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Title: Approximating the MaxMin and MinMax Area Triangulations using Angular Constraints
Authors: Mark Keil, J
Vassilev, Tzvetalin
Keywords: Computational Geometry
Planar Point Set
Angle Restricted Triangulation
Delauney Triangulation
Issue Date: 2010
Publisher: Institute of Mathematics and Informatics Bulgarian Academy of Sciences
Citation: Serdica Journal of Computing, Vol. 4, No 3, (2010), 321p-334p
Abstract: We consider sets of points in the two-dimensional Euclidean plane. For a planar point set in general position, i.e. no three points collinear, a triangulation is a maximal set of non-intersecting straight line segments with vertices in the given points. These segments, called edges, subdivide the convex hull of the set into triangular regions called faces or simply triangles. We study two triangulations that optimize the area of the individual triangles: MaxMin and MinMax area triangulation. MaxMin area triangulation is the triangulation that maximizes the area of the smallest area triangle in the triangulation over all possible triangulations of the given point set. Similarly, MinMax area triangulation is the one that minimizes the area of the largest area triangle over all possible triangulations of the point set. For a point set in convex position there are O(n^2 log n) time and O(n^2) space algorithms that compute these two optimal area triangulations. No polynomial time algorithm is known for the general case. In this paper we present an approach
Description: * A preliminary version of this paper was presented at XI Encuentros de GeometrĀ“ia Computacional, Santander, Spain, June 2005.
ISSN: 1312-6555
Appears in Collections:Volume 4 Number 3

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