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<html>
<head>
<title>
CIRCLE_SEGMENT - Area, Height, Angle, Sampling and Quadrature
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">
<h1 align = "center">
CIRCLE_SEGMENT <br> Area, Height, Angle, Sampling and Quadrature
</h1>
<hr>
<p>
<b>CIRCLE_SEGMENT</b>
is a C++ library which
carries out various computations associated with a circle segment,
using gnuplot to illustrate some of the computations.
</p>
<p>
Begin with a circle of radius R. Choose two points P1 and P2 on the
circle, and draw the chord P1:P2. This chord divides the circle
into two pieces, each of which is called a circle segment.
Consider one of the pieces. The "angle" THETA of this segment is the
angle P1:C:P2, where C is the center of the circle. Let Q be the point
on the chord P1:P2 which is closest to C. The "height" H of the segment
is the distance from Q to the perimeter of the circle.
</p>
<p>
This library considers various computations, including:
<ul>
<p>
Determine the angle THETA, given R and H.
</p>
<p>
Determine the height H, given R and THETA.
</p>
<p>
Determine the height H, given R and AREA.
</p>
<p>
Determine the width W, given R and H.
</p>
<p>
Determine the area, given R and H.
</p>
<p>
Determine the centroid, given R and H.
</p>
<p>
Select points uniformly at random from a segment, given R and H.
</p>
<p>
Determine a cumulative density function (CDF) for the height H2
of a circle segment defined by a point selected at random from
a circle segment of height H.
</p>
<p>
Determine a quadrature rule that can be used to estimate integrals
of functions f(x,y) over the segment.
</p>
</ul>
</p>
<p>
<b>CIRCLE_SEGMENT</b> creates some graphics plots using gnuplot.
</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>CIRCLE_SEGMENT</b> is available in
<a href = "../../c_src/circle_segment/circle_segment.html">a C version</a> and
<a href = "../../cpp_src/circle_segment/circle_segment.html">a C++ version</a> and
<a href = "../../f77_src/circle_segment/circle_segment.html">a FORTRAN77 version</a> and
<a href = "../../f_src/circle_segment/circle_segment.html">a FORTRAN90 version</a> and
<a href = "../../m_src/circle_segment/circle_segment.html">a MATLAB version</a>.
</p>
<h3 align = "center">
Related Data and Programs:
</h3>
<p>
<a href = "../../cpp_src/circle_rule/circle_rule.html">
CIRCLE_RULE</a>,
a C++ library which
computes quadrature rules for the unit circle in 2D, that is,
the circumference of the circle of radius 1 and center (0,0).
</p>
<p>
<a href = "../../cpp_src/geometry/geometry.html">
GEOMETRY</a>,
a C++ library which
performs geometric calculations in 2, 3 and M dimensional space,
including the computation of angles, areas, containment, distances,
intersections, lengths, and volumes.
</p>
<p>
<a href = "../../cpp_src/gnuplot/gnuplot.html">
GNUPLOT</a>,
C++ programs which
illustrate how a program can write data and command files
so that gnuplot can create plots of the program results.
</p>
<p>
<a href = "../../cpp_src/stroud/stroud.html">
STROUD</a>,
a C++ library which
defines quadrature rules for a variety of M-dimensional regions,
including the interior of the square, cube and hypercube, the pyramid,
cone and ellipse, the hexagon, the M-dimensional octahedron,
the circle, sphere and hypersphere, the triangle, tetrahedron and simplex,
and the surface of the circle, sphere and hypersphere.
</p>
<h3 align = "center">
Source Code:
</h3>
<p>
<ul>
<li>
<a href = "circle_segment.cpp">circle_segment.cpp</a>, the source code.
</li>
<li>
<a href = "circle_segment.hpp">circle_segment.hpp</a>, the include file.
</li>
<li>
<a href = "circle_segment.sh">circle_segment.sh</a>,
BASH commands to compile the source code.
</li>
</ul>
</p>
<h3 align = "center">
Examples and Tests:
</h3>
<p>
<ul>
<li>
<a href = "circle_segment_prb.cpp">circle_segment_prb.cpp</a>,
a sample calling program.
</li>
<li>
<a href = "circle_segment_prb.sh">circle_segment_prb.sh</a>,
BASH commands to compile and run the sample program.
</li>
<li>
<a href = "circle_segment_prb_output.txt">circle_segment_prb_output.txt</a>,
the output file.
</li>
</ul>
</p>
<p>
Test number 6 creates some samples of points in circle segments, and
writes out data files and gnuplot command files to create graphics:
<ul>
<li>
<a href = "sample01_boundary.txt">sample01_boundary.txt</a>,
data defining the boundary of the circle segment.
</li>
<li>
<a href = "sample01_commands.txt">sample01_commands.txt</a>,
commands to gnuplot to create a plot.
</li>
<li>
<a href = "sample01_data.txt">sample01_data.txt</a>,
the sample data.
</li>
<li>
<a href = "sample01.png">sample01.png</a>,
the plot
</li>
<li>
<a href = "sample02_boundary.txt">sample02_boundary.txt</a>,
data defining the boundary of the circle segment.
</li>
<li>
<a href = "sample02_commands.txt">sample02_commands.txt</a>,
commands to gnuplot to create a plot.
