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<html>
<head>
<title>
SPHERE_LEBEDEV_RULE_DISPLAY -
Display Sphere + 3D Lebedev Quadrature Points in the MATLAB Graphics Window
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">
<h1 align = "center">
SPHERE_LEBEDEV_RULE_DISPLAY <br>
Display Sphere + 3D Lebedev Quadrature Points <br>
in the MATLAB Graphics Window
</h1>
<hr>
<p>
<b>SPHERE_LEBEDEV_RULE_DISPLAY</b>
is a MATLAB program which
reads the name of a data file
defining a Lebedev quadrature rule for the sphere,
reads the file, creates an "XYZ" file containing the coordinates
of the quadrature poins, and then
and displays a unit sphere and the points in the MATLAB graphics window.
</p>
<p>
The Lebedev quadrature rule file contains a table of values of theta,
phi, and weights. The angles are measured in degrees. So it is helpful
to have this program read the data, convert angles to radians, compute
the XYZ coordinates (and save the values in a file) and then display
the point set.
</p>
<h3 align = "center">
Usage:
</h3>
<p>
<blockquote>
<b>sphere_lebedev_rule_display</b> ( <i>'prefix'</i> )
</blockquote>
where
<ul>
<li>
<i>'prefix'</i> is the prefix of the file containing the
Lebedev rule. If the file was 'lebedev_041.txt', then
the prefix would be 'lebedev_041'. The XYZ file that is
created will use the same prefix, followed by '.xyz'.
</li>
</ul>
</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>SPHERE_LEBEDEV_RULE_DISPLAY</b> is available in
<a href = "../../m_src/sphere_lebedev_rule_display/sphere_lebedev_rule_display.html">a MATLAB version</a>.
</p>
<h3 align = "center">
Related Data and Programs:
</h3>
<p>
<a href = "../../m_src/ball_and_stick_display/ball_and_stick_display.html">
BALL_AND_STICK_DISPLAY</a>,
a MATLAB program which
demonstrates the creation of a 3D "ball and stick" image;
</p>
<p>
<a href = "../../m_src/mpas_grid_display/mpas_grid_display.html">
MPAS_GRID_DISPLAY</a>,
MATLAB programs which
can read an MPAS NETCDF grid file and display the primary polygonal
mesh or the dual triangular mesh.
</p>
<p>
<a href = "../../m_src/quad_surface_display/quad_surface_display.html">
QUAD_SURFACE_DISPLAY</a>,
a MATLAB program which
reads files defining a 3D quadrilateral mesh surface and displays it
within MATLAB.
</p>
<p>
<a href = "../../m_src/sphere_cvt/sphere_cvt.html">
SPHERE_CVT</a>,
a MATLAB library which
creates a mesh of well-separated points on a unit sphere by applying the
Centroidal Voronoi Tessellation (CVT) iteration.
</p>
<p>
<a href = "../../m_src/sphere_delaunay/sphere_delaunay.html">
SPHERE_DELAUNAY</a>,
a MATLAB program which
computes the Delaunay triangulation of points on a sphere.
</p>
<p>
<a href = "../../f_src/sphere_design_rule/sphere_design_rule.html">
SPHERE_DESIGN_RULE</a>,
a FORTRAN90 library which
returns point sets on the surface of the unit sphere, known as "designs",
which can be useful for estimating integrals on the surface, among other uses.
</p>
<p>
<a href = "../../datasets/sphere_grid/sphere_grid.html">
SPHERE_GRID</a>,
a dataset directory which
contains grids of points, lines, triangles or quadrilaterals on a sphere;
</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, over the unit sphere.
</p>
<p>
<a href = "../../m_src/sphere_lebedev_rule/sphere_lebedev_rule.html">
SPHERE_LEBEDEV_RULE</a>,
a MATLAB library which
computes Lebedev quadrature rules for the unit sphere;
</p>
<p>
<a href = "../../m_src/sphere_voronoi/sphere_voronoi.html">
SPHERE_VORONOI</a>,
a MATLAB program which
computes the Voronoi diagram of points on a sphere.
