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Algorithms for computing the approximation of offsets of toric Bézier curves

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Abstract

Algorithms for curve offsetting are of great importance in computer-aided design, computer-aided manufacture, and numerical control of machines. Toric surfaces, a kind of rational parametric surfaces, have been proposed for use in these areas. When the parameter domain is one dimensional, they are called toric curves, and it has been proved that such curves have many desirable properties for applications in geometric design, such as the construction of blending surfaces. This paper investigates algorithms for constructing offset curves of toric curves, including algorithms based on control polygons or on degree elevation, as well as approximate offsetting algorithms. These algorithms are able to deal with curves exhibiting self-intersections and cusps. Examples of constructing non-self-intersecting offset curves and comparison with other methods are proposed. Some illustrative examples are presented.

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Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grant Nos. 11801053, 12071057) and the Fundamental Research Funds for the Central Universities (Grant Nos. 3132022203).

Funding

This work was supported by the National Natural Science Foundation of China (Grant Nos. 11801053, 12071057) and the Fundamental Research Funds for the Central Universities (Grant Nos. 3132022203).

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Authors and Affiliations

  1. School of Science, Dalian Maritime University, Dalian, 116026, China

    Xuanyi Zhao & Ying Wang

  2. College of Mathematics and Information Science, Henan Normal University, Xinxiang, 453007, China

    Jinggai Li

  3. School of Mathematical Sciences, Dalian University of Technology, Dalian, 116024, China

    Chungang Zhu

Authors
  1. Xuanyi Zhao
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  2. Ying Wang
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  3. Jinggai Li
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  4. Chungang Zhu
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Contributions

All the authors contributed to the study conception and design. Material preparation, data collection and analysis were performed by [Xuanyi Zhao], [Ying Wang], [Jinggai Li] and [Chungang Zhu]. The first draft of the manuscript was written by [Xuanyi Zhao] and all the authors commented on previous versions of the manuscript. All the authors read and approved the final manuscript.

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Correspondence to Chungang Zhu.

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Communicated by Justin Wan.

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Zhao, X., Wang, Y., Li, J. et al. Algorithms for computing the approximation of offsets of toric Bézier curves. Comp. Appl. Math. 41, 221 (2022). https://doi.org/10.1007/s40314-022-01941-z

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  • DOI: https://doi.org/10.1007/s40314-022-01941-z

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