α Extension of the Cubic Ball Curve
Ball curve； curve design； shape parameter Abstract. Ball curve is found similar to Bézier curve，also it has a good property of shape preserving，and in some respects，it has better properties than the Bézier curve. Therefore, In the shape design，Ball curve is paid more and more attention, it has a wide application. By introducing the concept of weights in NURBS curve into a blending technique, the paper extends the representation of the cubic Ball curve. The generalized cubic Ball curve is denoted as α extension cubic Ball curve, whose shape-control capability is shown to be much better than that of Ball curve. The representation and properties of the extension curve are studied. The curve is easy and intuitive to reshape by varying the parameters; so it is useful in some applications of CAD/CAM.
C. W. Wang, "α Extension of the Cubic Ball Curve", Applied Mechanics and Materials, Vol. 235, pp. 85-89, 2012