TRIANGULATION_REFINE
Refine a Triangulation

TRIANGULATION_REFINE is a MATLAB program which reads information describing a triangulation of a set of points and creates a refined triangulation.

The refined triangulation is created by dividing each triangle into four similar subtriangles. The mesh size parameter h will be halved by such a procedure. If the input triangulation is Delaunay, then so will be the output triangulation.

The program can handle triangulations that use 3 or 6 nodes per triangle.

The input and output files use the simple TABLE format; comment lines begin with a "#" character. Otherwise, each line of the file contains one set of information, either the coordinates of a node (for a node file), or the indices of nodes that make up a triangle, (for a triangle file).

The input file nodes.txt contains the node information for the triangulation. Each data line contains the X and Y coordinates of a single node.

The input file triangles.txt contains the triangle information for the triangulation. Each line contains the indices of 3 or 6 nodes that form a triangle.

Usage:

triangulation_refine ( 'nodes.txt', 'triangles.txt' )

The program creates a new node file called nodes.ref.txt and a new triangle file called triangles.ref.txt.

Related Data and Programs:

TABLE is the format used for the input and output files.

TABLE_DELAUNAY is an executable FORTRAN90 program which can read a file of point coordinates and construct the Delaunay triangulation for that set of points.

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

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

TRIANGULATION_BOUNDARY_NODES is an executable MATLAB program that reads data defining a triangulation, determines which nodes lie on the boundary, and writes their coordinates to a file.

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

TRIANGULATION_Q2L is an executable MATLAB 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 MATLAB program that reads data defining a triangulation and computes a number of quality measures.

TRIANGULATION_RCM is an executable MATLAB 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 available in a C++ version and a FORTRAN90 version and . a MATLAB version.

TRIANGULATION_TRIANGLE_NEIGHBORS is an executable MATLAB program that 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.

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

Source Code:

• triangulation_refine.m, is the main program for TRIANGULATION_REFINE.
• 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 file used to write a DTABLE.
• 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 a DTABLE to a 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.
• i4_modp.m, returns the nonnegative remainder of integer division.
• i4_wrap.m, forces an integer to lie between given limits by wrapping.
• i4col_compare.m, compares columns I and J of an I4COL.
• i4col_sort_a.m, ascending sorts an I4COL.
• i4col_sorted_unique_count.m, counts unique elements in an I4COL.
• i4col_swap.m, swaps columns I and J of an I4COL.
• i4i4_sort_a.m, ascending sorts a pair of I4's.
• i4mat_transpose_print.m, prints an I4MAT, transposed.
• 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 to an integer table file.
• itable_write.m, writes an ITABLE file.
• r8_epsilon.m, returns the R8 roundoff unit.
• r8mat_transpose_print.m, prints an R8MAT, transposed.
• r8mat_transpose_print_some.m, prints some of an R8MAT, transposed.
• s_blank_delete.m, removes blanks from a string, left justifying the remainder.
• s_index_last_c.m, finds the LAST occurrence of a given character.
• 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_refine_compute.m, computes a refined order3 triangulation.
• triangulation_order3_refine_size.m, sizes a refined order3 triangulation.
• triangulation_order6_refine_compute.m, computes a refined order6 triangulation.
• triangulation_order6_refine_size.m, sizes a refined order6 triangulation.

Examples and Tests:

BOX_ORDER3 is an example of the refinement of a 3-node triangulation of a rectangular box.

• box_order3_nodes.txt, the nodes for a 3-node triangulation.
• box_order3_triangles.txt, the triangles for an order 3 triangulation.
• box_order3.png, a PNG image of the triangulation, created by TRIANGULATION_PLOT.
• box_order3_nodes.ref.txt, the nodes for the refined triangulation.
• box_order3_triangles.ref.txt, the triangles for the refined triangulation.
• box_order3.ref.png, a PNG image of the refined triangulation, created by TRIANGULATION_PLOT.
• box_order3.out, output printed by the program.

IRREG_ORDER6 is an example of the refinement of a 6-node triangulation of an irregular region with a hole:

• irreg_order6_nodes.txt, the nodes for a 6-node triangulation.
• irreg_order6_triangles.txt, the triangles for an order 6 triangulation.
• irreg_order6.png, a PNG image of the triangulation, created by TRIANGULATION_PLOT.
• irreg_order6_nodes.ref.txt, the nodes for the refined triangulation.
• irreg_order6_triangles.ref.txt, the triangles for the refined triangulation.
• irreg_order6.ref.png, a PNG image of the refined triangulation, created by TRIANGULATION_PLOT.
• irreg_order6.out, output printed by the program.

HOUSE_ORDER6 is an example of the refinement of a simple 6-node triangulation of a "house" diagram that involved 3 triangles.

• house_order6_nodes.txt, the nodes for a 6-node triangulation.
• house_order6_triangles.txt, the triangles for an order 6 triangulation.
• house_order6.png, a PNG image of the triangulation, created by TRIANGULATION_PLOT.
• house_order6_nodes.ref.txt, the nodes for the refined triangulation.
• house_order6_triangles.ref.txt, the triangles for the refined triangulation.
• house_order6.ref.png, a PNG image of the refined triangulation, created by TRIANGULATION_PLOT.
• house_order6.out, output printed by the program.

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