TRIANGULATION_TRIANGLE_NEIGHBORS
Triangle Neighbors
in a Triangulation {#triangulation_triangle_neighbors-triangle-neighbors-in-a-triangulation align="center"}
TRIANGULATION_TRIANGLE_NEIGHBORS is a C++ 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.
triangulation_triangle_neighbors prefix
where prefix is the common filename prefix:
- prefix_nodes.txt contains the node coordinates,
- prefix_elements.txt contains the element definitions.
- prefix_element_neighbors.txt will contain the triangle neighbors.
The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.
TRIANGULATION_TRIANGLE_NEIGHBORS is available in a C version and a C++ version and a FORTRAN90 version and a MATLAB version.
MESH_BANDWIDTH, is a C++ program which returns the geometric bandwidth associated with a mesh of elements of any order and in a space of arbitrary dimension.
MESH_TO_XML, a C++ program which reads information defining a 1D, 2D or 3D mesh, namely a file of node coordinates and a file of elements defined by node indices, and creates a corresponding XML file for input to DOLFIN or FENICS.
NEIGHBORS_TO_METIS_GRAPH, a C++ 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 C++ library which carries out reverse Cuthill-McKee computations.
TABLE_DELAUNAY, a C++ program which triangulates a set of nodes whose coordinates are stored in a file.
TET_MESH_RCM, a FORTRAN90 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 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_MASK, a C++ program which takes an existing triangulation and deletes triangles and their corresponding nodes as requested by the user.
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 can reorder the nodes of a triangulation so that the bandwidth of the associated adjacency matrix is reduced.
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.
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.
- Marc deBerg, Marc Krevald, Mark Overmars, Otfried Schwarzkopf,
Computational Geometry,
Springer, 2000,
ISBN: 3-540-65620-0. - Joseph ORourke,
Computational Geometry,
Second Edition,
Cambridge, 1998,
ISBN: 0521649765,
LC: QA448.D38.
- triangulation_triangle_neighbors.cpp, the source code.
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.
- MAIN is the main program for TRIANGULATION_TRIANGLE_NEIGHBORS.
- CH_CAP capitalizes a single character.
- CH_EQI is true if two characters are equal, disregarding case.
- CH_TO_DIGIT returns the integer value of a base 10 digit.
- FILE_COLUMN_COUNT counts the columns in the first line of a file.
- FILE_EXIST reports whether a file exists.
- FILE_ROW_COUNT counts the number of row records in a file.
- I4_MAX returns the maximum of two I4's.
- I4_MIN returns the minimum of two I4's.
- I4MAT_DATA_READ reads data from an I4MAT file.
- I4MAT_HEADER_READ reads the header from an I4MAT file.
- I4MAT_TRANSPOSE_PRINT_SOME prints some of an I4MAT, transposed.
- I4MAT_WRITE writes an I4MAT file with no header.
- I4ROW_COMPARE compares two rows of a integer array.
- I4ROW_SORT_A ascending sorts the rows of an I4ROW.
- I4ROW_SWAP swaps two rows of an I4ROW.
- R8MAT_DATA_READ reads the data from an R8MAT file.
- R8MAT_HEADER_READ reads the header from an R8MAT file.
- R8MAT_TRANSPOSE_PRINT_SOME prints some of an R8MAT, transposed.
- S_LEN_TRIM returns the length of a string to the last nonblank.
- S_TO_I4 reads an I4 from a string.
- S_TO_I4VEC reads an I4VEC from a string.
- S_TO_R8 reads an R8 from a string.
- S_TO_R8VEC reads an R8VEC from a string.
- S_WORD_COUNT counts the number of "words" in a string.
- SORT_HEAP_EXTERNAL externally sorts a list of items into ascending order.
- TIMESTAMP prints the current YMDHMS date as a time stamp.
- TRIANGULATION_ORDER3_NEIGHBOR_TRIANGLES determines triangle neighbors.
- TRIANGULATION_ORDER6_NEIGHBOR_TRIANGLES determines triangle neighbors.
You can go up one level to the C++ source codes.
Last revised on 22 August 2009.