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<html>
<head>
<title>
SIMPLEX_GRID - Regular Grid Within a Simplex
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">
<h1 align = "center">
SIMPLEX_GRID <br> Regular Grid Within a Simplex
</h1>
<hr>
<p>
<b>SIMPLEX_GRID</b>
is a C++ library which
generates a grid of points
over the interior of a simplex in M dimensions.
</p>
<h3 align = "center">
Licensing:
</h3>
<p>
The computer code and data files described and made available on this web page
are distributed under
<a href = "../../txt/gnu_lgpl.txt">the GNU LGPL license.</a>
</p>
<h3 align = "center">
Languages:
</h3>
<p>
<b>SIMPLEX_GRID</b> is available in
<a href = "../../c_src/simplex_grid/simplex_grid.html">a C version</a> and
<a href = "../../cpp_src/simplex_grid/simplex_grid.html">a C++ version</a> and
<a href = "../../f77_src/simplex_grid/simplex_grid.html">a FORTRAN77 version</a> and
<a href = "../../f_src/simplex_grid/simplex_grid.html">a FORTRAN90 version</a> and
<a href = "../../m_src/simplex_grid/simplex_grid.html">a MATLAB version</a> and
<a href = "../../py_src/simplex_grid/simplex_grid.html">a Python version</a>.
</p>
<h3 align = "center">
Related Data and Programs:
</h3>
<p>
<a href = "../../cpp_src/asa299/asa299.html">
ASA299</a>,
a C++ library which
computes the lattice points in an M-dimensional simplex,
by Chasalow and Brand;
this is a version of Applied Statistics Algorithm 299;
</p>
<p>
<a href = "../../cpp_src/ball_grid/ball_grid.html">
BALL_GRID</a>,
a C++ library which
computes a grid of points
over the interior of a ball in 3D.
</p>
<p>
<a href = "../../cpp_src/circle_arc_grid/circle_arc_grid.html">
CIRCLE_ARC_GRID</a>,
a C++ program which
computes points equally spaced
along a circular arc in 2D.
</p>
<p>
<a href = "../../cpp_src/cube_grid/cube_grid.html">
CUBE_GRID</a>,
a C++ library which
computes a grid of points
over the interior of a cube in 3D.
</p>
<p>
<a href = "../../cpp_src/disk_grid/disk_grid.html">
DISK_GRID</a>,
a C++ library which
computes a grid of points
over the interior of a disk in 2D.
</p>
<p>
<a href = "../../cpp_src/ellipse_grid/ellipse_grid.html">
ELLIPSE_GRID</a>,
a C++ library which
computes a grid of points
over the interior of an ellipse in 2D.
</p>
<p>
<a href = "../../cpp_src/ellipsoid_grid/ellipsoid_grid.html">
ELLIPSOID_GRID</a>,
a C++ library which
computes a grid of points
over the interior of an ellipsoid in 3D.
</p>
<p>
<a href = "../../cpp_src/fem_basis/fem_basis.html">
FEM_BASIS</a>,
a C++ library which
can define basis functions for the finite element method (FEM)
for any degree in an M-dimensional simplex (1D interval, 2D triangle,
3D tetrahedron, and higher dimensional generalizations.)
</p>
<p>
<a href = "../../cpp_src/hypercube_grid/hypercube_grid.html">
HYPERCUBE_GRID</a>,
a C++ library which
computes a grid of points
over the interior of a hypercube in M dimensions.
</p>
<p>
<a href = "../../cpp_src/line_grid/line_grid.html">
LINE_GRID</a>,
a C++ library which
computes a grid of points
over the interior of a line segment in 1D.
</p>
<p>
<a href = "../../cpp_src/polygon_grid/polygon_grid.html">
POLYGON_GRID</a>,
a C++ library which
generates a grid of points
over the interior of a polygon in 2D.
</p>
<p>
<a href = "../../cpp_src/pyramid_grid/pyramid_grid.html">
PYRAMID_GRID</a>,
a C++ library which
computes a grid of points
over the interior of the unit pyramid in 3D;
</p>
<p>
<a href = "../../cpp_src/simplex_coordinates/simplex_coordinates.html">
SIMPLEX_COORDINATES</a>,
a C++ library which
computes the Cartesian coordinates of the vertices of
a regular simplex in M dimensions.
</p>
<p>
<a href = "../../cpp_src/simplex_gm_rule/simplex_gm_rule.html">
SIMPLEX_GM_RULE</a>,
a C++ library which
defines Grundmann-Moeller quadrature rules
over the interior of a triangle in 2D, a tetrahedron in 3D, or
over the interior of the simplex in M dimensions.
</p>
<p>
<a href = "../../cpp_src/simplex_integrals/simplex_integrals.html">
SIMPLEX_INTEGRALS</a>,
a C++ library which
returns the exact value of the integral of any monomial
over the interior of the unit simplex in M dimensions.
