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2010•Journal of Beijing Electronic Science and Technology InstituteRequires access

α Extension of the Cubic Bézier Curve

Chengwei Wang

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Abstract

By introducing the concept of weights in NURBS curve into a blending technique,we extend the representation of the cubic Bezier curve.The generalized cubic Bezier curve is denoted as α Extension cubic Bezier curve,whose shape-control capability is shown to be much better than that of Bezier curve.The representation and properties of the extension curve is studied.The curve is easy and intuitive to reshape by varying the parameters;so it is useful in some applications of CAD/CAM .

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What this paper is about

By introducing the concept of weights in NURBS curve into a blending technique,we extend the representation of the cubic Bezier curve.The generalized cubic Bezier curve is denoted as α Extension cubic Bezier curve,whose shape-control capability is shown to be much better than that of Bezier curve.The representation and properties of the extension curve is studied.The curve is easy and intuitive to reshape by varying the parameters;so it is useful in some applications of CAD/CAM .

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Available abstract

By introducing the concept of weights in NURBS curve into a blending technique,we extend the representation of the cubic Bezier curve.The generalized cubic Bezier curve is denoted as α Extension cubic Bezier curve,whose shape-control capability is shown to be much better than that of Bezier curve.The representation and properties of the extension curve is studied.The curve is easy and intuitive to reshape by varying the parameters;so it is useful in some applications of CAD/CAM .

Key concepts: Bézier curve, Extension (predicate logic), Representation (politics), Cubic form, Mathematics, Tripling-oriented Doche–Icart–Kohel curve, Computer science, Curve fitting

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