摘要： 提出一种二进制的几何非线性逼近型细分格式。在该格式中，新点不全是旧点的线性组合，其中一个新点是通过在法向量方向偏移所产生，且法向量在每次细分中能自适应计算。引入一些参数来控制细分过程，且参数对曲线形状的影响是局部的。实例证明，通过选择适当的参数值，产生的细分曲线具有保凸性和 连续性。

关键词: 非线性细分, 逼近型, 法向量, 保凸

Abstract: A new binary univariate nonlinear geometric approximating-type subdivision format is proposed in this paper. In this new format, instead of using linear combination of old vertices, one of new vertices is defined by displacement vector on normal vector direction . The normal vectors used in this format are computed adaptively in each iteration. Several parameters are used for the control of the subdivision process, and the influence of every parameter is local. It is shown that curves generated by this scheme can achieve convexity-preservation property, and the limit curve is smooth with wide range of free parameters.

Key words: nonlinear subdivision, approximating-type, normal vector, convexity preserving

中图分类号: 

• TP391.72