An approximation of circular arcs by quartic Bézier curves

Kim, Seon-Hong; Ahn, Young Joon

doi:10.1016/j.cad.2007.01.004

Cited by 60 publications

(19 citation statements)

References 12 publications

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“…Kim and Ahn [29] proposed an approximation method of circular arcs by quartic Bézier curves. If we specify the control points P 0 , P 1 , P 2 and P 4 according to Kim and Ahn's method, then the resulting jerk-energy-minimizing Bézier curve can be seen as an approximation of circular arc (see Figure 8(a)).…”

Section: Modeling Of Circle-like Curvesmentioning

confidence: 99%

Geometric construction of energy-minimizing Béezier curves

Wang

Chen

2011

Sci. China Inf. Sci.

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Modeling energy-minimizing curves have many applications and are a basic problem of Geometric Modeling. In this paper, we propose the method for geometric design of energy-minimizing Bézier curves. Firstly, the necessary and sufficient condition on the control points for Bézier curves to have minimal internal energy is derived. Based on this condition, we propose the geometric constructions of three kinds of Bézier curves with minimal internal energy including stretch energy, strain energy and jerk energy. Given some control points, the other control points can be determined as the linear combination of the given control points. We compare the three kinds of energy-minimizing Bézier curves via curvature combs and curvature plots, and present the collinear properties of quartic energy-minimizing Bézier curves. We also compare the proposed method with previous methods on efficiency and accuracy. Finally, several applications of the curve generation technique, such as curve interpolation with geometric constraints and modeling of circle-like curves are discussed.

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Section: Modeling Of Circle-like Curvesmentioning

confidence: 99%

Geometric construction of energy-minimizing Béezier curves

Wang

Chen

2011

Sci. China Inf. Sci.

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“…There are methods in the literature that are G 1 − and G 2 −continuous, see for example [6], [9], [10], [13], [14], [16], [17], [18], [19], [22].…”

Section: Conclusion and Open Problemsmentioning

confidence: 99%

Quartic approximation of circular arcs using equioscillating error function

Rababah

2016

ijacsa

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Abstract-A high accuracy quartic approximation for circular arc is given in this article. The approximation is constructed so that the error function is of degree 8 with the least deviation from the x-axis; the error function equioscillates 9 times; the approximation order is 8. The numerical examples demonstrate the efficiency and simplicity of the approximation method as well as satisfying the properties of the approximation method and yielding the highest possible accuracy.

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“…The approximation of circular arcs by quartic Bézier curves with approximation order eight were represented in [6][7][8]. Fang [9] presented a method for approximating conic sections using quintic polynomial curves.…”

Section: Introductionmentioning

confidence: 99%

A Highly Accurate Approximation of Conic Sections by Quartic Bézier Curves

Zhi¹,

Wei²,

Tan

et al. 2016

ACM

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Abstract:A new approximation method for conic section by quartic Bézier curves is proposed. This method is based on the quartic Bézier approximation of circular arcs. We give the upper bound of Hausdorff distance between the conic section and the quartic Bézier curve, and also show that the approximation order is eight. And we prove that our approximation method has a smaller upper bound than previous quartic Bézier approximation methods. A quartic G 2 -continuous spline approximation of conic sections is obtained by using the subdivision scheme at the shoulder point of the conic section.

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An approximation of circular arcs by quartic Bézier curves

Cited by 60 publications

References 12 publications

Geometric construction of energy-minimizing Béezier curves

Geometric construction of energy-minimizing Béezier curves

Quartic approximation of circular arcs using equioscillating error function

A Highly Accurate Approximation of Conic Sections by Quartic Bézier Curves

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