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2005•Journal of Zhejiang University ScienceRequires access

Bézier curves with shape parameter

Wentao Wang, Guozhao Wang

Open publisher page 25 citations

Abstract

In this paper, Bezier basis with shape parameter is constructed by an integral approach. Based on this basis, we define the Bezier curves with shape parameter. The Bezier basis curves with shape parameter have most properties of Bernstein basis and the Bezier curves. Moreover the shape parameter can adjust the curves' shape with the same control polygon. As the increase of the shape parameter, the Bezier curves with shape parameter approximate to the control polygon. In the last, the Bezier surface with shape parameter is also constructed and it has most properties of Bezier surface.

About this research paper

What this paper is about

In this paper, Bezier basis with shape parameter is constructed by an integral approach. Based on this basis, we define the Bezier curves with shape parameter. The Bezier basis curves with shape parameter have most properties of Bernstein basis and the Bezier curves. Moreover the shape parameter can adjust the curves' shape with the same control polygon. As the increase of the shape parameter, the Bezier curves with shape parameter approximate to the control polygon. In the last, the Bezier surface with shape parameter is also constructed and it has most properties of Bezier surface.

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OpenAlex reports 25 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

In this paper, Bezier basis with shape parameter is constructed by an integral approach. Based on this basis, we define the Bezier curves with shape parameter. The Bezier basis curves with shape parameter have most properties of Bernstein basis and the Bezier curves. Moreover the shape parameter can adjust the curves' shape with the same control polygon. As the increase of the shape parameter, the Bezier curves with shape parameter approximate to the control polygon. In the last, the Bezier surface with shape parameter is also constructed and it has most properties of Bezier surface.

Key concepts: Bézier curve, Shape parameter, Polygon (computer graphics), Basis (linear algebra), Mathematics, Basis function, Surface (topology), Geometry

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