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Journal of Applied Mathematics
Volume 2013, Article ID 171392, 9 pages
Research Article

Quasi-Bézier Curves with Shape Parameters

Faculty of Science, Ningbo University of Technology, Ningbo 315211, China

Received 2 October 2012; Revised 7 February 2013; Accepted 24 February 2013

Academic Editor: Juan Manuel Peña

Copyright © 2013 Jun Chen. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The universal form of univariate Quasi-Bézier basis functions with multiple shape parameters and a series of corresponding Quasi-Bézier curves were constructed step-by-step in this paper, using the method of undetermined coefficients. The series of Quasi-Bézier curves had geometric and affine invariability, convex hull property, symmetry, interpolation at the endpoints and tangent edges at the endpoints, and shape adjustability while maintaining the control points. Various existing Quasi-Bézier curves became special cases in the series. The obvious geometric significance of shape parameters made the adjustment of the geometrical shape easier for the designer. The numerical examples indicated that the algorithm was valid and can easily be applied.