TRIANGULATION_Q2L
6-Node Triangulation to 3-Node Triangulation


TRIANGULATION_Q2L, a C++ code which reads information describing a triangulation of a set of points using 6-node ("quadratic") triangles, and creates a 3-node ("linear") triangulation.

The same nodes are used, but each 6-node triangle is broken up into four smaller 3-node triangles.

Thus, the program might be given the following 4 triangles:

        11-12-13-14-15
         |\    |\    |
         | \   | \   |
         6  7  8  9 10
         |   \ |   \ |
         |    \|    \|
         1--2--3--4--5
      

It would make a new triangulation involving 16 triangles:

        11-12-13-14-15
         |\ |\ |\ |\ |
         | \| \| \| \|
         6--7--8--9-10
         |\ |\ |\ |\ |
         | \| \| \| \|
         1--2--3--4--5
      

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 prefix_elements.txt contains the triangle information for the 6-node triangulation. Each line contains the indices of six nodes that form a triangle, in counterclockwise order. The first three indices are the vertices, in counterclockwise order. The fourth index is the midside node between vertices 1 and 2, the fifth the midside between vertices 2 and 3, and the sixth the midside between vertices 3 and 1.

The output file prefix_q2l_elements.txt contains the triangle information for the 3-node triangulation. The vertices for each triangle are listed in counterclockwise order. There are 4 times as many triangles in this triangulation.

Usage:

triangulation_q2l prefix
where prefix is the common filename prefix:

Licensing:

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

Languages:

TRIANGULATION_Q2L is available in a C++ version and a FORTRAN90 version and a MATLAB version.

Related Data and Programs:

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

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

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

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

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

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

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

TRIANGULATION_NODE_TO_ELEMENT, a C++ program which reads files describing a set of nodes, their triangulation, and the value of one or more quantities at each node, and outputs a file that averages the quantities for each element. This operation in effect creates an "order1" finite element model of the data.

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_ORIENT, a C++ 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, a C++ program which reads data defining a triangulation and creates a PostScript image of the nodes and triangles.

triangulation_q2l_test

TRIANGULATION_QUAD, a C++ program which estimates the integral of a function over a triangulated region.

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

TRIANGULATION_RCM, a C++ 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 C++ 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 C++ program which 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.
  2. Joseph ORourke,
    Computational Geometry,
    Cambridge University Press,
    Second Edition, 1998.

Source Code:


Last revised on 06 May 2020.