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2002•Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIERequires access

Generalized Bezier curve: α Bezier curve

Guicang Zhang, Yu‐Jin Zhang, Shaojun Cui, Huifang Feng

Open publisher page 2 citations

Abstract

Combining the concept of weights in rational curves with singular blending technique, we have generalized Bézier curve to a generalized Bézier curve denoted as a -Bézier curve. Its shape-control capability is much better than that of Bézier curve; thus, ? Bézier curve is more useful in free curve and surface designing. Bézier curve can be converted into an a Bézier curve by adding blending parameter to control vertices of Bézier curve. The properties of a Bézier curve are studied in details, and the effects of the blending parameters are investigated. By varying the blending parameters the curve can be reshaped, so it is brightly useful in the applications of CAD/CAM.

About this research paper

What this paper is about

Combining the concept of weights in rational curves with singular blending technique, we have generalized Bézier curve to a generalized Bézier curve denoted as a -Bézier curve. Its shape-control capability is much better than that of Bézier curve; thus, ? Bézier curve is more useful in free curve and surface designing. Bézier curve can be converted into an a Bézier curve by adding blending parameter to control vertices of Bézier curve. The properties of a Bézier curve are studied in details, and the effects of the blending parameters are investigated. By varying the blending parameters the curve can be reshaped, so it is brightly useful in the applications of CAD/CAM.

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Available abstract

Combining the concept of weights in rational curves with singular blending technique, we have generalized Bézier curve to a generalized Bézier curve denoted as a -Bézier curve. Its shape-control capability is much better than that of Bézier curve; thus, ? Bézier curve is more useful in free curve and surface designing. Bézier curve can be converted into an a Bézier curve by adding blending parameter to control vertices of Bézier curve. The properties of a Bézier curve are studied in details, and the effects of the blending parameters are investigated. By varying the blending parameters the curve can be reshaped, so it is brightly useful in the applications of CAD/CAM.

Key concepts: Bézier curve, Tripling-oriented Doche–Icart–Kohel curve, Curve fitting, Computer science, Mathematics, Geometry, Mathematical analysis, Elliptic curve

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