一类带参数的插值逼近型曲线细分

A family of interproximate subdivision schemes with parameters for curves

文章从融合型细分格式出发,将控制点集分成插值点集和逼近点集,递归定义出每次细分后新边点及新顶点的几何规则,进而建立一类新型静态二重插值逼近型细分框架。该细分框架不仅包含一些已有的经典细分格式,还派生出一些新型细分格式。它可以同时插值指定点并逼近其余点,且极限曲线是C^(2)连续的;此外该文还建立了一套插值点选取规则。利用该细分框架及插值点选取规则,可以实现对复杂图形的再现,其效果优于现有的各类细分算法。

Based on the combined subdivision scheme,a new stationary binary interproximate subdivision framework is established by recursively defining geometric rules of new edge points and new vertex points in each step.The data points are divided into interpolating point set and approximating point set.The framework not only contains some existing classical subdivision schemes,but also includes some brand-new subdivision schemes.The subdivision schemes of the framework can interpolate the given points and approximate the other points simultaneously,and the limit curves are C^(2) continuous.Furthermore,a set of selection rules for interpolating points are constructed.Complex graphs can be reproduced by using the subdivision framework and the selection rules.Numerical examples show that the effect is better than that of the existing subdivision algorithms.