A new method approximating offset curve by Bézier curve using parallel derivative curves

Kim, Soo Won; Lee, Ryeong; Ahn, Young Joon

doi:10.1007/s40314-017-0437-x

Cited by 2 publications

(1 citation statement)

References 20 publications

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“…In [3], rational offset curves based on the quadratic approximation of the circular arc are approximated. Recently, offset approximation curves based on the circular arc approximations are presented [4][5][6] yielding rational offset approximation which are the convolution of the unit normal vector and the given curve. The offset approximation in this paper is based on the best uniform approximation of the circular arc and yields a polynomial offset approximation curve.…”

Section: Introductionmentioning

confidence: 99%

Approximating offset Curves using Bezier curves with high accuracy

Rababah¹,

Jaradat²

2020

IJECE

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In this paper, a new method for the approximation of offset curves is presented using the idea of the parallel derivative curves. The best uniform approximation of degree 3 with order 6 is used to construct a method to find the approximation of the offset curves for Bezier curves. The proposed method is based on the best uniform approximation, and therefore; the proposed method for constructing the offset curves induces better outcomes than the existing methods.

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Section: Introductionmentioning

confidence: 99%

Approximating offset Curves using Bezier curves with high accuracy

Rababah¹,

Jaradat²

2020

IJECE

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$ 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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A new method approximating offset curve by Bézier curve using parallel derivative curves

Cited by 2 publications

References 20 publications

Approximating offset Curves using Bezier curves with high accuracy

Approximating offset Curves using Bezier curves with high accuracy

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

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