Optimal approximation of spherical squares by tensor product quadratic Bézier patches

Vavpetič, Aleš (avtor), Žagar, Emil (avtor)

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.

• Jezik: Angleški jezik
• Ključne besede: Bézier patches, spherical squares, optimal approximation, sphere approximation
• Vrsta gradiva: Članek v reviji
• Tipologija: 1.01 - Izvirni znanstveni članek
• Organizacija: FMF - Fakulteta za matematiko in fiziko
• Status publikacije: Objavljeno
• Različica publikacije: Objavljena publikacija
• Leto izida: 2023
• Št. strani: 12 str.
• Številčenje: Vol. 457, art. 128196
• PID: 20.500.12556/RUL-152828
• UDK: 519.6
• ISSN pri članku: 0096-3003
• DOI: 10.1016/j.amc.2023.128196
• COBISS.SI-ID: 161773059
• Datum objave v RUL: 08.12.2023

Gradivo je del revije

• Naslov: Applied mathematics and computation
• Skrajšan naslov: Appl. math. comput.
• Založnik: Elsevier
• ISSN: 0096-3003
• COBISS.SI-ID: 24983808

Licence

• Licenca: CC BY-NC-ND 4.0, Creative Commons Priznanje avtorstva-Nekomercialno-Brez predelav 4.0 Mednarodna
• Povezava: http://creativecommons.org/licenses/by-nc-nd/4.0/deed.sl
• Opis: Najbolj omejujoča licenca Creative Commons. Uporabniki lahko prenesejo in delijo delo v nekomercialne namene in ga ne smejo uporabiti za nobene druge namene.

Sekundarni jezik

• Jezik: Slovenski jezik
• Ključne besede: Bézierjeve krpe, sferični kvadrati, optimalna aproksimacija, aproksimacija sfere