Abstract: The purpose of the present study is to enhance the continuity of the transition curve at the endpoints, and give it the shape adjustment ability relative to the fixed base curves. Starting from the equation of the transition curve, according to the predetermined goal about the continuous order, the basic conditions that need to be satisfied by the blending functions are deduced. The blending function is expressed as a linear combination of Bernstein basis functions, and the combination coefficients are to be determined. Based on the basic conditions and the endpoint properties of Bernstein basis functions, an equation set about the undetermined coefficients is obtained. The initial expression of the blending function is obtained by solving the equation set. By using the degree elevation formula, the degree of the initial expression is raised twice. Then, the free parameter is introduced into the expression of the blending function. The blending function features in symmetry, midpoint property, monotonicity and boundedness. Additionally, the paper analyzes that value range of free parameter that can ensure the curve of the blending function has a unique inflection point. For general parameter values, the transition curve can reach 3 C continuity. For special parameter values, the transition curve can reach 4 C continuity. Furthermore, the shape characteristics of the transition curve are analyzed, and the numerical examples have also verified the correctness and effectiveness of the proposed method.

Key words: curve design, transition curve, shape blending, shape adjustment