stripack_delaunay


stripack_delaunay, a Fortran90 code which interactively determines the Delaunay diagram of a set of points on a sphere.

The set of points is read from a file, and the Delaunay triangulation, once computed, is written out to another file, described as a series of triplets of point indexes.

According to Steven Fortune, it is possible to compute the Delaunay triangulation of points on the surface of a sphere by computing their convex hull, regarded as a 3D pointset. If the sphere is the unit sphere at the origin, the facet normals are the Voronoi vertices.

Usage:

stripack_delaunay node_filename
where

Licensing:

The information on this web page is distributed under the MIT license.

Languages:

stripack_delaunay is available in a Fortran90 version.

Related Data and Programs:

stripack_delaunay_test

geometry, a Fortran90 code which computes various geometric quantities, including grids on spheres.

sphere_cvt, a Fortran90 code which creates a mesh of well-separated points on a unit sphere using Centroidal Voronoi Tessellations.

sphere_delaunay, a Fortran90 code which computes the Delaunay triangulation of points on a sphere.

sphere_design_rule, a Fortran90 code which returns point sets on the surface of the unit sphere, known as "designs", which can be useful for estimating integrals on the surface, among other uses.

sphere_grid, a dataset directory containing files which describe sets of points on the unit sphere.

sphere_quad, a Fortran90 code which approximates an integral over the surface of the unit sphere by applying a triangulation to the surface;

sphere_stereograph, a Fortran90 code which computes the stereographic mapping between points on the unit sphere and points on the plane Z = 1; a generalized mapping is also available.

sphere_voronoi, a Fortran90 code which computes and plots the Voronoi diagram of points on the unit sphere.

stripack, a Fortran90 code which can compute the Delaunay triangulation or Voronoi diagram of a set of points on the unit sphere.

stripack_voronoi, a Fortran90 code which reads a set of points on the unit sphere, computes the Voronoi diagram, and writes it to a file.

Reference:

  1. Thomas Ericson, Victor Zinoviev,
    Codes on Euclidean Spheres,
    Elsevier, 2001,
    ISBN: 0444503293,
    LC: QA166.7E75
  2. Gerald Folland,
    How to Integrate a Polynomial Over a Sphere,
    American Mathematical Monthly,
    Volume 108, Number 5, May 2001, pages 446-448.
  3. Jacob Goodman, Joseph ORourke, editors,
    Handbook of Discrete and Computational Geometry,
    Second Edition,
    CRC/Chapman and Hall, 2004,
    ISBN: 1-58488-301-4,
    LC: QA167.H36.
  4. AD McLaren,
    Optimal Numerical Integration on a Sphere,
    Mathematics of Computation,
    Volume 17, Number 84, October 1963, pages 361-383.
  5. Robert Renka,
    Algorithm 772:
    STRIPACK: Delaunay Triangulation and Voronoi Diagram on the Surface of a Sphere,
    ACM Transactions on Mathematical Software,
    Volume 23, Number 3, September 1997, pages 416-434.
  6. Edward Saff, Arno Kuijlaars,
    Distributing Many Points on a Sphere,
    The Mathematical Intelligencer,
    Volume 19, Number 1, 1997, pages 5-11.

Source Code:


Last revised on 31 August 2020.