TRIANGULATION_MASK is a FORTRAN90 program which reads the nodes and triangles that define a triangulation, calls a user routine which determines whether each triangle is to be preserved or discarded ("masked") from the triangulation, and writes out new node and triangle files that define the masked triangulation.
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.
One motivation for creating this program is as follows. Suppose we have a set of points that lie on the boundary or inside of a non-convex region. If we naively call an unconstrained Delaunay triangulation routine, such as TABLE_DELAUNAY, then because the region is not convex, it is possible to create triangles which lie outside the region.
An easy way to correct this problem is to call a user routine and pass it the indices and coordinates of each triangle. The user can then decide to drop any triangle whose centroid, say, lies outside the region.
Other masking criteria might drop triangles that are too small, or that have too small an angle, or that lie inside some interior hole. These choices are entirely up to the user.
The user masking subroutine has the form:
subroutine triangle_mask ( dim_num, triangle_order, nodes, coord, mask )with arguments:
The user masking routine must be compiled and linked with the software, perhaps with a command like:
F90 triangulation_mask.o triangle_mask.f90We will assume that the executable is renamed to triangulation_mask.
The program is the executed with a command like:
triangulation_mask prefixwhere 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_MASK is available in a C++ version and a FORTRAN90 version and a MATLAB version.
TABLE_DELAUNAY, a FORTRAN90 program which can compute 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_ORIENT, a FORTRAN90 program which reads data defining a triangulation and reorients those triangles that have negative orientation.
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.
P15 is a triangulation created by calling DISTMESH, then removing duplicate points by calling TABLE_MERGE, then creating a Delaunay triangulation by calling TABLE_DELAUNAY, Unfortunately, this results in many triangles that lie outside the region of interest.
SMALL is a triangulation of the 25 lattice points on the [0,4]x[0,4] square. Our masking operation should cut out a lower left triangular corner and a section from the upper right.
You can go up one level to the FORTRAN90 source codes.