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<a name="Convex-Hull"></a>
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<p>
Next: <a href="Interpolation-on-Scattered-Data.html#Interpolation-on-Scattered-Data" accesskey="n" rel="next">Interpolation on Scattered Data</a>, Previous: <a href="Voronoi-Diagrams.html#Voronoi-Diagrams" accesskey="p" rel="prev">Voronoi Diagrams</a>, Up: <a href="Geometry.html#Geometry" accesskey="u" rel="up">Geometry</a> &nbsp; [<a href="index.html#SEC_Contents" title="Table of contents" rel="contents">Contents</a>][<a href="Concept-Index.html#Concept-Index" title="Index" rel="index">Index</a>]</p>
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<a name="Convex-Hull-1"></a>
<h3 class="section">30.3 Convex Hull</h3>

<p>The convex hull of a set of points is the minimum convex envelope
containing all of the points.  Octave has the functions <code>convhull</code>
and <code>convhulln</code> to calculate the convex hull of 2-dimensional and
N-dimensional sets of points.
</p>
<a name="XREFconvhull"></a><dl>
<dt><a name="index-convhull"></a><em><var>H</var> =</em> <strong>convhull</strong> <em>(<var>x</var>, <var>y</var>)</em></dt>
<dt><a name="index-convhull-1"></a><em><var>H</var> =</em> <strong>convhull</strong> <em>(<var>x</var>, <var>y</var>, <var>z</var>)</em></dt>
<dt><a name="index-convhull-2"></a><em><var>H</var> =</em> <strong>convhull</strong> <em>(<var>x</var>)</em></dt>
<dt><a name="index-convhull-3"></a><em><var>H</var> =</em> <strong>convhull</strong> <em>(&hellip;, <var>options</var>)</em></dt>
<dt><a name="index-convhull-4"></a><em>[<var>H</var>, <var>V</var>] =</em> <strong>convhull</strong> <em>(&hellip;)</em></dt>
<dd><p>Compute the convex hull of a 2-D or 3-D set of points.
</p>
<p>The hull <var>H</var> is a linear index vector into the original set of points
that specifies which points form the enclosing hull.  For 2-D inputs only,
the output is ordered in a counterclockwise manner around the hull.
</p>
<p>The input <var>x</var> may also be a matrix with two or three columns where the
first column contains x-data, the second y-data, and the optional third
column contains z-data.
</p>
<p>An optional final argument, which must be a string or cell array of strings,
contains options passed to the underlying qhull command.
See the documentation for the Qhull library for details
<a href="http://www.qhull.org/html/qh-quick.htm#options">http://www.qhull.org/html/qh-quick.htm#options</a>.
The default option is <code>{&quot;Qt&quot;}</code>.
</p>
<p>If <var>options</var> is not present or <code>[]</code> then the default arguments are
used.  Otherwise, <var>options</var> replaces the default argument list.
To append user options to the defaults it is necessary to repeat the
default arguments in <var>options</var>.  Use a null string to pass no arguments.
</p>
<p>If the second output <var>V</var> is requested the volume of the enclosing
convex hull is calculated.
</p>

<p><strong>See also:</strong> <a href="#XREFconvhulln">convhulln</a>, <a href="Delaunay-Triangulation.html#XREFdelaunay">delaunay</a>, <a href="Voronoi-Diagrams.html#XREFvoronoi">voronoi</a>.
</p></dd></dl>


<a name="XREFconvhulln"></a><dl>
<dt><a name="index-convhulln"></a><em><var>h</var> =</em> <strong>convhulln</strong> <em>(<var>pts</var>)</em></dt>
<dt><a name="index-convhulln-1"></a><em><var>h</var> =</em> <strong>convhulln</strong> <em>(<var>pts</var>, <var>options</var>)</em></dt>
<dt><a name="index-convhulln-2"></a><em>[<var>h</var>, <var>v</var>] =</em> <strong>convhulln</strong> <em>(&hellip;)</em></dt>
<dd><p>Compute the convex hull of the set of points <var>pts</var>.
</p>
<p><var>pts</var> is a matrix of size [n, dim] containing n points in a space of
dimension dim.
</p>
<p>The hull <var>h</var> is an index vector into the set of points and specifies
which points form the enclosing hull.
</p>
<p>An optional second argument, which must be a string or cell array of
strings, contains options passed to the underlying qhull command.  See the
documentation for the Qhull library for details
<a href="http://www.qhull.org/html/qh-quick.htm#options">http://www.qhull.org/html/qh-quick.htm#options</a>.
The default options depend on the dimension of the input:
</p>
<ul>
<li> 2D, 3D, 4D: <var>options</var> = <code>{&quot;Qt&quot;}</code>

</li><li> 5D and higher: <var>options</var> = <code>{&quot;Qt&quot;, &quot;Qx&quot;}</code>
</li></ul>

<p>If <var>options</var> is not present or <code>[]</code> then the default arguments are
used.  Otherwise, <var>options</var> replaces the default argument list.
To append user options to the defaults it is necessary to repeat the
default arguments in <var>options</var>.  Use a null string to pass no arguments.
</p>
<p>If the second output <var>v</var> is requested the volume of the enclosing
convex hull is calculated.
</p>
<p><strong>See also:</strong> <a href="#XREFconvhull">convhull</a>, <a href="Delaunay-Triangulation.html#XREFdelaunayn">delaunayn</a>, <a href="Voronoi-Diagrams.html#XREFvoronoin">voronoin</a>.
</p></dd></dl>


<p>An example of the use of <code>convhull</code> is
</p>
<div class="example">
<pre class="example">x = -3:0.05:3;
y = abs (sin (x));
k = convhull (x, y);
plot (x(k), y(k), &quot;r-&quot;, x, y, &quot;b+&quot;);
axis ([-3.05, 3.05, -0.05, 1.05]);
</pre></div>

<p>The output of the above can be seen in <a href="#fig_003aconvhull">Figure 30.5</a>.
</p>
<div class="float"><a name="fig_003aconvhull"></a>
<div align="center"><img src="convhull.png" alt="convhull">
</div>
<div class="float-caption"><p><strong>Figure 30.5: </strong>The convex hull of a simple set of points</p></div></div>
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Next: <a href="Interpolation-on-Scattered-Data.html#Interpolation-on-Scattered-Data" accesskey="n" rel="next">Interpolation on Scattered Data</a>, Previous: <a href="Voronoi-Diagrams.html#Voronoi-Diagrams" accesskey="p" rel="prev">Voronoi Diagrams</a>, Up: <a href="Geometry.html#Geometry" accesskey="u" rel="up">Geometry</a> &nbsp; [<a href="index.html#SEC_Contents" title="Table of contents" rel="contents">Contents</a>][<a href="Concept-Index.html#Concept-Index" title="Index" rel="index">Index</a>]</p>
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