TRIANGULATION_BOUNDARY_NODES
Boundary Nodes of a Triangulation

TRIANGULATION_BOUNDARY_NODES is a C++ program, using double precision arithmetic, 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!

Related Programs:

TABLE_DELAUNAY is an executable C++ program for the triangulation of a set of nodes whose coordinates are stored in a file.

TRIANGLE is an executable C program which computes a triangulation of a geometric region.

TRIANGULATION is a C++ library of routines for carrying out various operations on order 3 ("linear") or order 6 ("quadratic") triangulations.

TRIANGULATION_BOUNDARY_NODES is also available in a FORTRAN90 version and a MATLAB version.

TRIANGULATION_DISPLAY_OPEN_GL is an executable C++ program which reads files defining a triangulation and displays an image using Open GL.

TRIANGULATION_L2Q is an executable C++ program that reads data defining a 3-node triangulation and generates midside nodes and writes out the corresponding 6-node triangulation.

TRIANGULATION_MASK is an executable C++ program, which takes an existing triangulation and deletes triangles and their corresponding nodes as requested by the user.

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

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

TRIANGULATION_ORIENT is an executable C++ program that reads data defining a triangulation, makes sure that every triangle has positive orientation, and if not, writes a corrected triangle file.

TRIANGULATION_PLOT is an executable C++ program that reads data defining a triangulation and creates a PostScript image of the nodes and triangles.

TRIANGULATION_Q2L is an executable C++ program that reads data defining a 6-node triangulation, and subdivides each triangle into 4 3-node triangles, writing the resulting triangulation to a file.

TRIANGULATION_QUALITY is an executable C++ program that reads data defining a triangulation and computes a number of quality measures.

TRIANGULATION_RCM is an executable C++ program that 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 is an executable C++ program that 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 is an executable C++ program that reads data defining a triangulation, determines the neighboring triangles of each triangle, and writes that information to a file.

Usage:

triangulation_boundary_nodes nodes.txt triangles.txt

reads the triangulation information from nodes.txt and triangles.txt and determines the boundary nodes.

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.C, the source code.
• triangulation_boundary_nodes.csh, commands to compile the source code.

Examples and Tests:

CHANNEL is a rectangular channel, 3 units wide and 1 unit high. It is triangulated using order 6 triangles.

• channel.65.nodes.txt, the node file.
• channel.65.triangles6.txt, the triangles.
• channel.65.triangles6.png, a PNG image of the triangulated region.
• channel.65.out, the printed output from a run of the sample program.
• channel.65.nodes.boundary.txt, the boundary node file computed by the program.
• channel.65.nodes.boundary.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.621.nodes.txt, the node file.
• lake.621.triangles3.txt, the triangles.
• lake.621.triangles3.png, a PNG image of the triangulated region.
• lake.621.out, the printed output from a run of the sample program.
• lake.621.nodes.boundary.txt, the boundary node file computed by the program.
• lake.621.nodes.boundary.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.
• DTABLE_CLOSE_WRITE closes a file to which a DTABLE was to be written.
• DTABLE_DATA_READ reads the data from a DTABLE file.
• DTABLE_DATA_WRITE writes data to a DTABLE file.
• DTABLE_HEADER_READ reads the header from a DTABLE file.
• DTABLE_HEADER_WRITE writes the header of a DTABLE file.
• DTABLE_WRITE writes information to a DTABLE file.
• FILE_COLUMN_COUNT counts the number of columns in the first line of a file.
• FILE_NAME_EXT_GET determines the "extension" of a file name.
• FILE_NAME_EXT_SWAP replaces the current "extension" of a file name.
• 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_TRANSPOSE_PRINT_SOME prints some of an I4MAT, transposed.
• ITABLE_DATA_READ reads data from an ITABLE file.
• ITABLE_HEADER_READ reads the header from an ITABLE file.
• R8_EPSILON returns the R8 roundoff unit.
• R8MAT_TRANSPOSE_PRINT_SOME prints some of an R8MAT, transposed.
• S_INDEX_LAST_C returns a pointer to the last occurrence of a given character.
• 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 integer vector 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.
• TIMESTRING returns the current YMDHMS date as a string.
• 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.