Transforming triangulations

@article{Lawson1972TransformingT,
  title={Transforming triangulations},
  author={Charles L. Lawson},
  journal={Discret. Math.},
  year={1972},
  volume={3},
  pages={365-372}
}
  • C. Lawson
  • Published 1972
  • Mathematics
  • Discret. Math.
Transforming triangulations in polygonal domains
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.
Geometric graphs which are 1-skeletons of unstacked triangulated polygons
Transforming Triangulations on Nonplanar Surfaces
TLDR
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
  • G. Farin
  • Mathematics
    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
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
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References

A Census of Planar Triangulations
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