</p>
<p>
<a href = "../../cpp_src/sphere_voronoi_display_opengl/sphere_voronoi_display_opengl.html">
SPHERE_VORONOI_DISPLAY_OPENGL</a>,
a C++ program which
displays a sphere and randomly selected generator points, and then
gradually colors in points in the sphere that are closest to each generator.
</p>
<p>
<a href = "../../m_src/sphere_xyz_display/sphere_xyz_display.html">
SPHERE_XYZ_DISPLAY</a>,
a MATLAB program which
reads XYZ information defining points in 3D,
and displays a unit sphere and the points in the MATLAB 3D graphics window.
</p>
<p>
<a href = "../../cpp_src/sphere_xyz_display_opengl/sphere_xyz_display_opengl.html">
SPHERE_XYZ_DISPLAY_OPENGL</a>,
a C++ program which
reads XYZ information defining points in 3D,
and displays a unit sphere and the points, using OpenGL.
</p>
<p>
<a href = "../../m_src/sphere_xyzf_display/sphere_xyzf_display.html">
SPHERE_XYZF_DISPLAY</a>,
a MATLAB program which
reads XYZF information defining points and faces,
and displays a unit sphere, the points, and the faces,
in the MATLAB graphics window. This can be used, for instance, to
display Voronoi diagrams or Delaunay triangulations on the unit sphere.
</p>
<p>
<a href = "../../m_src/tri_surface_display/tri_surface_display.html">
TRI_SURFACE_DISPLAY</a>,
a MATLAB program which
reads data defining a triangular mesh of a 3D surface and displays it.
</p>
<p>
<a href = "../../m_src/xyz_display/xyz_display.html">
XYZ_DISPLAY</a>,
a MATLAB program which
reads XYZ information defining points in 3D,
and displays an image in the MATLAB graphics window.
</p>
<p>
<a href = "../../cpp_src/xyz_display_opengl/xyz_display_opengl.html">
XYZ_DISPLAY_OPENGL</a>,
a C++ program which
reads a set of 3D points from
a file and plots them in an OpenGL graphics window.
</p>
<h3 align = "center">
Source Code:
</h3>
<p>
<ul>
<li>
<a href = "sphere_lebedev_rule_display.m">sphere_lebedev_rule_display.m</a>
the source code.
</li>
<li>
<a href = "sphere_xyz_display.m">sphere_xyz_display.m</a>
code called by the main source code to display the final plot.
</li>
</ul>
</p>
<h3 align = "center">
Examples and Tests:
</h3>
<p>
<ul>
<li>
<a href = "lebedev_009.txt">lebedev_009.txt</a>, 38 point rule, precision 9.
</li>
<li>
<a href = "lebedev_009.png">lebedev_009.png</a>,
a snapshot of the 3D image.
</li>
<li>
<a href = "lebedev_013.txt">lebedev_013.txt</a>, 74 point rule, precision 13.
</li>
<li>
<a href = "lebedev_013.png">lebedev_013.png</a>,
a snapshot of the 3D image.
</li>
<li>
<a href = "lebedev_025.txt">lebedev_025.txt</a>, 230 point rule, precision 25.
</li>
<li>
<a href = "lebedev_025.png">lebedev_025.png</a>,
a snapshot of the 3D image.
</li>
<li>
<a href = "lebedev_041.txt">lebedev_041.txt</a>, 590 point rule, precision 41.
</li>
<li>
<a href = "lebedev_041.png">lebedev_041.png</a>,
a snapshot of the 3D image.
</li>
<li>
<a href = "lebedev_071.txt">lebedev_071.txt</a>, 1730 point rule, precision 71.
</li>
<li>
<a href = "lebedev_071.png">lebedev_071.png</a>,
a snapshot of the 3D image.
</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 09 September 2010.
</i>
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