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<html>
<head>
<title>
POLYGON_GRID - Grid Points in a Polygon
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">
<h1 align = "center">
POLYGON_GRID <br> Grid Points in a Polygon
</h1>
<hr>
<p>
<b>POLYGON_GRID</b>
is a C++ library which
generates a grid of points
over the interior of a polygon in 2D.
</p>
<p>
The program relies on a simple idea in which the "vertex centroid"
(average of the vertices) is computed, allowing the polygon to be
triangulated. Each triangle can then easily be gridded. The collection
of triangular grids joins up to form a grid over the polygon, although
the spacing of the the grid points will vary from triangle to triangle.
</p>
<p>
The program really only works properly for convex polygons. If the
polygon is not convex, then the vertex centroid need not lie inside
the polygon, consequently the grid points may also seem misaligned.
</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_GRID</b> is available in
<a href = "../../c_src/polygon_grid/polygon_grid.html">a C version</a> and
<a href = "../../cpp_src/polygon_grid/polygon_grid.html">a C++ version</a> and
<a href = "../../f77_src/polygon_grid/polygon_grid.html">a FORTRAN77 version</a> and
<a href = "../../f_src/polygon_grid/polygon_grid.html">a FORTRAN90 version</a> and
<a href = "../../m_src/polygon_grid/polygon_grid.html">a MATLAB version</a> and
<a href = "../../py_src/polygon_grid/polygon_grid.html">a Python version</a>.
</p>
<h3 align = "center">
Related Data and Programs:
</h3>
<p>
<a href = "../../cpp_src/ball_grid/ball_grid.html">
BALL_GRID</a>,
a C++ library which
computes a grid of points
over the interior of a ball in 3D.
</p>
<p>
<a href = "../../cpp_src/circle_arc_grid/circle_arc_grid.html">
CIRCLE_ARC_GRID</a>,
a C++ program which
computes points equally spaced along a circular arc;
</p>
<p>
<a href = "../../cpp_src/cube_grid/cube_grid.html">
CUBE_GRID</a>,
a C++ library which
computes a grid of points
over the interior of a cube in 3D.
</p>
<p>
<a href = "../../cpp_src/disk_grid/disk_grid.html">
DISK_GRID</a>,
a C++ library which
computes a grid of points
over the interior of a disk in 2D.
</p>
<p>
<a href = "../../cpp_src/ellipse_grid/ellipse_grid.html">
ELLIPSE_GRID</a>,
a C++ library which
computes a grid of points
over the interior of an ellipse in 2D.
</p>
<p>
<a href = "../../cpp_src/ellipsoid_grid/ellipsoid_grid.html">
ELLIPSOID_GRID</a>,
a C++ library which
computes a grid of points
over the interior of an ellipsoid in 3D.
</p>
<p>
<a href = "../../cpp_src/hypercube_grid/hypercube_grid.html">
HYPERCUBE_GRID</a>,
a C++ library which
computes a grid of points
over the interior of a hypercube in M dimensions.
</p>
<p>
<a href = "../../cpp_src/line_grid/line_grid.html">
LINE_GRID</a>,
a C++ library which
computes a grid of points
over the interior of a line segment in 1D.
</p>
<p>
<a href = "../../cpp_src/pyramid_grid/pyramid_grid.html">
PYRAMID_GRID</a>,
a C++ library which
computes a grid of points
over the interior of the unit pyramid in 3D;
</p>
<p>
<a href = "../../cpp_src/simplex_grid/simplex_grid.html">
SIMPLEX_GRID</a>,
a C++ library which
generates a grid of points
over the interior of a simplex in M dimensions.
</p>
<p>
<a href = "../../cpp_src/sphere_fibonacci_grid/sphere_fibonacci_grid.html">
SPHERE_FIBONACCI_GRID</a>,
a C++ library which
uses a Fibonacci spiral to create a grid of points
on the surface of the unit sphere in 3D.
</p>
<p>
<a href = "../../cpp_src/sphere_grid/sphere_grid.html">
SPHERE_GRID</a>,
a C++ library which
provides a number of ways of generating grids of points, or of
points and lines, or of points and lines and faces,
on the surface of the unit sphere in 3D.
</p>
<p>
<a href = "../../cpp_src/sphere_llq_grid/sphere_llq_grid.html">
SPHERE_LLQ_GRID</a>,
a C++ library which
uses longitudes and latitudes to create grids of points,
lines, and quadrilaterals
on the surface of the unit sphere in 3D.
