Meshless Voronoi Basis Functions

MESHLESS is a FORTRAN90 program which generates a set of local basis functions, without the use of a mesh, by Lili Ju.

If N basis functions are desired in an arbitrary region, then N basis points are chosen at random in the region. Each point in the region is assigned to the nearest basis point. The basis points are then adjusted by taking the average of the associated points. If this process is repeated, the basis points will arrange themselves into generators of a centroidal Voronoi tessellation of the region.


The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.


MESHLESS is available in a FORTRAN90 version.

Related Data and Programs:

CVT, a FORTRAN90 library which computes points that form a Centroidal Voronoi Tessellation, which can be used by MESHLESS to assign node locations.

HALTON, a FORTRAN90 library which computes quasirandom Halton points, which can be used by MESHLESS to assign node locations.

PS_WRITE, a FORTRAN90 library which implements some PostScript graphics commands.


Lili Ju


  1. Qiang Du, Vance Faber, Max Gunzburger,
    Centroidal Voronoi Tessellations: Applications and Algorithms,
    SIAM Review, Volume 41, 1999, pages 637-676.
  2. Qiang Du, Max Gunzburger, Lili Ju,
    Meshfree, Probabilistic Determination of Point Sets and Support Regions for Meshfree Computing,
    Computer Methods in Applied Mechanics in Engineering,
    Volume 191, 2002, pages 1349-1366;
  3. Lili Ju, Qiang Du, Max Gunzburger,
    Probabilistic Methods for Centroidal Voronoi Tessellations and their Parallel Implementations,
    Parallel Computing, Volume 28, 2002, pages 1477-1500.

Source Code:

Examples and Tests:

List of Routines:

You can go up one level to the FORTRAN90 source codes.

Last revised on 12 November 2006.