ScholarLens Back to search
2009•Journal of Hefei University of TechnologyRequires access

Bézier curves with shape parameters

Yan Lan-lan

Open publisher page 2 citations

Abstract

A class of polynomial functions of 4th-degree with two parameters is presented,which is the extension of quadratic Bernstein and cubic λ-B basis functions.Then using the de Casteljau arithmetic,the generalized basis function of degree n +2 with two shape parameters is obtained.Based on this,a new type of curve with two shape parameters is defined.The new curve contains generalized Bezier curves and λ-Bezier curves.The properties of the new basis and the new curve are analyzed.Meanwhile,the geometry meaning of the shape parameters and the geometric drawing method of the new curve are given.

About this research paper

What this paper is about

A class of polynomial functions of 4th-degree with two parameters is presented,which is the extension of quadratic Bernstein and cubic λ-B basis functions.Then using the de Casteljau arithmetic,the generalized basis function of degree n +2 with two shape parameters is obtained.Based on this,a new type of curve with two shape parameters is defined.The new curve contains generalized Bezier curves and λ-Bezier curves.The properties of the new basis and the new curve are analyzed.Meanwhile,the geometry meaning of the shape parameters and the geometric drawing method of the new curve are given.

Why it matters

OpenAlex reports 2 citations for this work. Citation counts describe recorded attention and do not establish research quality.

Key contribution

A contribution statement is not available in the OpenAlex record.

Method / approach

Method details are not available in the OpenAlex metadata.

Main findings

Findings are not separately available in the OpenAlex metadata.

Limitations

Limitations are not available in the OpenAlex metadata.

Applications

Application details are not available in the OpenAlex metadata.

Available abstract

A class of polynomial functions of 4th-degree with two parameters is presented,which is the extension of quadratic Bernstein and cubic λ-B basis functions.Then using the de Casteljau arithmetic,the generalized basis function of degree n +2 with two shape parameters is obtained.Based on this,a new type of curve with two shape parameters is defined.The new curve contains generalized Bezier curves and λ-Bezier curves.The properties of the new basis and the new curve are analyzed.Meanwhile,the geometry meaning of the shape parameters and the geometric drawing method of the new curve are given.

Key concepts: Bézier curve, Mathematics, Shape parameter, Basis function, Basis (linear algebra), Bernstein polynomial, Degree (music), Quadratic equation

Related papers

Related paper 1Related paper 2Related paper 3
Back to paper searchBrowse research topicsOriginal source
Bézier curves with shape parameters — Research Paper | ScholarLens