TRIANGULATION_ORIENT
Positively Orient Triangles

TRIANGULATION_ORIENT is a C++ program which reads a triangulation, and reorients each triangle that has a negative area. If at least one such triangle is encountered, the program writes out a new copy of the triangle file in which all the triangles have been correctly oriented.

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.

For many applications, including computer graphics and finite element computations, it is assumed that the triangles are described with a positive orientation. That is, the nodes are listed in clockwise order.

TRIANGULATION_ORIENT can check whether every triangle in a triangulation has positive orientation, and can "repair" the file if it finds one or more triangles with a negative orientation.

A misoriented order 3 triangle:

The corrected order 3 triangle:

A misoriented order 6 triangle:

The corrected order 6 triangle:

Usage:

triangulation_orient node_file triangle_file: reads the triangulation described by the node file (containing node coordinates) and the triangle file (containing sets of 3 or 6 node indices), determines if any triangles need to be reoriented, and if so, writes out a corrected triangle file.

Licensing:

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

Related Data and Programs:

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

TABLE_DELAUNAY is an executable C++ program which computes the Delaunay triangulation of a set of points.

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

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.

Reference:

Franz Aurenhammer,
Voronoi diagrams - a study of a fundamental geometric data structure,
ACM Computing Surveys,
Volume 23, Number 3, September 1991, pages 345-405,
../../pdf/aurenhammer.pdf
Marc deBerg, Marc Krevald, Mark Overmars, Otfried Schwarzkopf,
Computational Geometry,
Springer, 2000,
ISBN: 3-540-65620-0.
Barry Joe,
GEOMPACK - a software package for the generation of meshes using geometric algorithms,
Advances in Engineering Software,
Volume 13, Number 5, 1991, pages 325-331.
Albert Nijenhuis, Herbert Wilf,
Combinatorial Algorithms for Computers and Calculators,
Second Edition,
Academic Press, 1978,
ISBN: 0-12-519260-6,
LC: QA164.N54.
Atsuyuki Okabe, Barry Boots, Kokichi Sugihara, Sung Nok Chiu,
Spatial Tesselations: Concepts and Applications of Voronoi Diagrams,
Second Edition,
Wiley, 2000,
ISBN: 0-471-98635-6,
LC: QA278.2.O36.
Joseph ORourke,
Computational Geometry,
Second Edition,
Cambridge, 1998,
ISBN: 0521649765,
LC: QA448.D38.
Per-Olof Persson, Gilbert Strang,
A Simple Mesh Generator in MATLAB,
SIAM Review,
Volume 46, Number 2, June 2004, pages 329-345.

Source Code:

triangulation_orient.C, the source code.
triangulation_orient.csh, commands to compile the source code.

Examples and Tests:

P15 is a triangulation created by DISTMESH. Unfortunately, 512 of the triangles have a negative orientation. In this example, TRIANGULATION_ORIENT was used to reorient those triangles.

p15_nodes.txt, a set of nodes.
p15_triangles.txt, a set of order 3 triangles.
p15_triangles.orient.txt, the set of order 3 triangles after TRIANGULATION_ORIENT has reoriented them.
p15_output.txt, the printed output from the program.

List of Routines:

MAIN is the main program for TRIANGULATION_ORIENT.
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.
I4MAT_TRANSPOSE_PRINT_SOME prints some of an I4MAT, transposed.
ITABLE_DATA_READ reads data from an ITABLE file.
ITABLE_DATA_WRITE writes data to an ITABLE file.
ITABLE_HEADER_READ reads the header from an ITABLE file.
ITABLE_HEADER_WRITE writes the header of an ITABLE file.
ITABLE_WRITE writes information to an ITABLE file.
R8_EPSILON returns the R8 roundoff unit.
R8MAT_TRANSPOSE_PRINT_SOME prints some of an R8MAT, transposed.
S_BLANK_DELETE removes blanks from a string, left justifying the remainder.
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.
TIMESTAMP prints the current YMDHMS date as a time stamp.
TIMESTRING returns the current YMDHMS date as a string.
TRIANGLE_AREA_2D computes the area of a triangle in 2D.

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

Last revised on 15 January 2007.

TRIANGULATION_ORIENT Positively Orient Triangles