Abstract
B3-splines are introduced in this paper with explicit expressions. The new splines are extensions of the B-spline but overcome the latter's weakness of not passing through interpolation points for curve or surface fitting. Between consecutive control points, three cubic functions are used. Computation is simple with data from prestored tables. No trial-and-error steps in selecting control points are necessary in order to create smooth interpolation. With other good properties, such as C 2-continuity and localization, the new splines can be implemented very well for interactive curve and surface fitting in computer-aided design (CAD). This paper describes the exact cubic expressions and their derivations. Their advantages over B-spline and Bézier spline for interactive applications are discussed.
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