TRIANGULATION_BOUNDARY_EDGES
Boundary Edges of a Triangulation


TRIANGULATION_BOUNDARY_EDGES is a MATLAB program which analyzes the triangulation of a region, identifies the edges that form the boundaries, organizes the boundary edges into one or more connected components, and writes a file describing the components and the sequence of boundary edges.

Either a 3-node or 6-node triangulation may be used.

Usage:

triangulation_boundary_edges ( '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_BOUNDARY_EDGES is available in a MATLAB version.

Related Programs:

MESH_TO_XML, a MATLAB program which reads information defining a 1D, 2D or 3D mesh, namely a file of node coordinates and a file of elements defined by node indices, and creates a corresponding XML file for input to DOLFIN or FENICS.

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

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_ORIENT, a MATLAB 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 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.

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.

Source Code:

Examples and Tests:

ELBOW is a curved region, looking like an elbow, that lies inside the unit square. It is triangulated using order 3 triangles. There are 320 nodes and 568 triangles. There are 66 nodes on the boundary.

ELL is an L-shaped region, using 96 triangles and 65 nodes. It is triangulated using order 3 triangles.

LAKE is an irregular lake-shaped region with an "island", which means the boundary is made of two components. It is triangulated using order 3 triangles.

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


Last revised on 02 December 2010.