Mesh Generation Test Regions

TEST_TRIANGULATION, a MATLAB library which sets up a number of triangulation test problems.

As far as possible, a uniform and abstract approach has been used. For each test region, a number of routines are provided, via which it is possible for the user to determine many things about the region. Often, just one or two routines would be needed for a particular purpose. The names of the routines, and their purposes are:

The test problems include:

  1. The unit circle;
  2. The unit circle with a circular hole;
  3. A square with a circular hole;
  4. A hexagon with a hexagonal hole;
  5. The horn;
  6. The superellipse with a superelliptical hole;
  7. The bicycle seat;
  8. The slice of pie with a circular hole and triangular notch;
  9. Jeff Borggaard's square with two hexagonal holes;
  10. The unit square;
  11. The L-shaped region;
  12. John Shadid's H-shaped region;
  13. The Sandia fork;
  14. Marcus Garvie's Lake Alpha, with Beta Island;
  15. Sangbum Kim's forward step;


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


TEST_TRIANGULATION is available in a FORTRAN90 version and a MATLAB version.

Related Data and Programs:

CVT_TRIANGULATION, a FORTRAN90 program which uses this library of test regions and attempts to create a CVT-based triangularization.

DISTMESH, a MATLAB program which can work from a simple description of the boundary of a region to produce a triangulation of that region.

MESH2D, a MATLAB library which can automatically create a triangular mesh for a given polygonal region, by Darren Engwirda.

test_triangulation, a MATLAB library which defines a number of test regions to be triangulated.


TRIANGULATION, a MATLAB library which carries out various operations on order 3 ("linear") or order 6 ("quadratic") triangulations.

TRIANGULATION_DISPLAY_OPENGL, a C++ program which reads files defining a triangulation and displays an image using Open GL.

TRIANGULATION_ORDER3, a data directory which describes the format for triangulations of order 3.

TRIANGULATION_ORDER6, a data directory which describes the format for triangulations of order 6.


  1. Per-Olof Persson and Gilbert Strang,
    A Simple Mesh Generator in MATLAB,
    SIAM Review,
    Volume 46, Number 2, June 2004, pages 329-345.

Source Code:

Last revised on 31 March 2019.