triangulation_histogram

triangulation_histogram, a Fortran90 code which computes the number of points from a dataset that are contained in each triangle of a triangulation.

One application of this code is simply to determine whether the dataset represents an approximately uniform sampling of the region covered by the triangulation.

Usage:

triangulation_histogram prefix data_filename

• prefix_nodes.txt, the node coordinates;
• prefix_elements.txt, the element definitions.

• data_filename is the name of the file containing the data points.

Licensing:

The information on this web page is distributed under the MIT license.

Languages:

triangulation_histogram is available in a C++ version and a Fortran90 version and a MATLAB version and an Octave version.

Related Data and codes:

random_data, a Fortran90 code which generates sample points for various probability distributions, spatial dimensions, and geometries;

triangle_histogram, a Fortran90 code which computes histograms of data on the unit triangle.

triangulation, a Fortran90 code which performs various operations on order 3 ("linear") or order 6 ("quadratic") triangulations.

triangulation_boundary_nodes, a Fortran90 code which reads data defining a triangulation, determines which nodes lie on the boundary, and writes their coordinates to a file.

triangulation_corner, a Fortran90 code which patches triangulations so that no triangle has two sides on the boundary.

triangulation_delaunay_discrepancy, a Fortran90 code which measures the amount by which a triangulation fails the local Delaunay test;

triangulation_display_opengl, a C++ code which reads files defining a triangulation and displays an image using OpenGL.

triangulation_l2q, a Fortran90 code which reads data defining a 3-node triangulation and generates midside nodes and writes out the corresponding 6-node triangulation.

triangulation_mask, a Fortran90 code 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_orient, a Fortran90 code 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 Fortran90 code which reads data defining a triangulation and creates a PostScript image of the nodes and triangles.

triangulation_q2l, a Fortran90 code 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 code which estimates the integral of a function over a triangulated region.

triangulation_quality, a Fortran90 code which reads data defining a triangulation and computes a number of quality measures.

triangulation_rcm, a Fortran90 code 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 code 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 code which reads data defining a triangulation, determines the neighboring triangles of each triangle, and writes that information to a file.

Source Code:

• triangulation_histogram.f90, the source code.

Examples and Tests:

• house3_nodes.txt, the nodes for the HOUSE3 triangulation.
• house3_elements.txt, the elements for the HOUSE3 triangulation.
• thousand_xy.txt, 1000 points in the region [0,2]x[0,3].
• house3_output.txt, the output file from the command triangulation_histogram house3 thousand_xy.txt

List of Routines:

• MAIN is the main code for TRIANGULATION_HISTOGRAM.
• CH_CAP capitalizes a single character.
• CH_EQI is a case insensitive comparison of two characters for equality.
• CH_TO_DIGIT returns the integer value of a base 10 digit.
• FILE_COLUMN_COUNT counts the number of columns in the first line of a file.
• FILE_EXIST reports whether a file exists.
• 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.
• 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 an R8MAT, transposed.
• S_TO_I4 reads an integer value 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.
• TRIANGULATION_AREAS computes triangle and triangulation areas.
• TRIANGULATION_HITS counts "data hits" in triangles and a triangulation.

You can go up one level to the Fortran90 source codes.