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<html>
<head>
<title>
POLYGON_PROPERTIES - Compute Properties of an Arbitrary Polygon
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">
<h1 align = "center">
POLYGON_PROPERTIES <br> Compute Properties of an Arbitrary Polygon
</h1>
<hr>
<p>
<b>POLYGON_PROPERTIES</b>
is a C++ 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">
Licensing:
</h3>
<p>
The computer code and data files 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_PROPERTIES</b> is available in
<a href = "../../c_src/polygon_properties/polygon_properties.html">a C version</a> and
<a href = "../../cpp_src/polygon_properties/polygon_properties.html">a C++ version</a> and
<a href = "../../f77_src/polygon_properties/polygon_properties.html">a FORTRAN77 version</a> and
<a href = "../../f_src/polygon_properties/polygon_properties.html">a FORTRAN90 version</a> and
<a href = "../../m_src/polygon_properties/polygon_properties.html">a MATLAB version</a>.
</p>
<h3 align = "center">
Related Data and Programs:
</h3>
<p>
<a href = "../../cpp_src/geometry/geometry.html">
GEOMETRY</a>,
a C++ library which
performs geometric calculations in 2, 3 and N dimensional space.
</p>
<p>
<a href = "../../cpp_src/hypersphere_properties/hypersphere_properties.html">
HYPERSPHERE_PROPERTIES</a>,
a C++ 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 = "../../cpp_src/polygon_integrals/polygon_integrals.html">
POLYGON_INTEGRALS</a>,
a C++ library which
returns the exact value of the integral of any monomial
over the interior of a polygon in 2D.
</p>
<p>
<a href = "../../cpp_src/polygon_monte_carlo/polygon_monte_carlo.html">
POLYGON_MONTE_CARLO</a>,
a C++ 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 = "../../cpp_src/polygon_triangulate/polygon_triangulate.html">
POLYGON_TRIANGULATE</a>,
a C++ library which
triangulates a possibly nonconvex polygon,
and which can use gnuplot to display the external edges and
internal diagonals of the triangulation.
</p>
<p>
<a href = "../../cpp_src/tetrahedron_properties/tetrahedron_properties.html">
TETRAHEDRON_PROPERTIES</a>,
a C++ program which
computes properties of a given tetrahedron.
</p>
<p>
<a href = "../../cpp_src/triangle_properties/triangle_properties.html">
TRIANGLE_PROPERTIES</a>,
a C++ program which
computes properties of a triangle whose vertex coordinates
are read from a file.
</p>
<h3 align = "center">
Reference:
</h3>
<p>
<ol>
<li>
Gerard Bashein, Paul Detmer,<br>
Centroid of a Polygon,<br>
in Graphics Gems IV,<br>
edited by Paul Heckbert,<br>
AP Professional, 1994,<br>
ISBN: 0123361559,<br>
LC: T385.G6974.
</li>
<li>
SF Bockman,<br>
Generalizing the Formula for Areas of Polygons to Moments,<br>
American Mathematical Society Monthly,<br>
Volume 96, Number 2, February 1989, pages 131-132.
</li>
<li>
Adrian Bowyer, John Woodwark,<br>
A Programmer's Geometry,<br>
Butterworths, 1983,<br>
ISBN: 0408012420.
</li>
<li>
Peter Schorn, Frederick Fisher,<br>
Testing the Convexity of a Polygon,<br>
in Graphics Gems IV,<br>
edited by Paul Heckbert,<br>
AP Professional, 1994,<br>
ISBN: 0123361559,<br>
LC: T385.G6974.
</li>
<li>
Moshe Shimrat,<br>
Algorithm 112:
Position of Point Relative to Polygon,<br>
Communications of the ACM,<br>
Volume 5, Number 8, August 1962, page 434.
</li>
<li>
Allen VanGelder,<br>
Efficient Computation of Polygon Area and Polyhedron Volume,<br>
in Graphics Gems V, <br>
edited by Alan Paeth,<br>
AP Professional, 1995,<br>
ISBN: 0125434553,<br>
LC: T385.G6975.
</li>
</ol>
</p>
<h3 align = "center">
Source Code:
</h3>
<p>
<ul>
<li>
<a href = "polygon_properties.cpp">polygon_properties.cpp</a>, the source code.
</li>
<li>
<a href = "polygon_properties.hpp">polygon_properties.hpp</a>, the include file.
</li>
<li>
<a href = "polygon_properties.sh">polygon_properties.sh</a>,
BASH commands to compile the source code.
