Coincidence condition of two Bézier curves of an arbitrary degree. (February 2016)

• Record Type: Journal Article
• Authors: Chen, Xiao-Diao; Yang, Chao; Ma, Weiyin
• Is Part Of: Computers & graphics. Volume 54(2016)
• Page Start: 121
• Page End: 126
• Publication Date: 2016-02
• Subjects: Coincidence detection -- Bézier curve -- Degeneration -- Conjecture; Computer graphics -- Periodicals; 006.6
• DOI: 10.1016/j.cag.2015.07.013
• Languages: English
• ISSNs: 0097-8493

Abstract

Abstract: This paper discusses the coincidence condition of two Bézier curves of the same degree, which is necessary for a curve/curve intersection algorithm. It proves that two Bézier curves of the same degree are coincident with each other if and only if they have a coincident control polygon or they can be reparameterized into the same non-reparameterizable Bézier curve of a lower degree. A simple method is also provided for detecting the reparameterizable case where a Bézier curve can be reparameterized into a non-reparameterizable one of a lower degree. Abstract : Graphical abstract: Abstract : Highlights: Present coincidence conditions of two Bézier curves of the same degree. The resulting coincidence check is different from the point inversion technique. Our method is done by using equality conditions of explicit expressions. Coincidence check of two Bézier curves with partial overlapping is also discussed.