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<html>
<head>
<title>
PYRAMID_GRID - Grid of Points Inside a Pyramid in 3D
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">
<h1 align = "center">
PYRAMID_GRID <br> Grid of Points Inside a Pyramid in 3D
</h1>
<hr>
<p>
<b>PYRAMID_GRID</b>
is a MATLAB library which
generates a grid of points
over the interior of a pyramid in 3D.
</p>
<p>
The pyramid has a square base. As it rises, the square cross
section smoothly shrinks to a point. Thus there are five vertices,
of which four are on the square base, and one is the apex. There
are 8 edges, consisting of the four edges of the square, and an
edge joining each base vertex to the apex vertex.
</p>
<p>
The unit pyramid is the set of points (X,Y,Z) such that:
<pre>
- ( 1 - Z ) <= X <= 1 - Z
- ( 1 - Z ) <= Y <= 1 - Z
0 <= Z <= 1.
</pre>
</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>PYRAMID_GRID</b> is available in
<a href = "../../c_src/pyramid_grid/pyramid_grid.html">a C version</a> and
<a href = "../../cpp_src/pyramid_grid/pyramid_grid.html">a C++ version</a> and
<a href = "../../f77_src/pyramid_grid/pyramid_grid.html">a FORTRAN77 version</a> and
<a href = "../../f_src/pyramid_grid/pyramid_grid.html">a FORTRAN90 version</a> and
<a href = "../../m_src/pyramid_grid/pyramid_grid.html">a MATLAB version</a> and
<a href = "../../py_src/pyramid_grid/pyramid_grid.html">a Python version</a>.
</p>
<h3 align = "center">
Related Data and Programs:
</h3>
<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 a grid of points
over the length of a circular arc in 2D;
</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
over the interior of an ellipsoid in 3D.
</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_exactness/pyramid_exactness.html">
PYRAMID_EXACTNESS</a>,
a MATLAB program which
investigates the monomial exactness of a quadrature rule
over the interior of the unit pyramid in 3D.
</p>
<p>
<a href = "../../m_src/pyramid_integrals/pyramid_integrals.html">
PYRAMID_INTEGRALS</a>,
a MATLAB library which
returns the exact value of the integral of any monomial
over the interior of the unit pyramid in 3D.
</p>
<p>
<a href = "../../m_src/pyramid_monte_carlo/pyramid_monte_carlo.html">
PYRAMID_MONTE_CARLO</a>,
a MATLAB library which
applies a Monte Carlo method to estimate integrals of a function
over the interior of the unit pyramid in 3D;
</p>
<p>
<a href = "../../m_src/pyramid_rule/pyramid_rule.html">
PYRAMID_RULE</a>,
a MATLAB program which
computes a quadrature rule
over the interior of the unit pyramid in 3D;
</p>
<p>
<a href = "../../m_src/simplex_grid/simplex_grid.html">
SIMPLEX_GRID</a>,
a MATLAB library which
generates a grid of points
over the interior of a 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 = "pyramid_grid_size.m">pyramid_grid_size.m</a>,
sizes a pyramid grid.
</li>
<li>
<a href = "pyramid_unit_grid.m">pyramid_unit_grid.m</a>,
computes grid points in the unit pyramid.
</li>
<li>
<a href = "pyramid_unit_grid_plot.m">pyramid_unit_grid_plot.m</a>,
sets up a GNUPLOT plot of a unit pyramid grid.
</li>
<li>
<a href = "pyramid_unit_vertices.m">pyramid_unit_vertices.m</a>,
returns the vertices of the unit pyramid.
</li>
<li>
<a href = "r8_print.m">r8_print.m</a>,
prints an R8.
</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 = "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 = "pyramid_grid_test.m">pyramid_grid_test.m</a>,
a sample calling program.
</li>
<li>
<a href = "pyramid_grid_test01.m">pyramid_grid_test01.m</a>,
computes the grid size for various values of N.
</li>
<li>
<a href = "pyramid_grid_test02.m">pyramid_grid_test02.m</a>,
computes a grid.
</li>
<li>
<a href = "pyramid_grid_test03.m">pyramid_grid_test03.m</a>,
computes a grid and creates a plot of it.
</li>
<li>
<a href = "pyramid_grid_test_output.txt">pyramid_grid_test_output.txt</a>,
the output file.
</li>
</ul>
</p>
<p>
PYRAMID_UNIT is a set of data defining a GNUPLOT image of a grid on
a unit pyramid.
<ul>
<li>
<a href = "pyramid_unit_commands.txt">pyramid_unit_commands.txt</a>,
a file of commands to be input to gnuplot.
</li>
<li>
<a href = "pyramid_unit_nodes.txt">pyramid_unit_nodes.txt</a>,
a file containing the coordinates of the grid points.
</li>
<li>
<a href = "pyramid_unit_vertices.txt">pyramid_unit_vertices.txt</a>,
a file containing the coordinates of the pyramid vertices.
</li>
<li>
<a href = "pyramid_unit.png">pyramid_unit.png</a>,
an image of the grid.
</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 14 August 2014.
</i>
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</html>