</li>
<li>
<a href = "sample02_data.txt">sample02_data.txt</a>,
the sample data.
</li>
<li>
<a href = "sample02.png">sample02.png</a>,
the plot
</li>
<li>
<a href = "sample03_boundary.txt">sample03_boundary.txt</a>,
data defining the boundary of the circle segment.
</li>
<li>
<a href = "sample03_commands.txt">sample03_commands.txt</a>,
commands to gnuplot to create a plot.
</li>
<li>
<a href = "sample03_data.txt">sample03_data.txt</a>,
the sample data.
</li>
<li>
<a href = "sample03.png">sample03.png</a>,
the plot
</li>
<li>
<a href = "sample04_boundary.txt">sample04_boundary.txt</a>,
data defining the boundary of the circle segment.
</li>
<li>
<a href = "sample04_commands.txt">sample04_commands.txt</a>,
commands to gnuplot to create a plot.
</li>
<li>
<a href = "sample04_data.txt">sample04_data.txt</a>,
the sample data.
</li>
<li>
<a href = "sample04.png">sample04.png</a>,
the plot
</li>
</ul>
</p>
<h3 align = "center">
List of Routines:
</h3>
<p>
<ul>
<li>
<b>CIRCLE_SEGMENT_ANGLE_FROM_CHORD</b> computes the angle of a circle segment.
</li>
<li>
<b>CIRCLE_SEGMENT_ANGLE_FROM_CHORD_ANGLES</b> computes angle of a circle segment.
</li>
<li>
<b>CIRCLE_SEGMENT_ANGLE_FROM_HEIGHT</b> computes the angle of a circle segment.
</li>
<li>
<b>CIRCLE_SEGMENT_AREA_FROM_ANGLE</b> computes the area of a circle segment.
</li>
<li>
<b>CIRCLE_SEGMENT_AREA_FROM_CHORD</b> computes the area of a circle segment.
</li>
<li>
<b>CIRCLE_SEGMENT_AREA_FROM_HEIGHT</b> computes the area of a circle segment.
</li>
<li>
<b>CIRCLE_SEGMENT_AREA_FROM_SAMPLE</b> computes the area of a circle segment.
</li>
<li>
<b>CIRCLE_SEGMENT_CDF</b> computes a CDF related to a circle segment.
</li>
<li>
<b>CIRCLE_SEGMENT_CENTROID_FROM_CHORD</b> computes the centroid of a circle segment.
</li>
<li>
<b>CIRCLE_SEGMENT_CENTROID_FROM_HEIGHT</b> computes centroid of a circle segment.
</li>
<li>
<b>CIRCLE_SEGMENT_CENTROID_FROM_SAMPLE</b> estimates a circle segment centroid.
</li>
<li>
<b>CIRCLE_SEGMENT_CONTAINS_POINT</b> reports whether a point is in a circle segment.
</li>
<li>
<b>CIRCLE_SEGMENT_HEIGHT_FROM_ANGLE:</b> height of a circle segment from angle.
</li>
<li>
<b>CIRCLE_SEGMENT_HEIGHT_FROM_AREA:</b> height of a circle segment from area.
</li>
<li>
<b>CIRCLE_SEGMENT_HEIGHT_FROM_CHORD:</b> height of a circle segment from chord.
</li>
<li>
<b>CIRCLE_SEGMENT_SAMPLE_FROM_CHORD</b> samples points from a circle segment.
</li>
<li>
<b>CIRCLE_SEGMENT_SAMPLE_FROM_HEIGHT</b> samples points from a circle segment.
</li>
<li>
<b>CIRCLE_SEGMENT_WIDTH_FROM_HEIGHT</b> computes the width of a circle segment.
</li>
<li>
<b>FILENAME_INC</b> increments a partially numeric file name.
</li>
<li>
<b>R8_ACOS</b> computes the arc cosine function, with argument truncation.
</li>
<li>
<b>R8_ASIN</b> computes the arc sine function, with argument truncation.
</li>
<li>
<b>R8_ATAN</b> computes the inverse tangent of the ratio Y / X.
</li>
<li>
<b>R8_EPSILON</b> returns the R8 round off unit.
</li>
<li>
<b>R8_MAX</b> returns the maximum of two R8's.
</li>
<li>
<b>R8_MIN</b> returns the minimum of two R8's.
</li>
<li>
<b>R8_UNIFORM_01</b> returns a pseudorandom R8 scaled to [0,1].
</li>
<li>
<b>R8MAT_UNIFORM_01_NEW</b> fills an R8MAT with pseudorandom values scaled to [0,1].
</li>
<li>
<b>R8VEC_LINSPACE_NEW</b> creates a vector of linearly spaced values.
</li>
<li>
<b>R8VEC_SUM</b> returns the sum of an R8VEC.
</li>
<li>
<b>R8VEC_UNIFORM_01_NEW</b> returns a unit pseudorandom R8VEC.
</li>
<li>
<b>TIMESTAMP</b> prints the current YMDHMS date as a time stamp.
</li>
<li>
<b>TRIDISOLVE</b> solves a tridiagonal system of linear equations.
</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 12 July 2013.
</i>
<!-- John Burkardt -->
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</html>