. Lecture Notes in Computer Science, vol 1663. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48447-7_2
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DOI: https://doi.org/10.1007/3-540-48447-7_2
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