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On Intersections of B-Spline Curves

Author

Listed:
  • Ying-Ying Yu

    (School of Mathematics, Liaoning Normal University, Dalian 116029, China)

  • Xin Li

    (School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, China)

  • Ye Ji

    (Delft Institute of Applied Mathematics, Delft University of Technology, 2628 CD Delft, The Netherlands)

Abstract

Bézier and B-spline curves are foundational tools for curve representation in computer graphics and computer-aided geometric design, with their intersection computation presenting a fundamental challenge in geometric modeling. This study introduces an innovative algorithm that quickly and effectively resolves intersections between Bézier and B-spline curves. The number of intersections between the two input curves within a specified region is initially determined by applying the resultant of a polynomial system and Sturm’s theorem. Subsequently, the potential region of the intersection is established through the utilization of the pseudo-curvature-based subdivision scheme and the bounding box detection technique. The projected Gauss-Newton method is ultimately employed to efficiently converge to the intersection. The robustness and efficiency of the proposed algorithm are demonstrated through numerical experiments, demonstrating a speedup of 3 to 150 times over traditional methods.

Suggested Citation

  • Ying-Ying Yu & Xin Li & Ye Ji, 2024. "On Intersections of B-Spline Curves," Mathematics, MDPI, vol. 12(9), pages 1-17, April.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:9:p:1344-:d:1385093
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    References listed on IDEAS

    as
    1. Yousif, Majeed A. & Hamasalh, Faraidun K., 2024. "The fractional non-polynomial spline method: Precision and modeling improvements," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 218(C), pages 512-525.
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