Adjustable Bézier Curves with Simple Geometric Continuity Conditions

This paper aims to simplify the continuity conditions of Bezier curves. For this purpose, a special family of Bezier curves with three parameters, to be called adjustable Bezier curves, is constructed. They have the same structure as the quartic Bezier curves. The newly constructed curves possess some of the basic properties of Bezier curves, such as the convex hull property, symmetry, geometric invariance, etc., and they have shape adjustability. Moreover, under the geometric continuity of order 1 ( G 1 ) conditions of the usual Bezier curves, the adjustable Bezier curves can reach geometric continuity of order k ( G k ); here, k is one of the parameters of the newly constructed curves. The recursive evaluation algorithm of the new curves is provided. We also discuss how to construct the adjustable Bezier curves with a given tangent polygon. Numerical examples illustrate the correctness and validity of the proposed method.