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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 MATLAB 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 = "../../m_src/asa299/asa299.html">
ASA299</a>,
a MATLAB 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 = "../../m_src/ball_grid/ball_grid.html">
BALL_GRID</a>,
a MATLAB library which
computes a grid of points
over the interior of a ball in 3D.
</p>
<p>
<a href = "../../m_src/circle_arc_grid/circle_arc_grid.html">
CIRCLE_ARC_GRID</a>,
a MATLAB program which
computes points equally spaced along a circular arc;
</p>
<p>
<a href = "../../m_src/cube_grid/cube_grid.html">
CUBE_GRID</a>,
a MATLAB library which
computes a grid of points
over the interior of a cube in 3D.
</p>
<p>
<a href = "../../m_src/disk_grid/disk_grid.html">
DISK_GRID</a>,
a MATLAB library which
computes a grid of points
over the interior of a disk in 2D.
</p>
<p>
<a href = "../../m_src/ellipse_grid/ellipse_grid.html">
ELLIPSE_GRID</a>,
a MATLAB library which
computes a grid of points
over the interior of an ellipse in 2D.
</p>
<p>
<a href = "../../m_src/ellipsoid_grid/ellipsoid_grid.html">
ELLIPSOID_GRID</a>,
a MATLAB library which
computes grid points that lie inside a 3D ellipsoid.
</p>
<p>
<a href = "../../m_src/fem_basis/fem_basis.html">
FEM_BASIS</a>,
a MATLAB 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 = "../../m_src/hypercube_grid/hypercube_grid.html">
HYPERCUBE_GRID</a>,
a MATLAB library which
computes a grid of points
over the interior of a hypercube in M dimensions.
</p>
<p>
<a href = "../../m_src/line_grid/line_grid.html">
LINE_GRID</a>,
a MATLAB library which
computes a grid of points
over the interior of a line segment in 1D.
</p>
<p>
<a href = "../../m_src/polygon_grid/polygon_grid.html">
POLYGON_GRID</a>,
a MATLAB library which
generates a grid of points
over the interior of a polygon in 2D.
</p>
<p>
<a href = "../../m_src/pyramid_grid/pyramid_grid.html">
PYRAMID_GRID</a>,
a MATLAB library which
computes a grid of points
over the interior of the unit pyramid in 3D;
</p>
<p>
<a href = "../../m_src/simplex_coordinates/simplex_coordinates.html">
SIMPLEX_COORDINATES</a>,
a MATLAB library which
computes the Cartesian coordinates of the vertices of
a regular simplex in M dimensions.
</p>
<p>
<a href = "../../m_src/simplex_gm_rule/simplex_gm_rule.html">
SIMPLEX_GM_RULE</a>,
a MATLAB library which
defines Grundmann-Moeller quadrature rules
over the interior of a simplex in M dimensions.
</p>
<p>
<a href = "../../m_src/simplex_integrals/simplex_integrals.html">
SIMPLEX_INTEGRALS</a>,
a MATLAB 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 = "../../m_src/simplex_monte_carlo/simplex_monte_carlo.html">
SIMPLEX_MONTE_CARLO</a>,
a MATLAB library which
uses the Monte Carlo method to estimate integrals
over the interior of the unit simplex in M dimensions.
</p>
<p>
<a href = "../../m_src/sphere_fibonacci_grid/sphere_fibonacci_grid.html">
SPHERE_FIBONACCI_GRID</a>,
a MATLAB 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 = "../../m_src/sphere_grid/sphere_grid.html">
SPHERE_GRID</a>,
a MATLAB 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 = "../../m_src/sphere_llq_grid/sphere_llq_grid.html">
SPHERE_LLQ_GRID</a>,
a MATLAB 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 = "../../m_src/square_grid/square_grid.html">
SQUARE_GRID</a>,
a MATLAB library which
computes a grid of points
over the interior of a square in 2D.
