Efficient merging of multiple segments of B\'ezier curves

TL;DR

This paper introduces a new, efficient method for merging segments of composite Bézier curves with endpoint continuity, utilizing dual Bernstein basis to reduce computational complexity.

Contribution

The paper presents a novel merging algorithm based on constrained dual Bernstein basis, significantly decreasing computational complexity compared to existing methods.

Findings

Reduced algorithmic complexity for merging Bézier segments

Utilizes dual Bernstein basis for control point computation

Faster evaluation schemes improve efficiency

Abstract

This paper deals with the merging problem of segments of a composite B\'ezier 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. Wo\'zny, 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.