The best uniform quadratic approximation of circular arcs with high accuracy

• Autorzy: Abedallah Rababah
• Języki publikacji: EN

Abstrakty

EN

In this article, the issue of the best uniform approximation of circular arcs with parametrically defined polynomial curves is considered. The best uniform approximation of degree 2 to a circular arc is given in explicit form. The approximation is constructed so that the error function is the Chebyshev polynomial of degree 4; the error function equioscillates five times; the approximation order is four. For θ = π/4 arcs (quarter of a circle), the uniform error is 5.5 × 10−3. The numerical examples demonstrate the efficiency and simplicity of the approximation method as well as satisfy the properties of the best uniform approximation and yield the highest possible accuracy.

Słowa kluczowe

EN

Bézier curves; Quadratic best uniform approximation; Circular arc; High accuracy; Approximation order; Equioscillation

Kategorie tematyczne

• 65D18: Computer graphics, image analysis, and computational geometry
• 65D17: Computer aided design (modeling of curves and surfaces)
• 41A10: Approximation by polynomials
• 41A50: Best approximation, Chebyshev systems
• 41A25: Rate of convergence, degree of approximation

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2016
• Tom: 14
• Numer: 1
• Strony: 118-127

Daty

wydano

2016-01-01

otrzymano

2015-09-19

zaakceptowano

2016-01-07

online

2016-03-03

Twórcy

autor

Abedallah Rababah

• Abedallah Rababah: Department of Mathematics and Statistics, Jordan University of Science and Technology, 22110 Irbid,

Identyfikatory

DOI

10.1515/math-2016-0012