triangulation_triangle_neighbors

triangulation_triangle_neighbors, a C code 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 contains the node coordinates,
• prefix_elements.txt contains the element definitions.
• prefix_element_neighbors.txt will contain the triangle neighbors.

Licensing:

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

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

TRIANGULATION, a C code which performs various operations on order 3 (linear) or order 6 (quadratic) triangulations.

TRIANGULATION_NODE_TO_ELEMENT, a C code 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_SVG, a C code which creates a Scalable Vector Graphics (SVG) image of a triangulation, which can be displayed by a web browser.

triangulation_triangle_neighbors_test

TRIG_TO_NEIB, a C code 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.c, the source code.
• triangulation_triangle_neighbors.sh, compiles the source code.