triangulation, a FORTRAN90 code which computes a triangulation of a set of points in 2D, and carries out various other related operations on triangulations of order 3 or 6.

The mesh is the collection of triangles. Each triangle is termed an "element". The points used to define the shape of the triangle (the corners, and sometimes a few more points) are called the "nodes".

Routines are available to:

Since triangulations are often used to define a finite element mesh, which in turn defines a sparse matrix, there are routines available which can define the sparse compressed column arrays needed for a sparse matrix associated with a mesh of order 3 or 6. The special case of the Taylor-Hood mixed element is also handled, which is essentially an order 6 grid counted twice and an order 3 grid that only uses the vertices of the order 6 grid.


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


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

Related Data and Programs:

CVT_TRIANGULATION, a FORTRAN90 code which uses routines from the test_triangulation library to create a CVT-based triangularization.

MESH_BANDWIDTH, a FORTRAN90 code which returns the geometric bandwidth associated with a mesh of elements of any order and in a space of arbitrary dimension.

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.

TABLE_DELAUNAY, a FORTRAN90 code which triangulates a set of nodes whose coordinates are stored in a file.

TEST_TRIANGULATION, a FORTRAN90 code which sets up a number of triangulation test problems.


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

TRIANGULATION_Q2L, a FORTRAN90 code which reads data defining a 6-node triangulation, and subdivides each triangle into 4 3-node triangles, writing the resulting triangulation to a file.

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.


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Source Code:

Last revised 10 September 2020.