TRIANGLE_HISTOGRAM
Histograms of Triangle Data

TRIANGLE_HISTOGRAM is a C++ program which creates a histogram of data in the unit triangle.

The unit triangle has the vertices (1,0), (0,1), (0,0).

"Data" in the unit triangle is assumed to take the form of a file, containing a list of points that lie in the triangle.

The sides of the triangle can each be divided into N subintervals, and by connecting them, the result is N*N subtriangles of the same area.

The program then determines the number of points that lie within each subtriangle, and prints this list.

This program is particularly suitable for investigating whether a set of points in the unit triangle are close to a uniformly sampling, or if there is some bias in the selection.

Usage:

triangle_histogram data_file n

• data_file is the file containing the sample points;
• n is the number of subintervals into which each side of the unit triangle is to be divided.

Licensing:

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

Languages:

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

Related Data and Programs:

RANDOM_DATA, a C++ program which produces random samples from a number of regions, including triangles.

TRIANGLE_MONTE_CARLO, a C++ program which uses the Monte Carlo method to estimate integrals over a triangle.

TRIANGLE_SAMPLES, a dataset directory which contains sets of sample points drawn from the unit triangle.

Reference:

1. Reuven Rubinstein,
   Monte Carlo Optimization, Simulation and Sensitivity of Queueing Networks,
   Krieger, 1992,
   ISBN: 0894647644,
   LC: QA298.R79.
2. Greg Turk,
   Generating Random Points in a Triangle,
   in Graphics Gems I,
   edited by Andrew Glassner,
   AP Professional, 1990,
   ISBN: 0122861663,
   LC: T385.G697

Source Code:

• triangle_histogram.cpp, the source code.
• triangle_histogram.sh, commands to compile the source code.

Examples and Tests:

B10000 is a "bad" set of sample points.

• b10000.txt, the sample points.
• b10000_output.txt, output from the command "triangle_histogram b10000.txt 4".

G10000 is a "good" set of sample points.

• g10000.txt, the sample points.
• g10000_output.txt, output from the command "triangle_histogram g10000.txt 4".

List of Routines:

• MAIN is the main program for TRIANGLE_HISTOGRAM.
• CH_CAP capitalizes a single character.
• CH_EQI is true if two characters are equal, disregarding case.
• CH_TO_DIGIT returns the integer value of a base 10 digit.
• FILE_COLUMN_COUNT counts the columns in the first line of a file.
• FILE_ROW_COUNT counts the number of row records in a file.
• I4_MAX returns the maximum of two I4's.
• I4_MIN returns the minimum of two I4's.
• I4VEC_MAX returns the value of the maximum element in an I4VEC.
• I4VEC_MEAN returns the mean of an I4VEC.
• I4VEC_MIN returns the value of the minimum element in an I4VEC.
• I4VEC_STD returns the standard deviation of an I4VEC.
• R8MAT_DATA_READ reads the 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_LEN_TRIM returns the length of a string to the last nonblank.
• S_TO_I4 reads an I4 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.

You can go up one level to the C++ source codes.