Print Email Facebook Twitter On Self-Intersections of Cubic Bézier Curves Title On Self-Intersections of Cubic Bézier Curves Author Yu, Ying-Ying (Liaoning Normal University) Li, Xin (Dalian Maritime University) Ji, Y. (TU Delft Numerical Analysis) Date 2024 Abstract Cubic Bézier curves are widely used in computer graphics and geometric modeling, favored for their intuitive design and ease of implementation. However, self-intersections within these curves can pose significant challenges in both geometric modeling and analysis. This paper presents a comprehensive approach to detecting and computing self-intersections of cubic Bézier curves. We introduce an efficient algorithm that leverages both the geometric properties of Bézier curves and numerical methods to accurately identify intersection points. The self-intersection problem of cubic Bézier curves is firstly transformed into a quadratic problem by eliminating trivial solutions. Subsequently, this quadratic system is converted into a linear system that may be easily analyzed and solved. Finally, the parameter values corresponding to the self-intersection points are computed through the solution of the linear system. The proposed method is designed to be robust and computationally efficient, making it suitable for real-time applications. Subject geometric modelingBézier curvesself-intersections To reference this document use: http://resolver.tudelft.nl/uuid:6c351747-4fbf-4ec1-9833-ef8b4fb11b87 DOI https://doi.org/10.3390/math12060882 ISSN 2227-7390 Source Mathematics, 12 (6) Part of collection Institutional Repository Document type journal article Rights © 2024 Ying-Ying Yu, Xin Li, Y. Ji Files PDF mathematics-12-00882-v2.pdf 2.59 MB Close viewer /islandora/object/uuid:6c351747-4fbf-4ec1-9833-ef8b4fb11b87/datastream/OBJ/view