function volume = sphere_cap_volume_3d ( r, h )
%*****************************************************************************80
%
%% sphere_cap_volume_3d() computes the volume of a spherical cap in 3D.
%
% Discussion:
%
% Draw any radius of the sphere and note the point P where the radius
% intersects the sphere. Consider the point on the radius line which is
% H units from P. Draw the circle that lies in the plane perpendicular to
% the radius, and which intersects the sphere. The circle divides the sphere
% into two pieces, and the corresponding disk divides the solid sphere into
% two pieces. The part of the solid sphere that includes the point P
% is the spherical cap of height (or thickness) H.
%
% Licensing:
%
% This code is distributed under the MIT license.
%
% Modified:
%
% 07 February 2005
%
% Author:
%
% John Burkardt
%
% Input:
%
% real R, the radius of the sphere.
%
% real H, the "height" of the spherical cap. H must
% be between 0 and 2 * R.
%
% Output:
%
% real VOLUME, the volume of the spherical cap.
%
if ( h <= 0.0 )
volume = 0.0;
elseif ( 2.0 * r <= h )
volume = ( 4.0 / 3.0 ) * pi * r * r * r;
else
volume = ( 1.0 / 3.0 ) * pi * h * h * ( 3.0 * r - h );
end
return
end