In [1], the author considered the problem of the optimal approximation of symmetric surfaces by biquadratic B\'ezier 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 B\'ezier 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.

翻译：文[1]研究了双二次Bézier片对对称曲面的最优逼近问题。遗憾的是，本文通过考虑球面正方形的最优逼近表明，其中的结果是不正确的。本文给出了详细分析及数值算法，根据（简化）径向误差提供了最佳逼近式，该结果与文[1]所得不同。随后，球体被两个与六个张量积二次Bézier片的连续样条逼近。进一步证明，逼近球体的六片$G^1$光滑样条存在，但并非一个良好的逼近。本文还探讨了球面矩形的逼近问题，数值示例表明在某些情况下可能存在多个最优逼近式，这使得问题极难处理。最后，提供的数值示例证实了理论结果。