期刊
COMPUTER AIDED GEOMETRIC DESIGN
卷 63, 期 -, 页码 66-77出版社
ELSEVIER SCIENCE BV
DOI: 10.1016/j.cagd.2018.05.002
关键词
Parametric polynomial curve; Circular arc; Geometric interpolation; Optimal solution
资金
- ARRS, Republic of Slovenia [P1-0288, J1-7256]
The aim of this paper is a construction of parametric polynomial interpolants of a circular arc possessing maximal geometric smoothness. Two boundary points of a circular arc are interpolated together with higher order geometric data. Construction of interpolants is done via a complex factorization of the implicit unit circle equation. The problem is reduced to solving only one nonlinear equation determined by a monotone function and the existence of the solution is proven for any degree of the interpolating polynomial. Precise starting points for the Newton-Raphson type iteration methods are provided and the best solutions are then given in a closed form. Interpolation by parametric polynomials of degree up to six is discussed in detail and numerical examples confirming theoretical results are included. (C) 2018 Elsevier B.V. All rights reserved.
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