Efficient merging of multiple segments of Bézier curves
This work addresses the efficiency of merging Bézier curve segments for computer-aided geometric design applications, offering a faster algorithm.
The paper presents a novel method for merging segments of Bézier curves with endpoint continuity constraints, achieving significantly lower computational complexity than existing methods through the use of constrained dual Bernstein polynomial basis.
This paper deals with the merging problem of segments of a composite Bézier curve, with the endpoints continuity constraints. We present a novel method which is based on the idea of using constrained dual Bernstein polynomial basis (P. Woźny, S. Lewanowicz, Comput. Aided Geom. Design 26 (2009), 566--579) to compute the control points of the merged curve. Thanks to using fast schemes of evaluation of certain connections involving Bernstein and dual Bernstein polynomials, the complexity of our algorithm is significantly less than complexity of other merging methods.