TRIANGULATION_TRIANGLE_NEIGHBORS
Triangle Neighbors
in a Triangulation

TRIANGULATION_TRIANGLE_NEIGHBORS is a MATLAB program which computes the three neighboring triangles of each triangle in a triangulation.

The user supplies a node file and a triangle file, containing the coordinates of the nodes, and the indices of the nodes that make up each triangle. Either 3-node or 6-node triangles may be used.

The program reads the data, computes the triangle neighbor information, and writes out the information to a file. In cases where one side of a triangle has no triangle neighbor, a value of -1 is assigned.

The triangle neighbor array is useful if the triangulation has to be searched to find the triangle containing a given point. It is also useful when analyzing the bandwidth of the adjacency matrix, or of a finite element matrix derived from the triangulation.

Usage:

triangulation_triangle_neighbors ( 'prefix' )

• 'prefix'_nodes.txt, the node coordinates (input);
• 'prefix'_elements.txt, the triangulation (input);
• 'prefix'_element_neighbors.txt, the triangle neighbors (output);

Licensing:

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

Languages:

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

Related Data and Programs:

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

NEIGHBORS_TO_METIS_GRAPH, a MATLAB program which reads a triangle mesh neighbor file created by TRIANGULATION_TRIANGLE_NEIGHBORS and writes a modified version of the same data suitable for input to the mesh partitioning program METIS.

RCM, a MATLAB library which uses the reverse Cuthill-McKee method for mesh renumbering.

TABLE_DELAUNAY, a FORTRAN90 program which triangulates nodes whose coordinates are stored in a file.

TET_MESH_RCM, a MATLAB library which applies the reverse Cuthill-McKee reordering to a tetrahedral mesh of nodes in 3D.

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

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

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

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

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

TRIANGULATION_DISPLAY, a MATLAB program which displays the nodes and elements of a triangulation on the MATLAB graphics screen;

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

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

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

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

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 MATLAB 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 MATLAB program which reads data defining a triangulation and creates a PostScript image of the nodes and triangles.

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

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

TRIANGULATION_RCM, a MATLAB program which can reorder the nodes of a triangulation so that the bandwidth of the associated adjacency matrix is reduced.

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

TRIG_TO_NEIB, a C program which reads "NODE" and "ELE" files (a format prescribed by triangle) describing a triangulation, and produces a file defining the neighbor triangles of each element; the program can also produce information about the Voronoi diagram. The program is by Lili Ju.

Reference:

1. Marc deBerg, Marc Krevald, Mark Overmars, Otfried Schwarzkopf,
   Computational Geometry,
   Springer, 2000,
   ISBN: 3-540-65620-0.
2. Joseph ORourke,
   Computational Geometry,
   Second Edition,
   Cambridge, 1998,
   ISBN: 0521649765,
   LC: QA448.D38.

Source Code:

• triangulation_triangle_neighbors.m, is the source code.

Examples and Tests:

BIG_CAVITY is a triangulation using 8,195 nodes and 4,000 elements.

• big_cavity_nodes.txt, the node coordinates.
• big_cavity_elements.txt, the triangulation;
• big_cavity_triangulation.png, a PNG image of the triangulation;
• big_cavity_element_neighbors.txt, the neighbor triangles.

BOX3 is a triangulation of order 3, using 20 nodes and 24 elements:

• box3_nodes.txt, the node coordinates.
• box3_elements.txt, the triangulation;
• box3_triangulation.png, a PNG image of the triangulation;
• box3_element_neighbors.txt, the neighbor triangles.

BOX6 is a triangulation of order 6:

• box6_nodes.txt, the node coordinates.
• box6_elements.txt, the triangulation;
• box6_triangulation.png, a PNG image the triangulation;
• box6_element_neighbors.txt, the neighbor triangles.

GREENLAND is a triangulation using 33,343 nodes and 64,125 elements.

• greenland_nodes.txt, the node coordinates.
• greenland_elements.txt, the triangulation;
• greenland_element_neighbors.txt, the neighbor triangles.

LAKE_COARSE is an irregular lake with an island.
There are 621 nodes and 974 elements and 1 hole.

• lake_coarse_nodes.txt, the node coordinates.
• lake_coarse_elements.txt, the triangulation;
• lake_coarse_triangulation.png, a PNG image of the triangulation.
• lake_coarse_element_neighbors.txt, the neighbor triangles.

LAKE3 is an irregular lake with an island.
The smallest angle is 23.46 degrees.
There are 1552 nodes and 2820 elements and 1 hole.

• lake3_nodes.txt, the node coordinates.
• lake3_elements.txt, the triangulation;
• lake3_triangulation.png, a PNG image of the triangulation.
• lake3_element_neighbors.txt, the neighbor triangles.

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