Algorithms for optimal area triangulations of a convex polygon

Authors:
J. Mark Keil;Tzvetalin S. Vassilev
Affiliations:
Department of Computer Science, University of Saskatchewan, Saskatoon, Saskatchewan, Canada;Department of Mathematics & Computer Science, North Carolina Central University, Durham, NC
Venue:
Computational Geometry: Theory and Applications
Year:
2006

Citing 3
Cited 2

Computational geometry: algorithms and applications

Computational geometry: algorithms and applications
Optimal area triangulation

Optimal area triangulation
Geometry and Topology for Mesh Generation (Cambridge Monographs on Applied and Computational Mathematics)

Geometry and Topology for Mesh Generation (Cambridge Monographs on Applied and Computational Mathematics)

A linear time algorithm for max-min length triangulation of a convex polygon

Information Processing Letters
Optimal higher order Delaunay triangulations of polygons

Computational Geometry: Theory and Applications

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Abstract

Given a convex polygon with n vertices in the plane, we are interested in triangulations of its interior, i.e., maximal sets of nonintersecting diagonals that subdivide the interior of the polygon into triangles. The MaxMin area triangulation is the triangulation of the polygon that maximizes the area of the smallest triangle in the triangulation. Similarly, the MinMax area triangulation is the triangulation that minimizes the area of the largest area triangle in the triangulation. We present algorithms that construct MaxMin and MinMax area triangulations of a convex polygon in O(n2 logn) time and O(n2) space. The algorithms use dynamic programming and a number of geometric properties that are established within the paper.