We consider whether any two triangulations of a polygon on a non-planar surface with a given metric can be transformed into each other by a sequence of edge flips. The answer is negative in general… Expand

This paper describes a storage-efficient method and associated algorithms for constructing and representing a triangulation of arbitrarily distributed points in the plane.

The answer is negative in general with some remarkable exceptions, such as polygons on the cylinder, and on the flat torus, and certain configurations of points on the cylinders.Expand

This paper uses the technology of weighted and regular triangulations to study discrete versions of the Laplacian on piecewise Euclidean manifolds. Regular triangulations are studied in some detail,… Expand

IEEE Transactions on Visualization and Computer Graphics

2012

We compare a variety of triangle shape measures using concepts such as smoothness and convexity. We show that one of these measures, the elongation measure, lends itself to an intuitive geometric… Expand

The authors begin by discussing the Delauny triangulation and algorithms for its construction. Degeneracy and the convexity check are then considered together with the preservation of edge… Expand

Let P be a closed region in the plane bounded by a simple closed curve, and let S be a simplicial dissection of P. We may say that S is a dissection of P into a finite number α of triangles so that… Expand