Some improvements on optimal multi-degree reduction of Bézier curves with geometric constraints. (February 2015)

• Record Type: Journal Article
• Authors: Lu, Lizheng
• Is Part Of: Computer aided design. Volume 59(2015)
• Page Start: 39
• Page End: 42
• Publication Date: 2015-02
• Subjects: Bézier curve -- Degree reduction -- Geometric constraint -- Shape preserving; Computer-aided design -- Periodicals; Engineering design -- Data processing -- Periodicals; Computer graphics -- Periodicals; Conception technique -- Informatique -- Périodiques; Infographie -- Périodiques; Computer graphics; Engineering design -- Data processing; Periodicals; Electronic journals; 620.00420285
• DOI: 10.1016/j.cad.2014.08.017
• Languages: English
• ISSNs: 0010-4485

Abstract

Abstract: Recently, Zhou et al. (2014) presented an efficient method for optimal multi-degree reduction of Bézier curves with geometric constraints. We notice that their method is unable to always preserve the original tangent directions at the endpoints, which is a desirable shape preserving property in geometric modeling and related applications. In order to satisfy this requirement, we impose a feasible region for the two parameters relating to the G 1 constraint and convert degree reduction with the feasible region into a constrained minimization problem. The projected Newton method employed for solutions exhibits faster convergence. Our method can produce the desired results which, however, cannot be achieved by the previous method in a few cases.