</li>
</ul>
</p>
<h3 align = "center">
Examples and Tests:
</h3>
<p>
<ul>
<li>
<a href = "polygon_properties_prb.cpp">polygon_properties_prb.cppa>,
a sample calling program.
</li>
<li>
<a href = "polygon_properties_prb.sh">polygon_properties_prb.sh</a>,
BASH commands to compile and run the sample program.
</li>
<li>
<a href = "polygon_properties_prb_output.txt">polygon_properties_prb_output.txt</a>,
the output file.
</li>
</ul>
</p>
<h3 align = "center">
List of Routines:
</h3>
<p>
<ul>
<li>
<b>ANGLE_HALF</b> finds half an angle.
</li>
<li>
<b>ANGLE_RAD</b> returns the angle in radians swept out between two rays.
</li>
<li>
<b>I4_MODP</b> returns the nonnegative remainder of I4 division.
</li>
<li>
<b>I4_WRAP</b> forces an I4 to lie between given limits by wrapping.
</li>
<li>
<b>POLYGON_ANGLES</b> computes the interior angles of a polygon.
</li>
<li>
<b>POLYGON_AREA</b> computes the area of a polygon.
</li>
<li>
<b>POLYGON_AREA_2</b> computes the area of a polygon.
</li>
<li>
<b>POLYGON_CENTROID</b> computes the centroid of a polygon.
</li>
<li>
<b>POLYGON_CENTROID_2</b> computes the centroid of a polygon.
</li>
<li>
<b>POLYGON_CONTAINS_POINT</b> finds if a point is inside a simple polygon.
</li>
<li>
<b>POLYGON_CONTAINS_POINT_2:</b> is a point inside a convex polygon.
</li>
<li>
<b>POLYGON_DIAMETER</b> computes the diameter of a polygon.
</li>
<li>
<b>POLYGON_EXPAND</b> expands a polygon.
</li>
<li>
<b>POLYGON_INRAD_DATA</b> determines polygonal data from its inner radius.
</li>
<li>
<b>POLYGON_INTEGRAL_1</b> integrates the function 1 over a polygon.
</li>
<li>
<b>POLYGON_INTEGRAL_X</b> integrates the function X over a polygon.
</li>
<li>
<b>POLYGON_INTEGRAL_XX</b> integrates the function X*X over a polygon.
</li>
<li>
<b>POLYGON_INTEGRAL_XY</b> integrates the function X*Y over a polygon.
</li>
<li>
<b>POLYGON_INTEGRAL_Y</b> integrates the function Y over a polygon.
</li>
<li>
<b>POLYGON_INTEGRAL_YY</b> integrates the function Y*Y over a polygon.
</li>
<li>
<b>POLYGON_IS_CONVEX</b> determines whether a polygon is convex.
</li>
<li>
<b>POLYGON_LATTICE_AREA</b> computes the area of a lattice polygon.
</li>
<li>
<b>POLYGON_OUTRAD_DATA</b> determines polygonal data from its outer radius.
</li>
<li>
<b>POLYGON_POINT_DIST:</b> distance ( polygon, point ).
</li>
<li>
<b>POLYGON_POINT_NEAR</b> computes the nearest point on a polygon.
</li>
<li>
<b>POLYGON_SIDE_DATA</b> determines polygonal data from its side length.
</li>
<li>
<b>R8_DEGREES</b> converts an angle from radian to degree measure.
</li>
<li>
<b>R8MAT_SOLVE</b> uses Gauss-Jordan elimination to solve an N by N linear system.
</li>
<li>
<b>R8MAT_TRANSPOSE_PRINT</b> prints an R8MAT, transposed.
</li>
<li>
<b>R8MAT_TRANSPOSE_PRINT_SOME</b> prints some of an R8MAT, transposed.
</li>
<li>
<b>R8VEC_PRINT</b> prints an R8VEC.
</li>
<li>
<b>SEGMENT_POINT_DIST:</b> distance ( line segment, point ).
</li>
<li>
<b>SEGMENT_POINT_NEAR:</b> nearest point on line segment to point.
</li>
<li>
<b>TIMESTAMP</b> prints the current YMDHMS date as a time stamp.
</li>
<li>
<b>TRIANGLE_AREA</b> computes the area of a triangle.
</li>
<li>
<b>TRIANGLE_BARYCENTRIC</b> finds the barycentric coordinates of a point.
</li>
<li>
<b>TRIANGLE_CONTAINS_POINT_1</b> finds if a point is inside a triangle.
</li>
</ul>
</p>
<p>
You can go up one level to <a href = "../cpp_src.html">
the C++ source codes</a>.
</p>
<hr>
<i>
Last revised on 09 May 2014.
</i>
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