circle_segment, a MATLAB code which carries out computations associated with a circle segment, including height, width, angle, area, centroid, sampling, and quadrature.

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. The "width" W of the segment is the length of P1:P2.

This library considers various computations, including:


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 MATLAB code 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 MATLAB code which performs geometric calculations in 2, 3 and M dimensional space, including the computation of angles, areas, containment, distances, intersections, lengths, and volumes.

stroud, a MATLAB code 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:

Last revised on 13 December 2018.