Degree reduction of Bézier curves with restricted control points area. (May 2015)

• Record Type: Journal Article
• Authors: Gospodarczyk, Przemysław
• Is Part Of: Computer aided design. Volume 62(2015)
• Page Start: 143
• Page End: 151
• Publication Date: 2015-05
• Subjects: Bézier curve -- Degree reduction -- Constrained least squares approximation; 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.2014.11.009
• Languages: English
• ISSNs: 0010-4485

Abstract

Abstract: In this paper, we propose a new approach to the problem of degree reduction of Bézier curves with respect to the least squares norm. We impose restrictions of the control points area to get more intuitive location of the control points. As a result, the degree reduced curve is suitable for further modification and applications. We present and compare two methods of solving the new problem. First one is based on quadratic programming approach and the other on BVLS algorithm. Some illustrative examples are given. Highlights: We propose a new approach to the problem of degree reduction of Bézier curves. We impose constraints of the control points area. The degree reduced curve is suitable for further modification and applications. We give and compare two methods of solving the new problem.