Abstract:

When composite curves are constructed, the control points of the adjacent curves must meet certain conditions. In order to simplify the conditions, a kind of hyperbolic polynomial curve with parameters, called H-Bézier curve, which has a structure similar to the quadratic Bézier curve, is constructed. This curve has many basic properties of Bézier curve, such as convex hull property, symmetry, geometric invariance, endpoint interpolation and end edge tangent property. Besides, the curve has shape adjustability and can represent hyperbola. If special parameters are chosen, then when the control points of two adjacent curves satisfy the  conditions for Bézier curve, they can achieve   continuity. In addition, the method of constructing H-Bézier with given tangent polygon is given. This method is simple and effective, and the entire curve is conformal to the tangent polygon. Using tensor product method, the H-Bézier curve can be extended to surface, which also has many good properties.

Key words: curve design;Bézier curve;continuity;shape parameter;tangent polygon