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<html>
<head>
<title>
HYPERSPHERE_SURFACE - Estimate Hypersurface Location
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">
<h1 align = "center">
HYPERSPHERE_SURFACE <br> Estimate Hypersurface Location
</h1>
<hr>
<p>
<b>HYPERSPHERE_SURFACE</b>
is a MATLAB library which
investigates a procedure for estimating the location of points on a
hypersurface implicitly defined by a characteristic function or by
a signed function.
</p>
<p>
In M dimensions, a characteristic function F for a region of points S
has the property that F(X) is 1 for points inside S, and 0
otherwise. A characteristic function is thus discontinous.
The set of discontinuity points for F is the boundary of S.
</p>
<p>
In M dimensions, suppose that the function F, presumably continuous,
takes on both positive and negative values. Then we may be interested
in the set of points X such that F(X) = 0, which we regard as the
boundary between the sets where F is negative or positive. Assuming
that F is continuous, or better yet, differentiable, then this boundary
may be substantially easier to locate than in the characteristic function
case.
</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>HYPERSPHERE_SURFACE</b> is available in
<a href = "../../m_src/hypersphere_surface/hypersphere_surface.html">a MATLAB version.</a>
</p>
<h3 align = "center">
Related Data and Programs:
</h3>
<p>
<a href = "../../m_src/edge/edge.html">
EDGE</a>,
a MATLAB library which
defines some test functions in 1D, 2D and 3D for the detection of edges.
</p>
<p>
<a href = "../../m_src/hypersphere_properties/hypersphere_properties.html">
HYPERSPHERE_PROPERTIES</a>,
a MATLAB library which
carries out various operations for an M-dimensional hypersphere, including
converting between Cartesian and spherical coordinates,
stereographic projection, sampling the surface of the sphere, and
computing the surface area and volume.
</p>
<p>
<a href = "../../m_src/levels/levels.html">
LEVELS</a>,
a MATLAB library which
makes a contour plot, choosing the contour levels using random sampling.
</p>
<p>
<a href = "../../m_src/shoreline/shoreline.html">
SHORELINE</a>,
a MATLAB program which
tries to identify and triangulate the 2D domain over which some
function f(x,y) is nonnegative.
</p>
<p>
<a href = "../../m_src/shoreline2/shoreline2.html">
SHORELINE2</a>,
a MATLAB program which
tries to identify and triangulate the 2D domain over which some
function f(x,y) is roughly zero.
</p>
<h3 align = "center">
Reference:
</h3>
<p>
<ol>
</ol>
</p>
<h3 align = "center">
Source Code:
</h3>
<p>
<ul>
<li>
<a href = "bisect_characteristic.m">bisect_characteristic.m</a>,
uses bisection to outline the transition surface for a given
characteristic function.
</li>
<li>
<a href = "cartesian_to_hypersphere.m">cartesian_to_hypersphere.m</a>,
converts from a cartesian to a hypersphere coordinate system.
</li>
<li>
<a href = "circle_characteristic.m">circle_characteristic.m</a>,
a characteristic function for a circle.
</li>
<li>
<a href = "cube_characteristic.m">cube_characteristic.m</a>,
a characteristic function for a cube (any dimension).
</li>
<li>
<a href = "exterior_point_characteristic.m">exterior_point_characteristic.m</a>,
searches for a point that is outside a surface defined
by a characteristic, and for which a base point inside the surface is
given, as well as the desired hypersphere angles of the exterior point.
</li>
<li>
<a href = "hypersphere_to_cartesian.m">hypersphere_to_cartesian.m</a>,
converts from a hypersphere to a cartesian coordinate system.
</li>
<li>
<a href = "interior_point_characteristic.m">interior_point_characteristic.m</a>
searches a hyperrectangle for a point that is inside a surface defined
by a characteristic.
</li>
<li>
<a href = "r8vec_print.m">r8vec_print.m</a>
prints an R8VEC.
</li>
<li>
<a href = "sphere_characteristic.m">sphere_characteristic.m</a>,
a characteristic function for a sphere (any dimension).
</li>
<li>
<a href = "timestamp.m">timestamp.m</a>
prints the YMDHMS date as a timestamp.
</li>
<li>
<a href = "triangle_characteristic.m">triangle_characteristic.m</a>,
a characteristic function for a triangle.
</li>
</ul>
</p>
<h3 align = "center">
Examples and Tests:
</h3>
<p>
<ul>
<li>
<a href = "hypersphere_surface_test.m">hypersphere_surface_test.m</a>,
calls all the tests.
</li>
<li>
<a href = "hypersphere_surface_test_output.txt">
hypersphere_surface_test_output.txt</a>,
the output file.
