Hyperbolic Bézier curves with shape parameters

Hyperbolic Bezier curve(briefly H-Bezier curve) with shape parameters and is presented.Analogous to the quadratic Bezier curves,each hyperbolic polynomial curve segment is generated by three consecutive control points.The curve possesses most of the properties of the quadratic Bezier curve.By taking the different values of and,the shape of the curve can be adjusted locally or totally.With increasing of the parameter and,the curve can approximate the control polygon.And hyperbolic polynomial curves can represent straight lines and hyperbolas exactly.