一类参数曲线的积累平均弧长参数化方法

通过用指定方法及约束准则进行局部插值, 为高效求解采用从局部传递到整体的思想, 给出积累平均弧长参数化法的一般框架, 并在该框架下给出3种具体的积累平均弧长参数化法及相应的数值算法. 积累平均弧长参数化法的目标是降低传统方法求得的曲线关于光顺性的目标函数值, 并使方法具有可根据设计者需求生成满足条件曲线的灵活性. 实例验算表明: 在同一约束准则下, 该方法求得的全局插值曲线的目标函数值小于弦长参数化和向心参数化所对应的目标函数值.

A Class of Parameterization Method of Accumulated Average Arc Length for Parametric Curves

By using the specified method and constraint criteria for local interpolation, and the idea of transferring from part to whole in order to solve the problem efficiently, the general framework of the accumulated average arc length parameterization method was given, and three concrete accumulation average arc length parameterization methods and corresponding numerical algorithms were given under the framework. The objective of the accumulated average arc length parameterization method was to reduce the objective function value of the curve with respect to the smoothness obtained by the traditional method, and make the method have the flexibility to generate the curve satisfying the conditions according to designer’s requirements. Examples show that under the same constraint criterion, the objective function values of global interpolation curves obtained by the method can be less than that corresponding to chord length parameterization and centripetal parameterization.