The Research On Singular Mixing Hyperbolic Bézier Curve

This paper researches the hyperbolic bézier curve, and introduces a H-Bézier basisfunction by adding two parameters to the singular mixing function. Theintroduction of the two parameters increases the flexibility of curve adjustments. Atthe same time, the properties of H-Bézier curve with singular mixing function andits continuity condition are given. This article includes five chapters: in the firstchapter, we introduce the development of CAGD briefly and the studied contents in thispaper. In the second chapter, we review some basic definitions, properties of bézier curveand surface, as well as the bézier curve with one and more shape parameters. In the thirdchapter, we review some properties of hyperbolic bézier curve and surface, as well as thehyperbolic bézier curve with one and more shape parameters. The fourth chapter is themain achievement of this paper, the basis function of hyperbolic bézier curve with singularmixing function and its properties are introduced firstly. Then the author presents a singularmixing hyperbolic bézier curve, also gives some related properties and prove them. At last,in the fifth chapter, we make a summary for the above work, innovation and practicalsignificance, and also outlook for further study.