TRIANGULATION_BOUNDARY_NODES
Boundary Nodes of a Triangulation

TRIANGULATION_BOUNDARY_NODES is a C++ program which analyzes the triangulation of a region, and lists those nodes which lie on the boundary of the triangulation.

Either a 3-node or 6-node triangulation may be used.

Although this boundary information is useful, it would be more useful to divide the boundary nodes up, if the boundary consists of more than one connected segment. Moreover, it would also be useful to report the sequence of nodes necessary to trace out a connected segment of the boundary. I imagine I will come back to work on those projects later!

Usage:

triangulation_boundary_nodes prefix

• prefix_nodes.txt contains the node coordinates,
• prefix_elements.txt contains the element definitions.
• prefix_boundary_nodes.txt will contain a 0 for each internal node, and a 1 for each boundary node.

Licensing:

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

Languages:

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

Related Programs:

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.

TABLE_DELAUNAY, a C++ program which triangulates a set of nodes whose coordinates are stored in a file.

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_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 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.

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_boundary_nodes.cpp, the source code.

Examples and Tests:

ELBOW is a curved region, looking like an elbow, that lies inside the unit square. It is triangulated using order 3 triangles. There are 320 nodes and 568 triangles. There are 66 nodes on the boundary.

• elbow_nodes.txt, the node file.
• elbow_nodes.png, a PNG image of the nodes.
• elbow_elements.txt, the triangles.
• elbow_output.txt, the printed output from a run of the sample program.
• elbow_boundary_nodes.txt, the boundary node file.
• elbow_boundary_nodes.png, a PNG image of the boundary nodes.

LAKE is an irregular lake-shaped region with an "island". It is triangulated using order 3 triangles.

• lake_nodes.txt, the node file.
• lake_nodes.png, a PNG image of the nodes.
• lake_elements.txt, the triangles.
• lake_output.txt, the printed output from a run of the sample program.
• lake_boundary_nodes.txt, the boundary node file.
• lake_boundary_nodes.png, a PNG image of the boundary nodes.

List of Routines:

• MAIN is the main program for TRIANGULATION_BOUNDARY_NODES.
• 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.
• I4COL_COMPARE compares columns I and J of a integer array.
• I4COL_SORT_A ascending sorts the columns of an integer array.
• I4COL_SWAP swaps two columns of an integer array.
• 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.
• 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.
• R8MAT_WRITE writes an R8MAT file with no header.
• 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_BOUNDARY_NODE indicates nodes on the boundary.
• TRIANGULATION_ORDER6_BOUNDARY_NODE indicates nodes on the boundary.

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