TRIANGULATION_ORIENT, a MATLAB 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
The corrected order 3 triangle:
3
/|
/ |
/ |
/ |
/ |
1-----2
A misoriented order 6 triangle:
2
/|
/ |
4 5
/ |
/ |
1--6--3
The corrected order 6 triangle:
3
/|
/ |
6 5
/ |
/ |
1--4--2
triangulation_orient ( 'prefix' )where 'prefix' is the common filename prefix:
The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.
TRIANGULATION_ORIENT is available in a C++ version and a FORTRAN90 version and a MATLAB version.
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 MATLAB library which carries out various operations on order 3 ("linear") or order 6 ("quadratic") triangulations.
TRIANGULATION_BOUNDARY_EDGES, a MATLAB program which reads data defining a triangulation, determines which edges lie on the boundary, organizes them into connected components, and writes this information to a file.
TRIANGULATION_BOUNDARY_NODES, a MATLAB program which reads data defining a triangulation, determines which nodes lie on the boundary, and writes their coordinates to a file.
TRIANGULATION_CORNER, a MATLAB program which patches triangulations so that no triangle has two sides on the boundary.
TRIANGULATION_DELAUNAY_DISCREPANCY, a MATLAB program which measures the amount by which a triangulation fails the local Delaunay test;
TRIANGULATION_DISPLAY, a MATLAB program which displays the nodes and elements of a triangulation on the MATLAB graphics screen;
TRIANGULATION_DISPLAY_OPENGL, a C++ program which reads files defining a triangulation and displays an image using Open GL.
TRIANGULATION_HISTOGRAM, a MATLAB program which computes histograms of data over a triangulation.
TRIANGULATION_L2Q, 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, a MATLAB program which takes an existing triangulation and deletes triangles and their corresponding nodes as requested by the user.
TRIANGULATION_ORDER3, a data directory which contains a description and examples of order 3 triangulations.
TRIANGULATION_ORDER6, a data directory which contains a description and examples of order 6 triangulations.
TRIANGULATION_PLOT, a MATLAB program which reads data defining a triangulation and creates a PostScript image of the nodes and triangles.
TRIANGULATION_Q2L, 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_QUAD, a MATLAB program which estimates the integral of a function over a triangulated region.
TRIANGULATION_QUALITY, a MATLAB program which reads data defining a triangulation and computes a number of quality measures.
TRIANGULATION_RCM, 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, 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, a MATLAB program which reads data defining a triangulation, determines the neighboring triangles of each triangle, and writes that information to a file.