保参数方向的形状可调过渡曲线与曲面

针对保参数方向构造过渡曲线曲面方法的不足， 构造了任意参数曲线曲面间既保持参数方向又具有形状可调性的C¹与C²连续过渡曲线曲面。首先，基于2类带1个自由参数的调配函数，分别构造满足C¹与C²连续的过渡曲线，并讨论基于能量优化模型的最佳过渡曲线构造问题；然后，将所提出的方法推广到过渡曲面的构造。 实例结果表明，2被过渡曲线曲面为任意参数曲线曲面时，利用该方法构造的过渡曲线曲面不仅与2被过渡曲线曲面的参数方向保持一致，而且可利用所带的自由参数对其形状进行调整。通过能量优化模型确定自由参数的取值，可获得尽可能光顺的过渡曲线曲面。 所提方法弥补了保参数方向构造过渡曲线曲面方法的不足，是一种实用的过渡曲线曲面构造方法。

The shape-adjustable transition curves and surfaces with parameter direction preserving

In view of the deficiency of the methods for constructing the transition curve and surface with parameter direction preserving， the C¹ and C² transition curves and surfaces with adjustable shape and parameter direction preserving between arbitrary parametric curves and surfaces are constructed. Firstly， the C¹ and C² transition curves are established on the base of two blending functions with a free parameter， and construction of the optimal transition curves based on energy optimization models is discussed. Then， the transition surfaces are similarly presented. Examples show that， the two transited curves and surfaces can be arbitrary parametric curves and surfaces when the proposed methods are used to construct transition curves and surfaces. The transition curves and surfaces not only maintain the parameter direction with the two transited curves and surfaces， but also can be adjusted by the free parameter. The value of the free parameters can be determined by the energy optimization model， which would obtain the transition curves and surfaces as smooth as possible. The proposed method is a practical method which overcomes the disadvantages of the methods for constructing the transition curve and surface with parameter direction preserving.