Remove Triangles from a Triangulation

TRIANGULATION_MASK is a C++ program which reads the nodes and triangles that define a triangulation, calls a user routine which determines whether each triangle is to be preserved or discarded ("masked") from the triangulation, and writes out new node and triangle files that define the masked triangulation.

The input file prefix_nodes.txt contains the node information for the triangulation. Each data line contains the X and Y coordinates of a single node.

The input file prefix_elements.txt contains the triangle information for the triangulation. Each line contains the indices of 3 or 6 nodes that form a triangle.

One motivation for creating this program is as follows. Suppose we have a set of points that lie on the boundary or inside of a non-convex region. If we naively call an unconstrained Delaunay triangulation routine, such as TABLE_DELAUNAY, then because the region is not convex, it is possible to create triangles which lie outside the region.

An easy way to correct this problem is to call a user routine and pass it the indices and coordinates of each triangle. The user can then decide to drop any triangle whose centroid, say, lies outside the region.

Other masking criteria might drop triangles that are too small, or that have too small an angle, or that lie inside some interior hole. These choices are entirely up to the user.


The user masking routine has the form:

bool triangle_mask ( int dim_num, int triangle_order, int nodes[], double coord[] )
with arguments:

The user masking routine must be compiled and linked with the software, perhaps with a command like:

g++ triangulation_mask.o triangle_mask.C
We will assume that the executable is renamed to triangulation_mask.

triangulation_mask 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 GNU LGPL license.


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

Related Data and Programs:

TABLE, a data format which is used for the input and output files.

TABLE_DELAUNAY, a C++ program which can compute the Delaunay triangulation of a set of points.

TRIANGLE, a C program which computes a triangulation of a geometric region.

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

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

TRIANGULATION_CORNER, a C++ program which patches triangulations so that no triangle has two sides on the boundary.

TRIANGULATION_DELAUNAY_DISCREPANCY, a C++ program which measures the amount by which a triangulation fails the local Delaunay test;

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

TRIANGULATION_HISTOGRAM, a C++ program which computes histograms of data over a triangulation.

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

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.

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

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

TRIANGULATION_ORIENT, a C++ program 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 C++ program which reads data defining a triangulation and creates a PostScript image of the nodes and triangles.

TRIANGULATION_Q2L, a C++ program 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 C++ program which estimates the integral of a function over a triangulated region.

TRIANGULATION_QUALITY, a C++ program which reads data defining a triangulation and computes a number of quality measures.

TRIANGULATION_RCM, a C++ program which reads data defining a triangulation, determines an ordering of the nodes that will reduce the bandwidth of the adjacency matrix, and writes the new triangulation information to a file.

TRIANGULATION_REFINE, a C++ program which reads data defining a triangulation, replaces each triangle by four congruent smaller ones, and writes the new triangulation information to a file.

TRIANGULATION_TRIANGLE_NEIGHBORS, a C++ program which reads data defining a triangulation, determines the neighboring triangles of each triangle, and writes that information to a file.


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Source Code:

Examples and Tests:

P15 is a triangulation created by calling DISTMESH, then removing duplicate points by calling TABLE_MERGE, then creating a Delaunay triangulation by calling TABLE_DELAUNAY, Unfortunately, this results in many triangles that lie outside the region of interest.

SMALL is a triangulation of the 25 lattice points on the [0,4]x[0,4] square. Our masking operation should cut out a lower left triangular corner and a section from the upper right.

List of Routines:

You can go up one level to the C++ source codes.

Last revised on 30 September 2010.