Computational Geometry Triangulation Planar Point Set Angle Restricted Triangulation Approximation 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.