On Intersections of B-Spline Curves

Ying-Ying Yu, Xin Li, Ye Ji

Research output: Contribution to journalArticleScientificpeer-review

127 Downloads (Pure)

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
Original languageEnglish
Article number1344
Number of pages17
JournalMathematics
Volume12
Issue number9
DOIs
Publication statusPublished - 2024

Keywords

  • geometric modeling;
  • Bézier curves
  • B-spline curves
  • intersection

Fingerprint

Dive into the research topics of 'On Intersections of B-Spline Curves'. Together they form a unique fingerprint.

Cite this