REGION_SAMPLE
Select Points from a Region

REGION_SAMPLE is a FORTRAN90 library which samples various computational regions.

A computational region is a (usually finite) subset of 2D, 3D or M-dimensional space, which is often an ideal model of some physically interesting space, such as a channel in which liquid is flowing, or the body of some metallic structure. For certain algorithms, it is necessary to "sample" this region, that is, to select, uniformly at random, a set of N points that lie in the region.

It's easy to do this for the unit square or hypercube, simply by invoking the pseudorandom number generator. It's also easy to extend this idea to any rectangular object. However, this gets more difficult to do when the region has a curved or complicated geometry, which might include holes.

One way to handle many different kinds of regions in a uniform way is to allow the sampling of the region to be carried out by a subroutine which "knows" the region's shape. The input to the subroutine is simply N, the number of points requested, and the routine generates the points using whatever method is appropriate. When all else fails, a rejection method can usually be used.

REGION_SAMPLE is simply a collection of some of the routines that have been used for such computations.

Licensing:

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

Related Data and Programs:

DISCRETE_PDF_SAMPLE a MATLAB program which demonstrates how to construct a Probability Density Function (PDF) from a table of sample data, and then to use that PDF to create new samples.

PLOT_POINTS is a FORTRAN90 program which can be used to create Encapsulated PostScript images (EPS files) from the output files.

RANDOM_DATA is a FORTRAN90 program which produces random data from a number of regions.

RBOX is a C program which produces random data from a number of regions.

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

RSITES is a C++ program which produces random data in an M-dimensional box.

TABLE is a format which is used to store the input and output files used by the program.

UNIFORM is a FORTRAN90 library which samples the uniform random distribution.

Source Code:

• region_sample.f90, the source code.
• region_sample.csh, commands to compile the source code.

Examples and Tests:

Test files you may copy include:

• region_sample_prb.f90, a sample calling program.
• region_sample_prb.csh, commands to compile and run the sample program.
• region_sample_prb_output.txt, the output file.

FORK is a subset of [0,100] x [0,100] comprising a rectangular "handle" and semicircular annulus that resembles an inverted tuning fork:

• fork_02_01000.txt, 1,000 sample points.
• fork_02_01000.png, a PNG image of the points.
• fork_02_10000.txt, 10,000 sample points.
• fork_02_10000.png, a PNG image of the points.

SPHERE is the interior of a sphere:

• sphere_02_00100.txt, 100 sample points.
• sphere_02_00100.png, a PNG image of the points.
• sphere_02_01000.txt, 1,000 sample points.
• sphere_02_01000.png, a PNG image of the points.

List of Routines:

• DTABLE_DATA_WRITE writes a real table dataset to a file.
• DTABLE_WRITE writes a real table dataset to a file.
• DTABLE_HEADER_WRITE writes the table header data to a file.
• FORK samples the fork region.
• GET_UNIT returns a free FORTRAN unit number.
• R8_UNIFORM_01 returns a unit pseudorandom R8.
• R8VEC_NORMAL_01 samples the standard normal probability distribution.
• R8VEC_PRINT prints an R8VEC.
• R8VEC_UNIFORM_01 returns a unit pseudorandom R8VEC.
• S_BLANK_DELETE removes blanks from a string, left justifying the remainder.
• SPHERE_SAMPLE samples points inside the unit sphere.
• TIMESTAMP prints the current YMDHMS date as a time stamp.
• TIMESTRING writes the current YMDHMS date into a string.

You can go up one level to the FORTRAN90 source codes.