基于能量优化的数据参数化方法

构造一条通过一组给定数据点的参数样条曲线的关键之一是选取节点.本文提出了一种基于离散能量模型的确定节点参数的新方法,该方法首先通过极小化离散能量模型的目标函数确定参数样条曲线在节点处的最佳切向角,然后以最佳切向角为参变量来计算节点参数.该方法所得到的方程为线性方程,便于求解.本文最后通过实例对新方法与累加弦长方法、向心参数化方法、修正弦长参数化方法以及ZCM方法进行了比较.

A New Method of Data Parameterization Based on Optimal Energy

A key issue in parametric curve interpolation is the selection of parametric knots. A new method based on the discrete energy model for determining parametric knots is presented. By minimizing the objective function of the discrete energy model and solving a system of linear equations, the new method can obtain the optimal tangent-angles generated by the fairer parametric curve over parametric knots and then employ those as variables to compute the parametric values of knots. The examples for comparing the shapes and errors of the curves by the new method are also included.