WADS 1999: Algorithms and Data Structures pp 13-24

# Line Simplification with Restricted Orientations

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1663)

## 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.

## Keywords

Line Segment Recursion Formula Line Simplification Reachable Region Orthogonal Orientation
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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