20.500.12556/RUL-152828 Optimal approximation of spherical squares by tensor product quadratic Bézier patches In cited article E. F. Eisele 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 mentioned article. 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 the theoretical results. Bézier patches spherical squares optimal approximation sphere approximation Bézierjeve krpe sferični kvadrati optimalna aproksimacija aproksimacija sfere true false true Angleški jezik Slovenski jezik Članek v reviji 2023-12-08 11:15:10 2023-12-08 11:15:15 2024-03-11 12:36:52 0000-00-00 00:00:00 2023 0 0 12 str. art. 128196 Vol. 457 Nov. 2023 0000-00-00 Zaloznikova Objavljeno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 519.6 0096-3003 10.1016/j.amc.2023.128196 161773059 1-s2.0-S009630032300365X-main.pdf 1-s2.0-S009630032300365X-main.pdf 1 2892C289B691A255BD850DFF9FD01745 d46f24316de35cefe7feea6f4ef5ec8e0514aa08c6e3b6f65ae0a526b25d9bfa 8adad1aa-95b3-11ee-9c20-0050569b8976 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=178509 https://www.sciencedirect.com/science/article/pii/S009630032300365X 1 ae6bcbeb-95b2-11ee-9c20-0050569b8976 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=178508 Fakulteta za matematiko in fiziko 0 0 0