Algorithms for optimal area triangulations of a convex polygon

Authors:
J. Mark Keil;Tzvetalin S. Vassilev
Affiliations:
Department of Computer Science, University of Saskatchewan, 110 Science Place, Saskatoon, Saskatchewan, S7N 5C9 Canada;Department of Mathematics & Computer Science, North Carolina Central University, 1801 Fayetteville Street, Durham, NC 27707, USA
Venue:
Computational Geometry: Theory and Applications
Year:
2006

Citing 3
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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 non-intersecting 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(n^2logn) time and O(n^2) space. The algorithms use dynamic programming and a number of geometric properties that are established within the paper.