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2019•Unpublished venueRequires access

Approximations of Circular Arcs by Quartic Bézier Curves

Han Earl Yang, Qiang Li, Xue-Zhang Liang

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Abstract

Bézier approximation method is an important tool in CAD/CAM, which is usually applied on the curve and surface construction. Based on [6]-[9],this paper selects two symmetrical internal nodes in (0,1) as the Hermite interpolation nodes to obtain two undetermined parameters of quartic Bézier approximation curve of the circular arc. Furthermore, we construct a quartic Bézier approximation scheme of circular arc with continuous curvature and higher approximation accuracy by a contraction transformation on the Bézier curve obtained by the interpolation approximation.

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What this paper is about

Bézier approximation method is an important tool in CAD/CAM, which is usually applied on the curve and surface construction. Based on [6]-[9],this paper selects two symmetrical internal nodes in (0,1) as the Hermite interpolation nodes to obtain two undetermined parameters of quartic Bézier approximation curve of the circular arc. Furthermore, we construct a quartic Bézier approximation scheme of circular arc with continuous curvature and higher approximation accuracy by a contraction transformation on the Bézier curve obtained by the interpolation approximation.

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Available abstract

Bézier approximation method is an important tool in CAD/CAM, which is usually applied on the curve and surface construction. Based on [6]-[9],this paper selects two symmetrical internal nodes in (0,1) as the Hermite interpolation nodes to obtain two undetermined parameters of quartic Bézier approximation curve of the circular arc. Furthermore, we construct a quartic Bézier approximation scheme of circular arc with continuous curvature and higher approximation accuracy by a contraction transformation on the Bézier curve obtained by the interpolation approximation.

Key concepts: Quartic function, Mathematics, Interpolation (computer graphics), Curvature, Arc (geometry), Arc length, Mathematical analysis, Bézier curve

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