Extensions of Hyperbolic Bézier Curves

Hyperbolic Bezier curve(briefly H-Bezier curve) with multiple shape parameters is presented in this paper.The curve not only possesses most of the properties of the Bezier curve,but also can be adjusted totally or locally by taking the different values of shape parameters,with increasing of the shape parameters the curve can well approximate the control polygon.Moreover,the curve can represent hyperbolas and catenary exactly.At last,the C1continuous joint of curve pieces is discussed and some examples are provided to illustrate the application in geometric modeling.