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Shape-Adjustable Generalized Bézier Rotation Surfaces with Multiple Shape Parameters

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Abstract

To tackle the problems in adjusting and controlling shapes of rotation surfaces, a new efficient method for quickly constructing generalized Bézier rotation surfaces with multiple shape parameters is proposed. Firstly, following the important idea of transfinite vectored rational interpolating function, the shape-adjustable generalized Bézier rotation surfaces are constructed using a generalized Bézier curve with multiple shape parameters. Secondly, the explicit function expression of the shape-adjustable generalized Bézier rotation surfaces is presented. The new rotation surfaces inherit the outstanding properties of the Bézier rotation surfaces, with a good performance on adjusting their local shapes by changing the shape parameters. Finally, some properties of the new rotation surfaces are discussed, and the influence rules of the shape parameters on the new rotation surfaces are studied. The modeling examples illustrate that the shape-adjustable generalized Bézier rotation surfaces provide a valuable way for the design of rotation surfaces.

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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

    Gang Hu & Junli Wu

  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. Gang Hu
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  2. Guo Wei
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  3. Junli Wu
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Correspondence to Gang Hu.

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Hu, G., Wei, G. & Wu, J. Shape-Adjustable Generalized Bézier Rotation Surfaces with Multiple Shape Parameters. Results Math 72, 1281–1313 (2017). https://doi.org/10.1007/s00025-017-0659-7

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  • DOI: https://doi.org/10.1007/s00025-017-0659-7

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