Integral Estimate Over a Triangulated Region

TRIANGULATION_QUAD is a C++ 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 C++ library which defines quadrature rules for a variety of multidimensional reqions.

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

TRIANGULATION_NODE_TO_ELEMENT, a C++ program 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.

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 C++ source codes.

Last revised on 15 October 2009.