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<html>
<head>
<title>
TRIANGLE_GRID - Triangular Grid of Points
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">
<h1 align = "center">
TRIANGLE_GRID <br> Triangular Grid of Points
</h1>
<hr>
<p>
<b>TRIANGLE_GRID</b>
is a C++ library which
generates a grid of points
over the interior of a triangle in 2D.
</p>
<p>
Starting with any 3 points A, B, and C that define a triangle,
we can divide each side of the triangle into N subintervals,
and create a triangular grid. This defines ((N+1)*(N+2))/2
points that lie on the intersections of grid lines. The
arrangement is suggested by this diagram:
<pre>
X
9 X
8 9 X
7 8 9 X
6 7 8 9 X
5 6 7 8 9 X
4 5 6 7 8 9 X
3 4 5 6 7 8 9 X
2 3 4 5 6 7 8 9 X
1 2 3 4 5 6 7 8 9 X
0 1 2 3 4 5 6 7 8 9 X
</pre>
</p>
<p>
The library includes a routine which allows the user to pick an
arbitrary triangle and an arbitrary number of subdivisions. It
then returns the triangular gridpoints defined by that choice.
</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>TRIANGLE_GRID</b> is available in
<a href = "../../c_src/triangle_grid/triangle_grid.html">a C version</a> and
<a href = "../../cpp_src/triangle_grid/triangle_grid.html">a C++ version</a> and
<a href = "../../f77_src/triangle_grid/triangle_grid.html">a FORTRAN77 version</a> and
<a href = "../../f_src/triangle_grid/triangle_grid.html">a FORTRAN90 version</a> and
<a href = "../../m_src/triangle_grid/triangle_grid.html">a MATLAB version</a> and
<a href = "../../py_src/triangle_grid/triangle_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/polygon_grid/polygon_grid.html">
POLYGON_GRID</a>,
a C++ library which
generates a grid of points
over the interior of a polygon in 2D.
</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 regular grid of points
over the interior of an arbitrary 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/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 = "triangle_grid.cpp">triangle_grid.cpp</a>, the source code.
</li>
<li>
<a href = "triangle_grid.hpp">triangle_grid.hpp</a>, the include file.
</li>
<li>
<a href = "triangle_grid.sh">triangle_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 = "triangle_grid_prb.cpp">triangle_grid_prb.cpp</a>,
a sample calling program.
</li>
<li>
<a href = "triangle_grid_prb.sh">triangle_grid_prb.sh</a>,
BASH commands to compile and run the sample program.
</li>
<li>
<a href = "triangle_grid_prb_output.txt">triangle_grid_prb_output.txt</a>,
the output file.
</li>
<li>
<a href = "triangle_grid_test01.xy">triangle_grid_test01.xy</a>,
a grid of 66 points, generated by subdividing by 10 each side
of the (0,0), (1,0), (1/2,sqrt(3)/2) triangle.
</li>
<li>
<a href = "triangle_grid_test01.png">triangle_grid_test01.png</a>,
an image of the points.
</li>
</ul>
</p>
<h3 align = "center">
List of Routines:
</h3>
<p>
<ul>
<li>
<b>TIMESTAMP</b> prints the current YMDHMS date as a time stamp.
</li>
<li>
<b>TRIANGLE_GRID</b> computes points on a triangular grid.
</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 02 September 2010.
</i>
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