TRIANGULATION_HISTOGRAM
Per-Triangle Histogram for Triangulation

TRIANGULATION_HISTOGRAM is a FORTRAN90 program which computes the number of points from a dataset that are contained in each triangle of a triangulation.

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

Languages:

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

Related Data and Programs:

RANDOM_DATA, a FORTRAN90 library which generates sample points for various probability distributions, spatial dimensions, and geometries;

TRIANGLE_HISTOGRAM, a FORTRAN90 program which computes histograms of data on the unit triangle.

TRIANGULATION, a FORTRAN90 library which performs 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_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_MASK, a FORTRAN90 program 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 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 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.

UNIFORM, a FORTRAN90 library which computes elements of a uniform pseudorandom sequence.

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 program 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.