Abstract
We define the rational ball Bezier curves in a three-dimensional affine space as a generalization of the disk Bezier curve introduced in the plane by Lin and Rokne (1998), and we give some basic properties. Then we give necessary and sufficient conditions for the piecewise connection with G 1 continuity for two adjacent ball Bezier curves by considering their envelopes. Thus we obtain the construction of a G 1 ball-spline curve. As an application of ball Bezier curves, we exhibit a new method for the approximation of a given space curve using a degree five G 1 ball-spline, the Hermite interpolation method, and the least square approximation.
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