Efficient merging of multiple segments of Bézier curves

2014/09/09 by Paweł Woźny, Woźny, Paweł, Przemysław Gospodarczyk +3
Computer Science · Engineering · #Advanced Numerical Analysis Techniques #Computational Geometry and Mesh Generation #FOS: Mathematics #Numerical Analysis (math.NA)

paper · pdf · doi:10.48550/arxiv.1409.2671

openalex publication_date 2014/09/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

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