Integral Estimate Over a Triangulated Region

TRIANGULATION_QUAD is a FORTRAN90 program which reads information defining a triangulation, and estimates the integral of a function whose values are given at the nodes.

Note that this program only expects to recieve values of the function f(x,y) at the nodes of the triangulation, that is, as a simple list of values. No formula for f is expected or used. A much better estimate for the integral might be possible if a formula for f(x,y) were available, in which case a higher order quadrature scheme could be employed.

This program should be able to compute exactly the integrals of 1, x, y, and any linear combination of these. It will only be able to approximate the integrals of other functions, and the accuracy of the approximation will depend in part on the size of the triangles in the triangulation.


triangulation_quad prefix
where 'prefix' is the common prefix for the node, element, and value files.


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


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

Related Data and Programs:

STROUD, a FORTRAN90 library which defines quadrature rules for a variety of multidimensional reqions.

TET_MESH_QUAD, a FORTRAN90 program which estimates the integral of a function over a region defined by a tetrahedral mesh.

TOMS706, a FORTRAN77 library which estimates the integral of a function over a triangulated region.

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

TRIANGULATION_ORDER3, a data directory which contains a description and examples of order 3 triangulations.

TRIANGULATION_ORDER6, a data directory which contains a description and examples of order 6 triangulations.

Source Code:

Examples and Tests:

EXAMPLE is a set of nodes in the unit square, which have been arranged into an order 3 triangulation.

List of Routines:

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

Last revised on 14 October 2009.