混合细分曲线及其应用  

Blending Subdivision Curves and Their Applications

作　　者：王栋[1] 张曦[2] 李桂清[2] 

机构地区：[1]华南农业大学信息学院,广州510642 [2]华南理工大学计算机科学与工程学院,广州510640

出　　处：《计算机辅助设计与图形学学报》2007年第3期286-291,共6页Journal of Computer-Aided Design & Computer Graphics

基　　金：国家自然科学基金(60673005);广东省自然科学基金(05006540;05006621)

摘　　要：构造了2个混合细分模式,一个是基于三次B样条细分的二分混合细分曲线族;另一个是基于一种三分三点逼近细分的三分混合细分曲线族.通过调整混合参数来控制曲线的收缩与膨胀幅度,利用生成函数技术和特征值方法对这2个带参数的细分模式的连续性进行了严格的理论分析.最后,通过选择合适的混合参数给出了一种曲线保长的动态细分方法.This paper designs two families of blending subdivisions based on known approximatory subdivisions. One is a binary blending subdivision based on the cubic B-splines, the other is a ternary blending subdivision based on the ternary 3-point subdivision. The approach provides a way to control the length of generated curves by introducing a blending parameter. Continuity analysis based on generating functions demonstrates that two families of blending subdivisions are C2 continuous in most cases. As an application, a length-preserving subdivision strategy is also proposed in the paper.

关 键 词：混合细分 连续性 生成函数 多分辨率 曲线保长 

分 类 号：TP391[自动化与计算机技术—计算机应用技术]