Area, Height, Angle, Sampling and Quadrature

CIRCLE_SEGMENT is 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:

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.

Related Data and Programs:

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.

Source Code:

Examples and Tests:

Test number 6 creates some samples of points in circle segments, and writes out data files and gnuplot command files to create graphics:

List of Routines:

You can go up one level to the C++ source codes.

Last revised on 12 July 2013.