In view of the existing potential functions' deficiency in the construction of the transition curve based on Metaball technology

a polynomial potential function with a parameter is constructed; then

the application of the potential function in constructing the transition curve is investigated. By properly selecting a class of Bézier curve with parameters

a polynomial potential function with a parameter is ingeniously constructed from the properties at the end points of the curve. Then

the influence of the potential function on the transition curve is investigated

and construction of the optimal transition curve based on the energy optimization method is presented. Examples show the feasibility of the method. The proposed potential function can not only make the transition curve achieve quasi C continuity at the end points but also adjust the shape of the transition curve by modifying the value of the parameter. After the optimal value of the parameter in the potential function is obtained

the smoothest transition curve would be obtained. The proposed potential function alleviates the deficiency of the existing potential functions in constructing the transition curve based on Metaball technology. Furthermore

the construction method of potential function is universal

and the potential functions with different characteristics can be constructed from different curve models.