参数曲线间具有极小能量的G^(2)连续过渡曲线构造

Construction of G^(2)Transition Curves with Minimal Energy between Parametric Curves

在构造参数曲线间满足G^(2)连续的过渡曲线时,需要选取自由参数的取值。因此,可对这些自由参数进行优化选取,以使得构造的过渡曲线满足特定要求。针对平面与空间2种情形,分别提出了利用能量极小化选取G^(2)连续过渡曲线所含自由参数的方法,其中平面情形以过渡曲线的弯曲能极小为目标,空间情形以过渡曲线的弯曲能和扭曲能同时极小为目标。为便于应用,基于MATLAB平台设计了所提出方法对应的图形用户界面,用户通过简单操作即可构造出任意2条参数曲线间的G^(2)连续过渡曲线。

When constructing G^(2)transition curves between parametric curves,it is necessary to select the values of free parameters.Hence,these free parameters can be optimized to make the transition curves meet some specific requirements.For the cases of planar transition curves and spatial transition curves,the methods of using energy minimization to select the free parameters are proposed respectively.In the planar case,the objective is to minimize the bending energy of the transition curves,and in the spatial case,the objective is to minimize the bending energy and twisting energy of the transition curves simultaneously.In order to facilitate the applications,the graphical user interface corresponding to the proposed methods is designed based on MATLAB platform.Users can construct the G^(2)transition curve between any two parametric curves through simple operation.