Specifications
Mathematics - 921.6 Numerical Methods
DOI: 10.4028/www.scientific.net/AMM.347-350.2712
Database: Compendex
Compilation and indexing terms, © 2013 Elsevier Inc.
7.
Accession number: 20133616696638
Title: A novel extension to the polynomial basis functions describing Bezier curves and surfaces
of degree n with multiple shape parameters
Authors: Qin, Xinqiang1 ; Hu, Gang1 ; Zhang, Nianjuan1 ; Shen, Xiaoli1 ; Yang, Yang1/秦新强;张
念娟;胡钢;;;
Author affiliation: 1 Department of Applied Mathematics, Xi'An University of Technology,
710048 Xi'an, China
Corresponding author: Qin, X. (xqqin@xaut.edu.cn)
Source title: Applied Mathematics and Computation
Abbreviated source title: Appl. Math. Comput.
Volume: 223
Issue date: 2013
Publication year: 2013
Pages: 1-16
Language: English
ISSN: 00963003
CODEN: AMHCBQ
Document type: Journal article (JA)
Publisher: Elsevier Inc., 360 Park Avenue South, New York, NY 10010, United States
Abstract: The construction of Be´zier curves using shape control parameters is one of the most
popular areas of research in computer aided geometric design (CAGD). A class of new polynomial
basis functions with n - 1 local shape control parameters is presented here to allow the
construction of Be´zier curves with n local shape control parameters, which is an extension to the
classical Bernstein basis functions of degree n. The properties of the proposed basis functions
and the corresponding piecewise polynomial curve with n - 1 local shape control parameters are
analyzed. This analysis shows that the new class of polynomial functions meets the conditions
required for both C0, C1 and C2 continuity as well as G0, G 1 and G2 continuity. Some curve
design applications are then discussed and an extended application for surface design is also
presented. The modeling examples illustrate that the new extension provides not only a better
approximation and mathematical description of Be´zier curves, but allows the shape parameters
to be altered, making it a valuable method for the design of curves and surfaces. © 2013 Elsevier
Inc. All rights reserved.
Number of references: 27
Main heading: Functions
Controlled terms: Computer aided design - Curve fitting - Polynomial approximation
Uncontrolled terms: Basis functions - Continuity conditions - Curve and surface -
Extension - Shape parameters
Classification code: 723.5 Computer Applications - 921 Mathematics - 921.6 Numerical