Circular arc approximation by hexic polynomial curves

Yoon, Hyeong Moon; Ahn, Young Joon

doi:10.1007/s40314-023-02315-9

Comp. Appl. Math.

2023

DOI: 10.1007/s40314-023-02315-9

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Circular arc approximation by hexic polynomial curves

Hyeong Moon Yoon,

Young Joon Ahn

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Cited by 3 publications

References 24 publications

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Optimal one-sided approximants of circular arc

Šadl Praprotnik,

Vavpetič,

Žagar

2024

Computer Aided Geometric Design

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Optimal one-sided approximants of circular arc

Šadl Praprotnik,

Vavpetič,

Žagar

2024

Computer Aided Geometric Design

View full text Add to dashboard Cite

$ G^2/C^1 $ Hermite interpolation of offset curves of parametric regular curves

Ahn

2023

MATH

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<abstract><p>In this paper we presented a method of $ G^2 $ Hermite interpolation of offset curves of regular plane curves based on approximating the normal vector fields. We showed that our approximant is also $ C^1 $ Hermite interpolation of the offset curve. Our method is capable of achieving circular precision. Another advantage of our method is that if the input curve is a polynomial curve, then our method also yields a polynomial curve. Our approximation method was applied to numerical examples and its numerical results were compared to previous offset approximation methods. It was observed that our method is almost optimal with respect to the number of control points of the approximation curves for the same tolerance.</p></abstract>

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An approximation method for convolution curves of regular curves and ellipses

Ahn

2024

MATH

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<p>In this paper, we present a method of $ G^2 $ Hermite interpolation of convolution curves of regular plane curves and ellipses. We show that our approximant is also a $ C^1 $ Hermite interpolation of the convolution curve. This method yields a polynomial curve if the trajectory curve is a polynomial curve. Our approximation method is applied to two previous numerical examples. The results of our method are compared with those of previous methods, and the merits and demerits are analyzed. Compared with previous methods, the merits of our method are that the approximant is $ G^2 $ and $ C^1 $ Hermite interpolation, and the degree of the approximant or the required number of segments of the approximant within error tolerances is small.</p>

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Circular arc approximation by hexic polynomial curves

Cited by 3 publications

References 24 publications

Optimal one-sided approximants of circular arc

Optimal one-sided approximants of circular arc

$ G^2/C^1 $ Hermite interpolation of offset curves of parametric regular curves

An approximation method for convolution curves of regular curves and ellipses

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