TRIANGULATION_ORIENT
Positively Orient Triangles

TRIANGULATION_ORIENT is a FORTRAN90 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 prefix_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 prefix_elements.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:

               2
              /|
             / |
            /  |
           /   |
          /    |
         1-----3
      

               3
              /|
             / |
            /  |
           /   |
          /    |
         1-----2
      

A misoriented order 6 triangle:

               2
              /|
             / |
            4  5
           /   |
          /    |
         1--6--3
      

               3
              /|
             / |
            6  5
           /   |
          /    |
         1--4--2
      

Usage:

triangulation_orient prefix

• prefix_nodes.txt contains the node coordinates,
• prefix_elements.txt contains the element definitions.
• prefix_orient_elements.txt will contains the oriented element definitions.

Licensing:

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

Languages:

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

Related Data and Programs:

TABLE_DELAUNAY, a FORTRAN90 program which computes the Delaunay triangulation of a set of points.

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

TRIANGULATION, a FORTRAN90 library which carries out various operations on order 3 ("linear") or order 6 ("quadratic") triangulations.

TRIANGULATION_BOUNDARY_NODES, a FORTRAN90 program which reads data defining a triangulation, determines which nodes lie on the boundary, and writes their coordinates to a file.

TRIANGULATION_CORNER, a FORTRAN90 program which patches triangulations so that no triangle has two sides on the boundary.

TRIANGULATION_DELAUNAY_DISCREPANCY, a FORTRAN90 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 FORTRAN90 program which computes histograms of data over a triangulation.

TRIANGULATION_L2Q, a FORTRAN90 program which reads data defining a 3-node triangulation and generates midside nodes and writes out the corresponding 6-node triangulation.

TRIANGULATION_MASK, a FORTRAN90 program which takes an existing triangulation and deletes triangles and their corresponding nodes as requested by the user.

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_PLOT, a FORTRAN90 program which reads data defining a triangulation and creates a PostScript image of the nodes and triangles.

TRIANGULATION_Q2L, a FORTRAN90 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 FORTRAN90 program which estimates the integral of a function over a triangulated region.

TRIANGULATION_QUALITY, a FORTRAN90 program which reads data defining a triangulation and computes a number of quality measures.

TRIANGULATION_RCM, a FORTRAN90 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 FORTRAN90 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 FORTRAN90 program which reads data defining a triangulation, determines the neighboring triangles of each triangle, and writes that information to a file.

Reference:

1. Franz Aurenhammer,
   Voronoi diagrams - a study of a fundamental geometric data structure,
   ACM Computing Surveys,
   Volume 23, Number 3, September 1991, pages 345-405.
2. Marc deBerg, Marc Krevald, Mark Overmars, Otfried Schwarzkopf,
   Computational Geometry,
   Springer, 2000,
   ISBN: 3-540-65620-0.
3. 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.
4. Albert Nijenhuis, Herbert Wilf,
   Combinatorial Algorithms for Computers and Calculators,
   Second Edition,
   Academic Press, 1978,
   ISBN: 0-12-519260-6,
   LC: QA164.N54.
5. 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.
6. Joseph ORourke,
   Computational Geometry,
   Second Edition,
   Cambridge, 1998,
   ISBN: 0521649765,
   LC: QA448.D38.
7. 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.f90, 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_elements.txt, a set of order 3 triangles.
• p15_orient_elements.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 a case insensitive comparison of two characters for equality.
• CH_TO_DIGIT returns the integer ( kind = 4 ) value of a base 10 digit.
• FILE_COLUMN_COUNT counts the number of columns in the first line of a file.
• FILE_ROW_COUNT counts the number of row records in a file.
• GET_UNIT returns a free FORTRAN unit number.
• I4MAT_DATA_READ reads data from an I4MAT file.
• I4MAT_HEADER_READ reads the header from an I4MAT.
• I4MAT_TRANSPOSE_PRINT_SOME prints some of the transpose of an I4MAT.
• I4MAT_WRITE writes an I4MAT file.
• MESH_BASE_ONE ensures that the element definition is one-based.
• R8MAT_DATA_READ reads data from an R8MAT file.
• R8MAT_HEADER_READ reads the header from an R8MAT file.
• R8MAT_TRANSPOSE_PRINT_SOME prints some of a R8MAT, transposed.
• 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.
• TIMESTAMP prints the current YMDHMS date as a time stamp.
• TRIANGLE_AREA_2D computes the area of a triangle in 2D.

You can go up one level to the FORTRAN90 source codes.