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Constructing local controlled developable H-Bézier surfaces by interpolating characteristic curves

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Abstract

The developable surface is always a hot issue in CAGD, CAD/CAM and used in many manufacturing planning operations, e.g., for ships, aircraft wing, automobiles and garments. In some special fields, the CAD model of developable surface is designed by interpolating a given spatial characteristic curve. In this paper, we present a class of methods to construct local controlled developable H-Bézier surfaces through a given characteristic curve. First, we introduce a class of generalized cubic H-Bézier basis functions, and utilize them to design the generalized cubic H-Bézier curves with shape parameters. Then we construct generalized cubic developable H-Bézier surfaces through a given space generalized cubic H-Bézier curve which serve as the line of curvature or geodesic. The shapes of the constructed surfaces can be adjusted and altered expediently using the shape parameters. Furthermore, the sufficient and necessary conditions for the interpolating developable H-Bézier surface to be a cylinder or a cone are deduced, respectively. Finally, we give some representative examples to illustrate the convenience and efficiency of the presented methods.

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Acknowledgements

The authors are very grateful to the reviewers for their insightful suggestions and comments, which helped us to improve the presentation and content of the paper. This work is supported by the National Natural Science Foundation of China (Grant nos. 51875454 and 61772416).

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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 & Xiaofeng Wang

  2. School of Computer Science and Engineering, Xi’an University of Technology, No. 5 South Jinhua Road, Xi’an, 710048, People’s Republic of China

    Gang Hu & Xiaofeng Wang

Authors
  1. Gang Hu
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  2. Junli Wu
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  3. Xiaofeng Wang
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Correspondence to Gang Hu.

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Hu, G., Wu, J. & Wang, X. Constructing local controlled developable H-Bézier surfaces by interpolating characteristic curves. Comp. Appl. Math. 40, 216 (2021). https://doi.org/10.1007/s40314-021-01587-3

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  • DOI: https://doi.org/10.1007/s40314-021-01587-3

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