Area, Height, Angle, Sampling and Quadrature

**CIRCLE_SEGMENT**,
a C++ library which
carries out various computations associated with a circle segment,
using gnuplot to illustrate some of the computations.

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.

This library considers various computations, including:

Determine the angle THETA, given R and H.

Determine the height H, given R and THETA.

Determine the height H, given R and AREA.

Determine the width W, given R and H.

Determine the area, given R and H.

Determine the centroid, given R and H.

Select points uniformly at random from a segment, given R and H.

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.

Determine a quadrature rule that can be used to estimate integrals of functions f(x,y) over the segment.

**CIRCLE_SEGMENT** creates some graphics plots using gnuplot.

The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.

**CIRCLE_SEGMENT** is available in
a C version and
a C++ version and
a FORTRAN90 version and
a MATLAB version.

CIRCLE_RULE, 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).

GEOMETRY, 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.

GNUPLOT, C++ programs which illustrate how a program can write data and command files so that gnuplot can create plots of the program results.

STROUD, 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.

- circle_segment.cpp, the source code.
- circle_segment.sh, compiles the source code.
- circle_segment.hpp, the include file.