<html lang="en">
<head>
<title>Convex Hull - GNU Octave</title>
<meta http-equiv="Content-Type" content="text/html">
<meta name="description" content="GNU Octave">
<meta name="generator" content="makeinfo 4.13">
<link title="Top" rel="start" href="index.html#Top">
<link rel="up" href="Geometry.html#Geometry" title="Geometry">
<link rel="prev" href="Voronoi-Diagrams.html#Voronoi-Diagrams" title="Voronoi Diagrams">
<link rel="next" href="Interpolation-on-Scattered-Data.html#Interpolation-on-Scattered-Data" title="Interpolation on Scattered Data">
<link href="http://www.gnu.org/software/texinfo/" rel="generator-home" title="Texinfo Homepage">
<meta http-equiv="Content-Style-Type" content="text/css">
<style type="text/css"><!--
pre.display { font-family:inherit }
pre.format { font-family:inherit }
pre.smalldisplay { font-family:inherit; font-size:smaller }
pre.smallformat { font-family:inherit; font-size:smaller }
pre.smallexample { font-size:smaller }
pre.smalllisp { font-size:smaller }
span.sc { font-variant:small-caps }
span.roman { font-family:serif; font-weight:normal; }
span.sansserif { font-family:sans-serif; font-weight:normal; }
--></style>
</head>
<body>
<div class="node">
<a name="Convex-Hull"></a>
<p>
Next: <a rel="next" accesskey="n" href="Interpolation-on-Scattered-Data.html#Interpolation-on-Scattered-Data">Interpolation on Scattered Data</a>,
Previous: <a rel="previous" accesskey="p" href="Voronoi-Diagrams.html#Voronoi-Diagrams">Voronoi Diagrams</a>,
Up: <a rel="up" accesskey="u" href="Geometry.html#Geometry">Geometry</a>
<hr>
</div>
<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.
<!-- convhull scripts/geometry/convhull.m -->
<p><a name="doc_002dconvhull"></a>
<div class="defun">
— Function File: <var>H</var> = <b>convhull</b> (<var>x, y</var>)<var><a name="index-convhull-2809"></a></var><br>
— Function File: <var>H</var> = <b>convhull</b> (<var>x, y, options</var>)<var><a name="index-convhull-2810"></a></var><br>
<blockquote><p>Compute the convex hull of the set of points defined by the
vectors <var>x</var> and <var>y</var>. The hull <var>H</var> is an index vector into
the set of points and specifies which points form the enclosing hull.
<p>An optional third 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>{"Qt"}</code>.
<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.
<!-- Texinfo @sp should work but in practice produces ugly results for HTML. -->
<!-- A simple blank line produces the correct behavior. -->
<!-- @sp 1 -->
<p class="noindent"><strong>See also:</strong> <a href="doc_002dconvhulln.html#doc_002dconvhulln">convhulln</a>, <a href="doc_002ddelaunay.html#doc_002ddelaunay">delaunay</a>, <a href="doc_002dvoronoi.html#doc_002dvoronoi">voronoi</a>.
</p></blockquote></div>
<!-- convhulln src/DLD-FUNCTIONS/convhulln.cc -->
<p><a name="doc_002dconvhulln"></a>
<div class="defun">
— Loadable Function: <var>h</var> = <b>convhulln</b> (<var>pts</var>)<var><a name="index-convhulln-2811"></a></var><br>
— Loadable Function: <var>h</var> = <b>convhulln</b> (<var>pts, options</var>)<var><a name="index-convhulln-2812"></a></var><br>
— Loadable Function: [<var>h</var>, <var>v</var>] = <b>convhulln</b> (<var><small class="dots">...</small></var>)<var><a name="index-convhulln-2813"></a></var><br>
<blockquote><p>Compute the convex hull of the set of points <var>pts</var> which is a matrix
of size [n, dim] containing n points in a space of dimension dim.
The hull <var>h</var> is an index vector into the set of points and specifies
which points form the enclosing hull.
<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:
<ul>
<li>2D, 3D, 4D: <var>options</var> = <code>{"Qt"}</code>
<li>5D and higher: <var>options</var> = <code>{"Qt", "Qx"}</code>
</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>If the second output <var>v</var> is requested the volume of the enclosing
convex hull is calculated.
<!-- Texinfo @sp should work but in practice produces ugly results for HTML. -->
<!-- A simple blank line produces the correct behavior. -->
<!-- @sp 1 -->
<p class="noindent"><strong>See also:</strong> <a href="doc_002dconvhull.html#doc_002dconvhull">convhull</a>, <a href="doc_002ddelaunayn.html#doc_002ddelaunayn">delaunayn</a>, <a href="doc_002dvoronoin.html#doc_002dvoronoin">voronoin</a>.
</p></blockquote></div>
<p>An example of the use of <code>convhull</code> is
<pre class="example"> x = -3:0.05:3;
y = abs (sin (x));
k = convhull (x, y);
plot (x(k), y(k), "r-", x, y, "b+");
axis ([-3.05, 3.05, -0.05, 1.05]);
</pre>
<p class="noindent">The output of the above can be seen in <a href="fig_003aconvhull.html#fig_003aconvhull">fig:convhull</a>.
<div class="float">
<a name="fig_003aconvhull"></a><div align="center"><img src="convhull.png" alt="convhull.png"></div>
<p><strong class="float-caption">Figure 30.5: The convex hull of a simple set of points</strong></p></div>
</body></html>
