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Inducing n-gon of an arrangement of lines
Transcript of Inducing n-gon of an arrangement of lines
L. Scharf & M. Scherfenberg
EuroCG'09 - Brussels, Belgium Presented by:
Department of Computer Science,
Dec 2009 Introduction History Initialization Every simple polygon induces an arrangement of lines, simply by extending its edges. Every arrangement of lines in the plane has an inducing polygon?? Lines that all intersect in one point and lines that form a 3×2 parallel grid serve as examples of such arrangements. When the lines of an arrangement are in general position, an inducing polygon with n edges exists and can be found in O(n^2) time. Bose et al. present an algorithm for constructing an inducing simple n-path in O(n^2) time.
That polyline can be extended to an inducing n-gon if there exists a line such that all intersection points of the arrangement lie on one side of that line.
If the polygon is allowed to have more than one edge collinear to some line, proved that an inducing polygon of size O(n) always exists and can be constructed in O(n^2) time. notations cases