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Offset Approximation of Hybrid Hyperbolic Polynomial Curves

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Abstract

In this paper, two methods for approximation of offset curves of H-Bézier curves and H-B spline curves are presented, which are based on the approximation of shifting control points and norm of parametric speed. Firstly, after calculating the perturbed vectors, the offset curve can be obtained by shifting the control points of the base curve. Then, both the Chebyshev approximation and optimal trigonometric polynomials approximation of parametric speed of base curve are presented, and two approximation functions of offset curves are also obtained. Finally, some examples are used to demonstrate their practicality.

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Authors and Affiliations

  1. Department of Applied Mathematics, Xi’an University of Technology, Xi’an, 710054, People’s Republic of China

    Huanxin Cao, Gang Hu & Suxia Zhang

  2. School of Mechanical and Precision Instrument Engineering, Xi’an University of Technology, Xi’an, People’s Republic of China

    Gang Hu

  3. University of North Carolina at Pembroke, Pembroke, NC, 28372, USA

    Guo Wei

Authors
  1. Huanxin Cao
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  2. Gang Hu
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  3. Guo Wei
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  4. Suxia Zhang
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Correspondence to Gang Hu.

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Cao, H., Hu, G., Wei, G. et al. Offset Approximation of Hybrid Hyperbolic Polynomial Curves. Results Math 72, 1055–1071 (2017). https://doi.org/10.1007/s00025-016-0545-8

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  • DOI: https://doi.org/10.1007/s00025-016-0545-8

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