function area = sphere_imp_zone_area_3d ( r, h1, h2 )
%*****************************************************************************80
%
%% sphere_imp_zone_area_3d() computes the surface area of a spherical zone in 3D.
%
% Discussion:
%
% An implicit sphere in 3D satisfies the equation:
%
% sum ( ( P(1:DIM_NUM) - CENTER(1:DIM_NUM) )^2 ) = R^2
%
% Draw any radius of the sphere and note the point P where the radius
% intersects the sphere. Now choose two points on the radius line, a
% distance H1 and H2 from the point P. Consider all the points on or within
% the sphere whose projection onto the radius lies between these two points.
% These points constitute the spherical zone, which can also be considered
% the difference of two spherical caps.
%
% 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 H1, H2, the distances that define the
% thickness of the zone. H1 and H2 must be between 0 and 2 * R.
%
% Output:
%
% real AREA, the area of the spherical zone.
%
h = abs ( h1 - h2 );
if ( h <= 0.0 )
area = 0.0;
elseif ( 2.0 * r <= h )
area = 4.0 * pi * r * r;
else
area = 2.0 * pi * r * h;
end
return
end