function volume = sphere_cap_volume_2d ( r, h )
%*****************************************************************************80
%
%% SPHERE_CAP_VOLUME_2D computes the volume of a spherical cap in 2D.
%
% Discussion:
%
% Draw any radius R of the circle and denote as P the point where the
% radius intersects the circle. Now consider the point Q which lies
% on the radius and which is H units from P. The line which is
% perpendicular to the radius R and passes through Q divides the
% circle into two pieces. The piece including the point P is the
% spherical (circular) cap of height (or thickness) H.
%
% Licensing:
%
% This code is distributed under the GNU LGPL license.
%
% Modified:
%
% 12 January 2021
%
% Author:
%
% John Burkardt
%
% Input:
%
% real R, the radius of the sphere.
%
% real H, the "height" of the spherical cap.
%
% Output:
%
% real VOLUME, the volume (area) of the spherical cap.
%
if ( h <= 0.0 )
volume = 0.0;
elseif ( 2.0 * r <= h )
volume = pi * r * r;
else
theta = 2.0 * asin ( sqrt ( r * r - ( r - h ) * ( r - h ) ) / r );
volume = r * r * ( theta - sin ( theta ) ) / 2.0;
if ( r < h )
volume = pi * r * r - volume;
end
end
return
end