function area = circle_lune_area_by_height_2d ( r, h )
%*****************************************************************************80
%
%% circle_lune_area_by_height_2d() computes the area of a circular lune.
%
% Discussion:
%
% Draw the chord connecting two points on the circumference of a circle.
% The region between the chord and the circumference is a "lune".
% We wish to know the area of this region.
%
% The distance from the center of the circle to the midpoint of the chord
% is the "height" H of the lune. It is natural to expect 0 <= H <= R.
% However, if we allow -R <= H < 0 as well, this allows us to include
% lunes which involve more than half the circle's area.
%
% If H < -R or R < H, then no lune is formed and we have zero area.
%
% Licensing:
%
% This code is distributed under the MIT license.
%
% Modified:
%
% 14 January 2018
%
% Author:
%
% John Burkardt
%
% Input:
%
% real R, the radius of the circle.
%
% real H, the height of the lune.
%
% Output:
%
% real AREA, the area of the lune.
%
if ( -r <= h & h <= r )
area = r^2 * acos ( h / r ) - h * sqrt ( r^2 - h^2 );
else
area = 0.0;
end
return
end