</p>
<p>
<a href = "../../cpp_src/simplex_monte_carlo/simplex_monte_carlo.html">
SIMPLEX_MONTE_CARLO</a>,
a C++ library which
uses the Monte Carlo method to estimate integrals
over the interior of the unit simplex in M dimensions.
</p>
<p>
<a href = "../../cpp_src/sphere_fibonacci_grid/sphere_fibonacci_grid.html">
SPHERE_FIBONACCI_GRID</a>,
a C++ library which
uses a Fibonacci spiral to create a grid of points
on the surface of the unit sphere in 3D.
</p>
<p>
<a href = "../../cpp_src/sphere_grid/sphere_grid.html">
SPHERE_GRID</a>,
a C++ library which
provides a number of ways of generating grids of points, or of
points and lines, or of points and lines and faces,
on the surface of the unit sphere in 3D.
</p>
<p>
<a href = "../../cpp_src/sphere_llq_grid/sphere_llq_grid.html">
SPHERE_LLQ_GRID</a>,
a C++ library which
uses longitudes and latitudes to create grids of points,
lines, and quadrilaterals
on the surface of the unit sphere in 3D.
</p>
<p>
<a href = "../../cpp_src/sphere_llt_grid/sphere_llt_grid.html">
SPHERE_LLT_GRID</a>,
a C++ library which
uses longitudes and latitudes to create grids of points,
lines, and triangles
on the surface of the unit sphere in 3D.
</p>
<p>
<a href = "../../cpp_src/square_grid/square_grid.html">
SQUARE_GRID</a>,
a C++ library which
computes a grid of points
over the interior of a square in 2D.
</p>
<p>
<a href = "../../cpp_src/tetrahedron_grid/tetrahedron_grid.html">
TETRAHEDRON_GRID</a>,
a C++ library which
computes a grid of points
over the interior of a tetrahedron in 3D.
</p>
<p>
<a href = "../../cpp_src/triangle_grid/triangle_grid.html">
TRIANGLE_GRID</a>,
a C++ library which
computes a grid of points
over the interior of a triangle in 2D.
</p>
<p>
<a href = "../../cpp_src/wedge_grid/wedge_grid.html">
WEDGE_GRID</a>,
a C++ library which
computes a grid of points
over the interior of the unit wedge in 3D.
</p>
<h3 align = "center">
Source Code:
</h3>
<p>
<ul>
<li>
<a href = "simplex_grid.cpp">simplex_grid.cpp</a>, the source code.
</li>
<li>
<a href = "simplex_grid.hpp">simplex_grid.hpp</a>, the include file.
</li>
<li>
<a href = "simplex_grid.sh">simplex_grid.sh</a>,
BASH commands to compile the source code.
</li>
</ul>
</p>
<h3 align = "center">
Examples and Tests:
</h3>
<p>
<ul>
<li>
<a href = "simplex_grid_prb.cpp">simplex_grid_prb.cpp</a>,
a sample calling program.
</li>
<li>
<a href = "simplex_grid_prb.sh">simplex_grid_prb.sh</a>,
BASH commands to compile and run the sample program.
</li>
<li>
<a href = "simplex_grid_prb_output.txt">simplex_grid_prb_output.txt</a>,
the output file.
</li>
</ul>
</p>
<h3 align = "center">
List of Routines:
</h3>
<p>
<ul>
<li>
<b>COMP_NEXT_GRLEX</b> returns the next composition in grlex order.
</li>
<li>
<b>COMP_RANDOM</b> selects a random composition of the integer N into K parts.
</li>
<li>
<b>I4_UNIFORM_AB</b> returns a scaled pseudorandom I4 between A and B.
</li>
<li>
<b>I4MAT_TRANSPOSE_PRINT</b> prints an I4MAT, transposed.
</li>
<li>
<b>I4MAT_TRANSPOSE_PRINT_SOME</b> prints some of the transpose of an I4MAT.
</li>
<li>
<b>KSUB_RANDOM</b> selects a random subset of size K from a set of size N.
</li>
<li>
<b>R8MAT_TRANSPOSE_PRINT</b> prints an R8MAT, transposed.
</li>
<li>
<b>R8MAT_TRANSPOSE_PRINT_SOME</b> prints some of an R8MAT, transposed.
</li>
<li>
<b>SIMPLEX_GRID_INDEX_ALL</b> returns all the simplex grid indices.
</li>
<li>
<b>SIMPLEX_GRID_INDEX_NEXT</b> returns the next simplex grid index.
</li>
<li>
<b>SIMPLEX_GRID_INDEX_SAMPLE</b> returns a random simplex grid index.
</li>
<li>
<b>SIMPLEX_GRID_INDEX_TO_POINT</b> returns points corresponding to simplex indices.
</li>
<li>
<b>SIMPLEX_GRID_SIZE</b> counts the grid points inside a simplex.
</li>
<li>
<b>TIMESTAMP</b> prints the current YMDHMS date as a time stamp.
</li>
</ul>
</p>
<p>
You can go up one level to <a href = "../cpp_src.html">
the C++ source codes</a>.
</p>
<hr>
<i>
Last revised on 31 July 2014.
</i>
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