On Intersections of B-Spline Curves

Ying-Ying Yu, Xin Li and Ye Ji ()
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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

Mathematics, 2024, vol. 12, issue 9, 1-17

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.

Keywords: geometric modeling; Bézier curves; B-spline curves; intersection (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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