中文摘要：

目的针对现有势函数在构造基于Metaball的过渡曲线时所存在的不足，构造了一类带参数的多项式势函数，并研究了该势函数在构造过渡曲线中的应用。方法首先恰当选取一种带参数的多项式B6zier曲线模型，巧妙地利用该曲线模型在端点处满足的性质构造出带参数的多项式势函数，然后研究了所构造的势函数对过渡曲线的影响，最后给出了基于能量优化法的最佳过渡曲线构造方法，并通过实例验证了其有效性。结果带参数的势函数不仅能使过渡曲线在端点处达到拟C^2连续，而且还可利用所带的参数对过渡曲线的形状进行调整。通过能量优化法确定势函数中参数的最优取值，可获得最为光顺的过渡曲线。结论所提出的势函数缓解了现有势函数在构造基于Metaball的过渡曲线时的不足。另外，势函数的构造方法还具有普适性，从不同的曲线模型出发可构造出具有不同特性的势函数。

英文摘要：

Objective 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 poten- tial function in constructing the transition curve is investigated. Method By properly selecting a class of B6zier 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 op- timal transition curve based on the energy optimization method is presented. Examples show the feasibility of the method. Result The proposed potential function can not only make the transition curve achieve quasi C2 continuity at the end points but also adjust the shape of the transition curve by modifying the value of the parameter. Mter the optimal value of the pa- rameter in the potential function is obtained, the smoothest transition curve would be obtained. Conclusion 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.