空间代数曲线的参数化逼近  

PARAMETRIC APPROXIMATION OF ALGEBRAIC SPACE CURVES

作　　者：贺志民[1] 方美娥[2] 

机构地区：[1]浙江林学院理学院,浙江杭州311300 [2]浙江大学计算机图形图像研究所,浙江杭州310027

出　　处：《计算机应用与软件》2008年第9期130-132,135,共4页Computer Applications and Software

基　　金：浙江省教育厅自然科学基金(20060676)

摘　　要：提出一种用三次B样条曲线逼近空间代数曲线的方法。对非奇异的情况,先用随机微分方程方法采样,然后对采样点进行聚类排序,最后用三次B样条曲线逼近有序点列;而对包含奇异点的情况,则将空间曲线双有理映射成平面曲线,采用已有的含奇异点的平面代数曲线的采样及排序方法来实现对应空间曲线的采样及排序。两种情况都获得了优于其它方法的逼近效果。A method of approximating algebraic space curves by cubic B-splines is proposed. For the case of nonsingular curves, stochastic differential sampling method is applied. Then, the sampling points are clustered and sorted. Finally, a cubic B-splines curve is used for the approximation of an ordered points range. While for the ease of singular curves, a curve is birationally mapped to a plane algebraic curve firstly. Then, the existed sampling and sorting methods for singular plane curves are used, and the sampling and sorting of algebraic space curves are realized. In the two cases, the approximation effects are better than those of other methods.

关 键 词：空间代数曲线 参数逼近 微分方程方法采样 聚类排序 三次B样条 

分 类 号：O241.82[理学—计算数学] O187.1[理学—数学]