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A Certified Cubic B-Spline Interpolation Method with Tangential Direction Constraints

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Abstract

Curve interpolation with B-spline is widely used in various areas. This problem is classic and recently raised in application scenario with new requirements such as path planning following the tangential vector field under certified error in CNC machining. This paper proposes an algorithm framework to solve Hausdorff distance certified cubic B-spline interpolation problem with or without tangential direction constraints. The algorithm has two stages: The first stage is to find the initial cubic B-spine fitting curve which satisfies the Hausdorff distance constraint; the second stage is to set up and solve the optimization models with certain constraints. Especially, the sufficient conditions of the global Hausdorff distance control for any error bound are discussed, which can be expressed as a series of linear and quadratic constraints. A simple numerical algorithm to compute the Hausdorff distance between a polyline and its B-spline interpolation curve is proposed to reduce our computation. Experimental results are presented to show the advantages of the proposed algorithms.

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Authors and Affiliations

  1. School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing, 100049, China

    Shitao He, Liyong Shen, Qin Wu & Chunming Yuan

  2. KLMM, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, China

    Qin Wu & Chunming Yuan

Authors
  1. Shitao He
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  2. Liyong Shen
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  3. Qin Wu
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  4. Chunming Yuan
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Corresponding author

Correspondence to Chunming Yuan.

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The authors declare no conflict of interest.

Additional information

This research was partially supported by the National Key Research and Development Program of China under Grant No. 2020YFA0713703, the National Science Foundation of China under Grant Nos. 11688101, 12371384, and 12271516, and the Fundamental Research Funds for the Central Universities.

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He, S., Shen, L., Wu, Q. et al. A Certified Cubic B-Spline Interpolation Method with Tangential Direction Constraints. J Syst Sci Complex 37, 1271–1294 (2024). https://doi.org/10.1007/s11424-024-2420-0

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  • DOI: https://doi.org/10.1007/s11424-024-2420-0

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