Line Simplification with Restricted Orientations
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.
KeywordsLine Segment Recursion Formula Line Simplification Reachable Region Orthogonal Orientation
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