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C 1 NURBS representations of G 1 composite rational Bézier curves

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Abstract

This paper is concerned with the re-representation of a G 1 composite rational Bézier curve. Although the rational Bézier curve segments that form the composite curve are G 1 continuous at their joint points, their homogeneous representations may not be even C 0 continuous in the homogeneous space. In this paper, an algorithm is presented to convert the G 1 composite rational Bézier curve into a NURBS curve whose nonrational homogeneous representation is C 1 continuous in the homogeneous space. This re-representation process involves reparameterization using Möbius transformations, smoothing multiplication and parameter scaling transformations. While the previous methods may fail in some situations, the method proposed in this paper always works.

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Authors and Affiliations

  1. School of Computer Engineering, Nanyang Technological University, Singapore, Singapore

    Jianmin Zheng

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  1. Jianmin Zheng
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Correspondence to Jianmin Zheng.

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Communicated by C.H. Cap.

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Zheng, J. C 1 NURBS representations of G 1 composite rational Bézier curves. Computing 86, 257–268 (2009). https://doi.org/10.1007/s00607-009-0057-4

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  • DOI: https://doi.org/10.1007/s00607-009-0057-4

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