function    [r, Area, d, dd] = minsurf(r1,r2,h1,h2)
%   minsurf computes the radius for the minimal surface area
%   for a double conefrustum.  Also returns the surface area and associated
%   partial derivatives.
r = (h2*r1+h1*r2)/(h1+h2) ; % start with the single frustum hypothesis
for i = 1:4
    [Area,d,dd] = doubleconesurf(r1,r,r2,h1,h2) ;
    r = r - d/dd ;
    if r < 0
        r = 0 ;
    end
end
[Area,d,dd] = doubleconesurf(r1,r,r2,h1,h2) ;
return