TRIANGULATION_BOUNDARY_NODES
Boundary Nodes of a Triangulation

TRIANGULATION_BOUNDARY_NODES is a MATLAB 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!

Licensing:

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

Related Programs:

TABLE_DELAUNAY is a FORTRAN90 program which triangulates a set of nodes whose coordinates are stored in a file.

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

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

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

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

TRIANGULATION_L2Q is 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 is a MATLAB program which takes an existing triangulation and deletes triangles and their corresponding nodes as requested by the user.

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

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

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

TRIANGULATION_Q2L is 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_QUALITY is a MATLAB program which reads data defining a triangulation and computes a number of quality measures.

TRIANGULATION_RCM is a MATLAB 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 is 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.

TRIANGULATION_TRIANGLE_NEIGHBORS is a MATLAB program which 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.

Tar File:

A GZIP'ed TAR file of the contents of this directory is available. This is only done as a convenience for users who want ALL the files, and don't want to download them individually. This is not a convenience for me, so don't be surprised if the tar file is somewhat out of date.

• triangulation_boundary_nodes_m_src.tar.csh the commands used to create the GZIP'ed TAR file.
• triangulation_boundary_nodes_m_src.tar.gz the GZIP'ed TAR file.

Source Code:

• triangulation_boundary_nodes.m is the main program for TRIANGULATION_BOUNDARY_NODES.
• ch_cap.m capitalizes a single character.
• ch_eqi.m is a case insensitive comparison of two characters for equality.
• ch_to_digit.m returns the integer value of a base 10 digit.
• dtable_close_write.m closes a double precision table file after it has been written.
• dtable_data_read.m reads data from a double precision table file.
• dtable_data_write.m writes data to a double precision table file.
• dtable_header_read.m reads the header from a double precision table file.
• dtable_header_write.m writes the header to a double precision table file.
• dtable_write.m writes the header and data to a double precision table file.
• file_column_count.m counts the number of columns in the first line of a file.
• file_name_ext_get.m determines the "extension" of a file name.
• file_name_ext_swap.m replaces the current "extension" of a file name.
• file_row_count.m counts the number of row records in a file.
• i4col_compare.m compares columns I and J of an I4COL.
• i4col_sort_a.m ascending sorts an I4COL.
• i4col_swap.m swaps columns I and J of an I4COL.
• i4mat_transpose_print_some.m prints some of the transpose of an I4MAT.
• itable_data_read.m reads data from an integer table file.
• itable_data_write.m writes data to an integer table file.
• itable_header_read.m reads the header from an integer table file.
• itable_header_write.m writes the header for an integer table file.
• itable_write.m writes the header and data to an integer table file.
• r8_epsilon.m returns the R8 roundoff unit.
• r8mat_transpose_print_some.m prints some of an R8MAT, transposed.
• s_index_last_c.m finds the LAST occurrence of a given substring.
• s_len_trim.m returns the length of a string to the last nonblank.
• s_word_count.m counts the number of "words" in a string.
• sort_heap_external.m externally sorts a list of items into ascending order.
• timestamp.m prints the current YMDHMS date as a time stamp.
• timestring.m writes the current YMDHMS date into a string.
• triangulation_order3_boundary_node.m indicates which nodes are on the boundary.
• triangulation_order6_boundary_node.m indicates which nodes are on the boundary.

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.output.txt, 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.
• channel.65.nodes.boundary.indices.txt, the boundary node index file.

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.triangles3.txt, the triangles.
• elbow.triangles3.png, a PNG image of the triangulated region, created by TRIANGULATION_PLOT.
• elbow.output.txt, the printed output from a run of the sample program.
• elbow.nodes.boundary.txt, the boundary node file.
• elbow.nodes.boundary.png, a PNG image of the boundary nodes, created by POINTS_DISPLAY.
• elbow.nodes.boundary.indices.txt, the boundary node index file.

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.output.txt, 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.
• lake.621.nodes.boundary.indices.txt, the boundary node index file.

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