</p>
<p>
<a href = "../../cpp_src/sphere_llt_grid/sphere_llt_grid.html">
SPHERE_LLT_GRID</a>,
a C++ library which
uses longitudes and latitudes to create grids of points,
lines, and triangles
on the surface of the unit sphere in 3D.
</p>
<p>
<a href = "../../cpp_src/square_grid/square_grid.html">
SQUARE_GRID</a>,
a C++ library which
computes a grid of points
over the interior of a square in 2D.
</p>
<p>
<a href = "../../cpp_src/tetrahedron_grid/tetrahedron_grid.html">
TETRAHEDRON_GRID</a>,
a C++ library which
computes a grid of points
over the interior of a tetrahedron in 3D.
</p>
<p>
<a href = "../../cpp_src/triangle_grid/triangle_grid.html">
TRIANGLE_GRID</a>,
a C++ library which
computes a grid of points
over the interior of a triangle in 2D.
</p>
<p>
<a href = "../../cpp_src/wedge_grid/wedge_grid.html">
WEDGE_GRID</a>,
a C++ library which
computes a grid of points
over the interior of the unit wedge in 3D.
</p>
<h3 align = "center">
Source Code:
</h3>
<p>
<ul>
<li>
<a href = "polygon_grid.cpp">polygon_grid.cpp</a>, the source code.
</li>
<li>
<a href = "polygon_grid.hpp">polygon_grid.hpp</a>, the include file.
</li>
<li>
<a href = "polygon_grid.sh">polygon_grid.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_grid_prb.cpp">polygon_grid_prb.cpp</a>,
a sample calling program.
</li>
<li>
<a href = "polygon_grid_prb.sh">polygon_grid_prb.sh</a>,
BASH commands to compile and run the sample program.
</li>
<li>
<a href = "polygon_grid_prb_output.txt">polygon_grid_prb_output.txt</a>,
the output file.
</li>
</ul>
</p>
<p>
ELL is an L-shaped (non-convex!) polygon for which the program
output doesn't look too bad, although the grid is degenerate.
<ul>
<li>
<a href = "ell_commands.txt">ell_commands.txt</a>,
the gnuplot command file.
</li>
<li>
<a href = "ell_grid.txt">ell_grid.txt</a>,
the grid point coordinates.
</li>
<li>
<a href = "ell_vertex.txt">ell_vertex.txt</a>
information about the polygon vertices and centroid that are
used to draw boundary lines.
</li>
<li>
<a href = "ell.png">ell.png</a>
a plot of the grid.
</li>
<li>
<a href = "ell.xy">ell.xy</a>
the grid points.
</li>
</ul>
</p>
<p>
QUAD is a quadrilateral polygon.
<ul>
<li>
<a href = "quad_commands.txt">quad_commands.txt</a>,
the gnuplot command file.
</li>
<li>
<a href = "quad_grid.txt">quad_grid.txt</a>,
the grid point coordinates.
</li>
<li>
<a href = "quad_vertex.txt">quad_vertex.txt</a>
information about the polygon vertices and centroid that are
used to draw boundary lines.
</li>
<li>
<a href = "quad.png">quad.png</a>
a plot of the grid.
</li>
<li>
<a href = "quad.xy">quad.xy</a>
the grid points.
</li>
</ul>
</p>
<p>
TRIANGLE is a triangular polygon.
<ul>
<li>
<a href = "triangle_commands.txt">triangle_commands.txt</a>,
the gnuplot command file.
</li>
<li>
<a href = "triangle_grid.txt">triangle_grid.txt</a>,
the grid point coordinates.
</li>
<li>
<a href = "triangle_vertex.txt">triangle_vertex.txt</a>
information about the polygon vertices and centroid that are
used to draw boundary lines.
</li>
<li>
<a href = "triangle.png">triangle.png</a>
a plot of the grid.
</li>
<li>
<a href = "triangle.xy">triangle.xy</a>
the grid points.
</li>
</ul>
</p>
<h3 align = "center">
List of Routines:
</h3>
<p>
<ul>
<li>
<b>POLYGON_GRID_COUNT</b> counts the grid points inside a polygon.
</li>
<li>
<b>POLYGON_GRID_DISPLAY</b> displays grid points inside a polygon.
</li>
<li>
<b>POLYGON_GRID_POINTS</b> computes points on a polygonal grid.
</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>R8MAT_WRITE</b> writes an R8MAT file.
</li>
<li>
<b>TIMESTAMP</b> prints the current YMDHMS date as a time stamp.
</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 11 May 2015.
</i>
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