</li>
<li>
<a href = "exterior_point_characteristic_test.m">
exterior_point_characteristic_test.m</a>,
tests exterior_point_characteristic().
</li>
<li>
<a href = "interior_point_characteristic_test.m">
interior_point_characteristic_test.m</a>,
tests interior_point_characteristic().
</li>
</ul>
</p>
<p>
The <b>circle</b> example works with the characteristic function of
a circle.
<ul>
<li>
<a href = "circle_plots.m">circle_plots.m</a>,
creates plots of the surface and R(Theta) function for a circle,
using a centered and an offcentered base point.
</li>
<li>
<a href = "circle_centered_plot.png">circle_centered_plot.png</a>,
a plot of the radial distance R as a function of angle THETA for a circle
defined by a characteristic function, using a centered base point.
</li>
<li>
<a href = "circle_centered_surface.png">circle_centered_surface.png</a>,
a plot of the transition surface for a circle defined by a characteristic
function, using a centered base point.
</li>
<li>
<a href = "circle_offcentered_plot.png">circle_offcentered_plot.png</a>,
a plot of the radial distance R as a function of angle THETA for a circle
defined by a characteristic function, using an offcentered base point.
</li>
<li>
<a href = "circle_offcentered_surface.png">circle_offcentered_surface.png</a>,
a plot of the transition surface for a circle defined by a characteristic
function, using an offcentered base point.
</li>
</ul>
</p>
<p>
The <b>cube</b> example works with the characteristic function of
a cube.
<ul>
<li>
<a href = "cube_plots.m">cube_plots.m</a>,
creates plots of the surface and R(Theta1,Theta2) function for a cube,
using a centered and an offcentered base point.
</li>
<li>
<a href = "cube_centered_plot.png">cube_centered_plot.png</a>,
a plot of the radial distance R as a function of the angles for a cube
defined by a characteristic function, using a centered base point.
</li>
<li>
<a href = "cube_centered_surface.png">cube_centered_surface.png</a>,
a plot of the transition surface for a cube defined by a characteristic
function, using a centered base point.
</li>
<li>
<a href = "cube_offcentered_plot.png">cube_offcentered_plot.png</a>,
a plot of the radial distance R as a function of the angles for a cube
defined by a characteristic function, using an offcentered base point.
</li>
<li>
<a href = "cube_offcentered_surface.png">cube_offcentered_surface.png</a>,
a plot of the transition surface for a cube defined by a characteristic
function, using an offcentered base point.
</li>
</ul>
</p>
<p>
The <b>sphere</b> example works with the characteristic function of
a sphere.
<ul>
<li>
<a href = "sphere_plots.m">sphere_plots.m</a>,
creates plots of the surface and R(Theta1,Theta2) function for a sphere,
using a centered and an offcentered base point.
</li>
<li>
<a href = "sphere_centered_plot.png">sphere_centered_plot.png</a>,
a plot of the radial distance R as a function of the angles
for a sphere defined by a characteristic function,
using a centered base point.
</li>
<li>
<a href = "sphere_centered_surface.png">sphere_centered_surface.png</a>,
a plot of the transition surface for a sphere defined by a characteristic
function, using a centered base point.
</li>
<li>
<a href = "sphere_offcentered_plot.png">sphere_offcentered_plot.png</a>,
a plot of the radial distance R as a function of the angles for
a sphere defined by a characteristic function,
using an offcentered base point.
</li>
<li>
<a href = "sphere_offcentered_surface.png">sphere_offcentered_surface.png</a>,
a plot of the transition surface for a sphere defined by a characteristic
function, using an offcentered base point.
</li>
</ul>
</p>
<p>
The <b>triangle</b> example works with the characteristic function of
a triangle.
<ul>
<li>
<a href = "triangle_plots.m">triangle_plots.m</a>,
displays plots of the surface and R(Theta) function for a triangle,
using a centered and an offcentered base point.
</li>
<li>
<a href = "triangle_centered_plot.png">triangle_centered_plot.png</a>,
a plot of the radial distance R as a function of angle THETA for a triangle
defined by a characteristic function, using a centered base point.
</li>
<li>
<a href = "triangle_centered_surface.png">triangle_centered_surface.png</a>,
a plot of the transition surface for a triangle defined by a characteristic
function, using a centered base point.
</li>
<li>
<a href = "triangle_offcentered_plot.png">triangle_offcentered_plot.png</a>,
a plot of the radial distance R as a function of angle THETA for a triangle
defined by a characteristic function, using an offcentered base point.
</li>
<li>
<a href = "triangle_offcentered_surface.png">triangle_offcentered_surface.png</a>,
a plot of the transition surface for a triangle defined by a characteristic
function, using an offcentered base point.
</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 05 May 2013.
</i>
<!-- John Burkardt -->
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