Circular sector area preserving approximation of circular arcs by geometrically smooth parametric polynomials

The quality of the approximation of circular arcs by parametric polynomials is usually measured by the Hausdorff distance. It is sometimes important that a parametric polynomial approximant additionally preserves some particular geometric property. In this paper we study the circular sector area pre...

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Bibliographic Details
Published in:Journal of computational and applied mathematics 2018-07, Vol.336, p.63-71
Main Author: Žagar, Emil
Format: Article
Language:English
Subjects:
Approximation order
Bézier curve
Circular arc
Circular sector area
Geometric continuity
Interpolation
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Summary:The quality of the approximation of circular arcs by parametric polynomials is usually measured by the Hausdorff distance. It is sometimes important that a parametric polynomial approximant additionally preserves some particular geometric property. In this paper we study the circular sector area preserving parametric polynomial approximants of circular arcs. A general approach to this problem is considered and corresponding (nonlinear) equations are derived. For the approximants possessing the maximal order of geometric smoothness, a scalar nonlinear equation is analyzed in detail for the parabolic, the cubic and the quartic case. The existence of the admissible solution is confirmed. Moreover, the uniqueness of the solution with the optimal approximation order with respect to the radial distance is proved. Theoretical results are confirmed by numerical examples.
ISSN:0377-0427
1879-1778
DOI:10.1016/j.cam.2017.12.024