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

Young Joon Ahn; Young Joon Ahn

doi:10.3934/math.20231587

AIMS Mathematics

2023, Volume 8, Issue 12: 31008-31021. doi: 10.3934/math.20231587

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Research article

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

Young Joon Ahn ^,

Department of Mathematics Education, Chosun University, Gwangju, 61452, South Korea

Received: 21 August 2023 Revised: 24 October 2023 Accepted: 02 November 2023 Published: 20 November 2023
MSC : 41A05, 65D17

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.
- offset approximation,
- Hermite interpolation,
- unit normal vector field,
- polynomial curve,
- circular precision
Citation: Young Joon Ahn. $ G^2/C^1 $ Hermite interpolation of offset curves of parametric regular curves[J]. AIMS Mathematics, 2023, 8(12): 31008-31021. doi: 10.3934/math.20231587

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Abstract

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.

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