# Approximating the MaxMin and MinMax Area Triangulations using Angular Constraints

• Volume: 4, Issue: 3, page 321-334
• ISSN: 1312-6555

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## Abstract

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* A preliminary version of this paper was presented at XI Encuentros de Geometr´ia Computacional, Santander, Spain, June 2005.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

## How to cite

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Mark Keil, J, and Vassilev, Tzvetalin. "Approximating the MaxMin and MinMax Area Triangulations using Angular Constraints." Serdica Journal of Computing 4.3 (2010): 321-334. <http://eudml.org/doc/11392>.

@article{MarkKeil2010,
abstract = {* A preliminary version of this paper was presented at XI Encuentros de Geometr´ia Computacional, Santander, Spain, June 2005.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},
author = {Mark Keil, J, Vassilev, Tzvetalin},
journal = {Serdica Journal of Computing},
keywords = {Computational Geometry; Triangulation; Planar Point Set; Angle Restricted Triangulation; Approximation; Delauney Triangulation; computational geometry; triangulation; planar point set; angle restricted triangulation; approximation; Delauney triangulation; MinMax area triangulation; MaxMin area triangulation; algorithms},
language = {eng},
number = {3},
pages = {321-334},
publisher = {Institute of Mathematics and Informatics Bulgarian Academy of Sciences},
title = {Approximating the MaxMin and MinMax Area Triangulations using Angular Constraints},
url = {http://eudml.org/doc/11392},
volume = {4},
year = {2010},
}

TY - JOUR
AU - Mark Keil, J
AU - Vassilev, Tzvetalin
TI - Approximating the MaxMin and MinMax Area Triangulations using Angular Constraints
JO - Serdica Journal of Computing
PY - 2010
PB - Institute of Mathematics and Informatics Bulgarian Academy of Sciences
VL - 4
IS - 3
SP - 321
EP - 334
AB - * A preliminary version of this paper was presented at XI Encuentros de Geometr´ia Computacional, Santander, Spain, June 2005.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
LA - eng
KW - Computational Geometry; Triangulation; Planar Point Set; Angle Restricted Triangulation; Approximation; Delauney Triangulation; computational geometry; triangulation; planar point set; angle restricted triangulation; approximation; Delauney triangulation; MinMax area triangulation; MaxMin area triangulation; algorithms
UR - http://eudml.org/doc/11392
ER -

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