A Storage-efficient Method for Construction of a Thiessen Triangulation

  title={A Storage-efficient Method for Construction of a Thiessen Triangulation},
  author={A. K. Cline and Robert J. Renka},
  journal={Rocky Mountain Journal of Mathematics},
This paper describes a storage-efficient method and associated algorithms for constructing and representing a triangulation of arbitrarily distributed points in the plane. 
Delaunay Triangulations and Voronoi Diagrams on Non-Planar Topologies
  • Z. Bao
  • Computer Science, Physics
  • 2001
Delaunay Triangulations and Voronoi Diagrams on Non-Planar Topologies are presented, which provide new insights into the construction of non-planar topologies.
Algorithm 624: Triangulation and Interpolation at Arbitrarily Distributed Points in the Plane
This algorithm is a 1966 American National Standard FORTRAN implementation of the methods discussed in [1] and [2]. The software consists of a set of triangulation modules (which have application in
A triangle-based $C^1$ interpolation method
This paper discusses methods and software for C/sup 1/ interpolation at arbitrarily distributed data points in the plane. The primary results presented here are derivative-estimation procedures which
A dynamic hierarchical subdivision algorithm for computing Delaunay triangulations and other closest-point problems
It is shown that the “oriented walk” search, when the total number of points is less than 417 or when the points are presorted by distance or coordinates, is successful.
A Review on Delaunay Refinement Techniques
Important works on the insertion of vertices in Delaunay triangulations and its dual graph, the Voronoi diagram, are described as a start point for one who needs to build a quality mesh using adaptive triangular-mesh refinement.
Parametrization and smooth approximation of surface triangulations
  • M. Floater
  • Mathematics, Computer Science
    Comput. Aided Geom. Des.
  • 1997
Bibliographic notes on Voronoi diagrams
This paper presents a comprehensive annotated bibliography on various theoretical and algorithmic aspects of Voronoi diagrams and related diagrams and solutions to the Euclidean traveling salesman problem.


A Two-Dimensional Mesh Verification Algorithm
For a particular format of lists, a set of conditions is given which is proven to be sufficient to guarantee such a “tiling” of some planar region without overlap or gaps.
Computing Dirichlet Tessellations in the Plane
A recursive algorithm for computing the Dirichlet tessellation in a highly efficient way is described, and the problems which arise in its implementation are discussed.
Closest-point problems
  • M. ShamosDan Hoey
  • Computer Science
    16th Annual Symposium on Foundations of Computer Science (sfcs 1975)
  • 1975
The purpose of this paper is to introduce a single geometric structure, called the Voronoi diagram, which can be constructed rapidly and contains all of the relevant proximity information in only linear space, and is used to obtain O(N log N) algorithms for most of the problems considered.
A Method of Bivariate Interpolation and Smooth Surface Fitting for Irregularly Distributed Data Points
A method of blvariate interpolation and smooth surface fitting is developed for z values given at points irregularly distributed in the x-y plane for Bivariate Interpolation and Smooth Surface Fitting for Irregularly Distributed Data Points.
A Critical Comparison of Some Methods for Interpolation of Scattered Data
A comparison of 29 methods for solution of the scattered data interpolation problem has been made and a large number of pages of perspective plots of surfaces are given.
A Storage-Efficient Method for Construction of a Thiessen Triangulation, ORNL/CSD-101
  • Oak Ridge National Laboratory,
  • 1982
Software for C1
  • Surface Interpolation,
  • 1977
Triangulation and bivariate interpolation for irregularly distributed data points
Transforming triangulations
Locally Equiangular Triangulations