Optimal approximation of spherical squares by tensor product quadratic Bézier patches

In [1], the author considered  the problem of the optimal approximation of symmetric surfaces by biquadratic Bézier 
patches. Unfortunately, the results therein are incorrect, which is shown in this paper by considering the optimal 
approximation of spherical squares. A detailed analysis and a numerical algorithm are given, providing the best
approximant according to the (simplified) radial error, which differs from the one obtained in [1]. 
The sphere is then approximated by the continuous spline of two and six tensor product quadratic 
Bézier patches. It is further shown that the $G^1$  smooth spline of six patches approximating the sphere exists, 
but it is not a good approximation. The problem of an approximation of spherical rectangles is also addressed and 
numerical examples indicate that several optimal approximants might exist in some cases, making the problem extremely 
difficult to handle. Finally, numerical examples are provided that confirm theoretical results.