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Cubic TC-Bézier curves with shape parameter

Xumin Liu

Open publisher page 2 citations

Abstract

For the problem of shape controlling in curves and surfaces design with free form, cubic TC-Bezier curves with shape parameter is constructed. Parameter affects geometric property of curves, the larger is , the curve comes more near the control polygon. Then it is demonstrated that many valuable curves can be expressed by TC-Bezier curves. And then 1 condition of cubic TC-Bezier curves and example in surface modeling are presented. The modeling examples illustrate that the new curve is very valuable for computer aided geometric design.

About this research paper

What this paper is about

For the problem of shape controlling in curves and surfaces design with free form, cubic TC-Bezier curves with shape parameter is constructed. Parameter affects geometric property of curves, the larger is , the curve comes more near the control polygon. Then it is demonstrated that many valuable curves can be expressed by TC-Bezier curves. And then 1 condition of cubic TC-Bezier curves and example in surface modeling are presented. The modeling examples illustrate that the new curve is very valuable for computer aided geometric design.

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

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Available abstract

For the problem of shape controlling in curves and surfaces design with free form, cubic TC-Bezier curves with shape parameter is constructed. Parameter affects geometric property of curves, the larger is , the curve comes more near the control polygon. Then it is demonstrated that many valuable curves can be expressed by TC-Bezier curves. And then 1 condition of cubic TC-Bezier curves and example in surface modeling are presented. The modeling examples illustrate that the new curve is very valuable for computer aided geometric design.

Key concepts: Bézier curve, Geometric design, Polygon (computer graphics), Shape parameter, Family of curves, Computer science, Geometric modeling, Curve fitting

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