triangulation_q2l, a FORTRAN90 code which reads information describing a triangulation of a set of points using 6-node ("quadratic") triangles, and creates a 3-node ("linear") triangulation.

The same nodes are used, but each 6-node triangle is broken up into four smaller 3-node triangles.

Thus, the program might be given the following 4 triangles:

         |\    |\    |
         | \   | \   |
         6  7  8  9 10
         |   \ |   \ |
         |    \|    \|

It would make a new triangulation involving 16 triangles:

         |\ |\ |\ |\ |
         | \| \| \| \|
         |\ |\ |\ |\ |
         | \| \| \| \|

The input and output files use the simple TABLE format; comment lines begin with a "#" character. Otherwise, each line of the file contains one set of information, either the coordinates of a node (for a node file), or the indices of nodes that make up a triangle, (for a triangle file).

The input file prefix_elements.txt contains the triangle information for the 6-node triangulation. Each line contains the indices of six nodes that form a triangle, in counterclockwise order. The first three indices are the vertices, in counterclockwise order. The fourth index is the midside node between vertices 1 and 2, the fifth the midside between vertices 2 and 3, and the sixth the midside between vertices 3 and 1.

The output file prefix_q2l_elements.txt contains the triangle information for the 3-node triangulation. The vertices for each triangle are listed in counterclockwise order. There are 4 times as many triangles in this triangulation.


triangulation_q2l prefix
where prefix is the common filename prefix:


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


triangulation_q2l is available in a C++ version and a FORTRAN90 version and a MATLAB version.

Related Data and Programs:

MESH_TO_XML, a FORTRAN90 code which reads information defining a 1D, 2D or 3D mesh, namely a file of node coordinates and a file of elements defined by node indices, and creates a corresponding XML file for input to DOLFIN or FENICS.

TRIANGULATION, a FORTRAN90 code which carries out various operations on order 3 ("linear") or order 6 ("quadratic") triangulations.

TRIANGULATION_BOUNDARY_NODES, a FORTRAN90 code which reads data defining a triangulation, determines which nodes lie on the boundary, and writes their coordinates to a file.

TRIANGULATION_HISTOGRAM, a FORTRAN90 code which computes histograms of data over a triangulation.

TRIANGULATION_L2Q, a FORTRAN90 code which reads data defining a 3-node triangulation and generates midside nodes and writes out the corresponding 6-node triangulation.

TRIANGULATION_MASK, a FORTRAN90 code which takes an existing triangulation and deletes triangles and their corresponding nodes as requested by the user.

TRIANGULATION_NODE_TO_ELEMENT, a FORTRAN90 code which reads files describing a set of nodes, their triangulation, and the value of one or more quantities at each node, and outputs a file that averages the quantities for each element. This operation in effect creates an "order1" finite element model of the data.

TRIANGULATION_ORIENT, a FORTRAN90 code which reads data defining a triangulation, makes sure that every triangle has positive orientation, and if not, writes a corrected triangle file.

TRIANGULATION_PLOT, a FORTRAN90 code which reads data defining a triangulation and creates a PostScript image of the nodes and triangles.

TRIANGULATION_QUAD, a FORTRAN90 code which estimates the integral of a function over a triangulated region.


TRIANGULATION_QUALITY, a FORTRAN90 code which reads data defining a triangulation and computes a number of quality measures.


  1. Marc deBerg, Marc Krevald, Mark Overmars, Otfried Schwarzkopf,
    Computational Geometry,
    Springer, 2000.
  2. Joseph ORourke,
    Computational Geometry,
    Cambridge University Press,
    Second Edition, 1998.

Source Code:

Last revised on 10 September 2020.