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<html>
<head>
<title>
POLYGON_TRIANGULATE - Triangulate a Polygon
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">
<h1 align = "center">
POLYGON_TRIANGULATE <br> Triangulate a Polygon
</h1>
<hr>
<p>
<b>POLYGON_TRIANGULATE</b>
is a MATLAB library which
triangulates a polygon in 2D.
</p>
<p>
The polygon is defined by an input file which gives the coordinates
of the vertices of the polygon, in counterclockwise order.
</p>
<p>
No consecutive pair of vertices should be equal; when describing a
polygon, sometimes the first and last vertices are equal. For this
program, that is not the case. To describe a square, your input
file should contain four pairs of coordinates, for instance.
</p>
<p>
The vertices should be listed in counterclockwise order. If you list
them in clockwise order, then the function will refuse to operate
on the data.
</p>
<p>
It is possible to create a polygon that has zero area. The function
will refuse to process such an object.
</p>
<p>
The polygon does not need to be convex. However, you should be careful
not to specify a polygon which crosses itself, since this means the
interior of the polygon is not well defined, and hence a triangulation
is not well defined. As a simple example of such a problem, consider
the four vertices of a square in counterclockwise order: V1, V2, V3, V4,
and list them instead as V1, V3, V2, V4. This shape cannot be
triangulated in the usual sense. However, the function may not
realize this, in which case it will return what it thinks is a
reasonable triangulation of the (unreasonable) data.
</p>
<p>
The output of the program is a list of the N-3 triples of nodes that
form the triangles of the triangulation.
</p>
<h3 align = "center">
Usage:
</h3>
<p>
<blockquote>
<i>triangles</i> = <b>polygon_triangulate</b> ( <i>n</i>, <i>x</i>, <i>y</i> )
</blockquote>
where
<ul>
<li>
<i>n</i> is the number of vertices,
</li>
<li>
<i>x</i> is the X coordinates of the vertices,
</li>
<li>
<i>y</i> is the Y coordinates of the vertices,
</li>
</ul>
returning
<ul>
<li>
<i>triangles</i>, which are <i>n-2</i> triples of vertex indices that
form the triangles of the triangulation.
</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>POLYGON_TRIANGULATE</b> is available in
<a href = "../../c_src/polygon_triangulate/polygon_triangulate.html">a C version</a> and
<a href = "../../cpp_src/polygon_triangulate/polygon_triangulate.html">a C++ version</a> and
<a href = "../../f77_src/polygon_triangulate/polygon_triangulate.html">a FORTRAN77 version</a> and
<a href = "../../f_src/polygon_triangulate/polygon_triangulate.html">a FORTRAN90 version</a> and
<a href = "../../m_src/polygon_triangulate/polygon_triangulate.html">a MATLAB version</a>.
</p>
<h3 align = "center">
Related Data and Programs:
</h3>
<p>
<a href = "../../m_src/convex_hull/convex_hull.html">
CONVEX_HULL</a>,
a MATLAB program which
demonstrates the computation of the convex hull of a set of 2D points.
</p>
<p>
<a href = "../../m_src/hand_data/hand_data.html">
HAND_DATA</a>,
MATLAB programs which
carry out some numerical exercises based on data that came from
tracing several points on a person's hand.
</p>
<p>
<a href = "../../m_src/polygon_integrals/polygon_integrals.html">
POLYGON_INTEGRALS</a>,
a MATLAB library which
returns the exact value of the integral of any monomial
over the interior of a polygon in 2D.
</p>
<p>
<a href = "../../m_src/polygon_monte_carlo/polygon_monte_carlo.html">
POLYGON_MONTE_CARLO</a>,
a MATLAB library which
applies a Monte Carlo method to estimate the integral of a function
over the interior of a polygon in 2D.
</p>
<p>
<a href = "../../m_src/polygon_properties/polygon_properties.html">
POLYGON_PROPERTIES</a>,
a MATLAB library which
computes properties of an arbitrary polygon in the plane, defined
by a sequence of vertices, including interior angles, area, centroid,
containment of a point, convexity, diameter, distance to a point,
inradius, lattice area, nearest point in set, outradius, uniform sampling.
</p>
<h3 align = "center">
Author:
</h3>
<p>
Based on a C function by Joseph ORourke;
MATLAB version by John Burkardt.
</p>
<h3 align = "center">
Reference:
</h3>
<p>
<ul>
<li>
Joseph ORourke,<br>
Computational Geometry in C,<br>
Second Edition,<br>
Cambridge, 1998,<br>
ISBN: 0521649765,<br>
LC: QA448.D38.
</li>
</ul>
</p>
<h3 align = "center">
Source Code:
</h3>
<p>
<ul>
<li>
<a href = "polygon_triangulate.m">polygon_triangulate.m</a>
the source code.
</li>
</ul>
</p>
<h3 align = "center">
Examples and Tests:
</h3>
<p>
<ul>
<li>
<a href = "polygon_triangulate_test.m">polygon_triangulate_test.m</a>
a sample calling program.
</li>
<li>
<a href = "polygon_triangulate_test_output.txt">polygon_triangulate_test_output.txt</a>
the output file.
</li>
</ul>
</p>
<p>
<b>COMB</b> is an example of a "comb" polygon of 10 vertices
<ul>
<li>
<a href = "comb_nodes.txt">comb_nodes.txt</a>,
the vertex coordinates.
</li>
<li>
<a href = "comb_elements.txt">comb_elements.txt</a>,
the triangles that make up the polygon.
</li>
<li>
<a href = "comb.png">comb.png</a>,
a PNG image of the triangulated polygon.
</li>
</ul>
</p>
<p>
<b>HAND</b> outlines a hand using 59 vertices.
<ul>
<li>
<a href = "hand_nodes.txt">hand_nodes.txt</a>,
the vertex coordinates.
</li>
<li>
<a href = "hand_elements.txt">hand_elements.txt</a>,
the triangles that make up the polygon.
</li>
<li>
<a href = "hand.png">hand.png</a>,
a PNG image of the triangulated polygon.
</li>
</ul>
</p>
<p>
<b>I18</b> is an example of a complicated nonconvex polygon, using 18 vertices.
<ul>
<li>
<a href = "i18_nodes.txt">i18_nodes.txt</a>,
the vertex coordinates.
</li>
<li>
<a href = "i18_elements.txt">i18_elements.txt</a>,
the triangles that make up the polygon.
</li>
<li>
<a href = "i18.png">i18.png</a>,
a PNG image of the triangulated polygon.
</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 04 May 2014.
</i>
<!-- John Burkardt -->
</body>
</html>