Transforming triangulations of polygons on non planar surfaces
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…
A Storage-efficient Method for Construction of a Thiessen Triangulation
This paper describes a storage-efficient method and associated algorithms for constructing and representing a triangulation of arbitrarily distributed points in the plane.
All triangulations are reachable via sequences of edge-flips: an elementary proof
- MathematicsComput. Aided Geom. Des.
Geometric graphs which are 1-skeletons of unstacked triangulated polygons
- MathematicsDiscret. Math.
Transforming Triangulations on Nonplanar Surfaces
- MathematicsSIAM J. Discret. Math.
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.
Geometric triangulations and discrete Laplacians on manifolds
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,…
Shape Measures for Triangles
- MathematicsIEEE Transactions on Visualization and Computer Graphics
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…
Automatic mesh generation using a modified Delaunay tessellation
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…
Flip distance between triangulations of a planar point set is APX-hard
- MathematicsComput. Geom.