</p>
<p>
<a href = "../../m_src/tetrahedron_grid/tetrahedron_grid.html">
TETRAHEDRON_GRID</a>,
a MATLAB library which
computes a grid of points
over the interior of a tetrahedron in 3D.
</p>
<p>
<a href = "../../m_src/triangle_grid/triangle_grid.html">
TRIANGLE_GRID</a>,
a MATLAB library which
computes a grid of points
over the interior of a triangle in 2D.
</p>
<p>
<a href = "../../m_src/wedge_grid/wedge_grid.html">
WEDGE_GRID</a>,
a MATLAB 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 = "comp_next_grlex.m">comp_next_grlex.m</a>,
returns the next composition of an integer N into K parts,
using the graded lexicographic ordering.
</li>
<li>
<a href = "comp_random.m">comp_random.m</a>,
returns a random composition of an integer N into K parts.
</li>
<li>
<a href = "i4_uniform_ab.m">i4_uniform_ab.m</a>,
returns a random integer between A and B.
</li>
<li>
<a href = "i4mat_transpose_print.m">i4mat_transpose_print.m</a>,
prints an I4MAT transposed.
</li>
<li>
<a href = "i4mat_transpose_print_some.m">i4mat_transpose_print_some.m</a>,
prints some of an I4MAT transposed.
</li>
<li>
<a href = "ksub_random.m">ksub_random.m</a>,
returns a random subset of K items from a set of N items.
</li>
<li>
<a href = "r8mat_transpose_print.m">r8mat_transpose_print.m</a>,
prints an R8MAT transposed.
</li>
<li>
<a href = "r8mat_transpose_print_some.m">r8mat_transpose_print_some.m</a>,
prints some of an R8MAT transposed.
</li>
<li>
<a href = "simplex_grid_index_all.m">simplex_grid_index_all.m</a>,
returns all the simplex grid indices.
</li>
<li>
<a href = "simplex_grid_index_next.m">simplex_grid_index_next.m</a>,
returns the next simplex grid index.
</li>
<li>
<a href = "simplex_grid_index_sample.m">simplex_grid_index_sample.m</a>,
returns a random simplex grid index.
</li>
<li>
<a href = "simplex_grid_index_to_point.m">simplex_grid_index_to_point.m</a>,
converts a simplex grid index to a physical point.
</li>
<li>
<a href = "simplex_grid_size.m">simplex_grid_size.m</a>,
returns the size of a grid using N subintervals in each of M dimensions.
</li>
<li>
<a href = "timestamp.m">timestamp.m</a>,
prints the current YMDHMS date as a time stamp.
</li>
</ul>
</p>
<h3 align = "center">
Examples and Tests:
</h3>
<p>
<ul>
<li>
<a href = "simplex_grid_test.m">simplex_grid_test.m</a>,
calls all the tests.
</li>
<li>
<a href = "simplex_grid_test_output.txt">simplex_grid_test_output.txt</a>,
the output file.
</li>
<li>
<a href = "simplex_grid_test01.m">simplex_grid_test01.m</a>,
tests simplex_grid_size().
</li>
<li>
<a href = "simplex_grid_test02.m">simplex_grid_test02.m</a>,
tests simplex_grid_index_next().
</li>
<li>
<a href = "simplex_grid_test03.m">simplex_grid_test03.m</a>,
tests simplex_grid_index_sample().
</li>
<li>
<a href = "simplex_grid_test04.m">simplex_grid_test04.m</a>,
tests simplex_grid_index_to_point().
</li>
<li>
<a href = "simplex_grid_test05.m">simplex_grid_test05.m</a>,
tests simplex_grid_index_all().
</li>
<li>
<a href = "simplex_grid_test06.m">simplex_grid_test06.m</a>,
tests simplex_grid_index_all().
</li>
</ul>
</p>
<p>
You can go up one level to <a href = "../m_src.html">
the MATLAB source codes</a>.
</p>
<hr>
<i>
Last revised on 31 July 2014.
</i>
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