不规则网格上的曲面设计方法  

Constructing Surface on Irregular Meshes

作　　者：何军[1] 张彩明[1,2] 杨兴强[1] 

机构地区：[1]山东大学计算机科学与技术学院,山东济南250101 [2]山东经济学院计算机科学与技术学院,山东济南250014

出　　处：《软件学报》2009年第6期1673-1684,共12页Journal of Software

基　　金：国家自然科学基金Nos.60603077,60633030;国家重点基础研究发展计划(973)No.2006CB303102~~

摘　　要：提出一种在不规则网格上构造曲面的方法.其基本思想是,通过均匀双三次B样条基函数的分解和子基函数的分类,将B样条曲面方法推广到任意四边形网格.给定一个任意四边形控制网格,首先对每个控制点构造一个基函数;所有控制点加权组合形成整体曲面.构造的曲面是分片双三次有理参数多项式曲面.此方法可以看成是均匀B样条曲面构造方法的扩展,如果控制网格是规则四边形网格,那么构造得到的曲面与均匀双三次B样条曲面是一致的.最后,实例证明此方法能够有效地构造曲面.A method is presented for constructing surfaces on irregular meshes. The basic idea is to extend the B-spline method to irregular meshes through the decomposition and classification of uniform bi-cubic B-spline basis function. Given a quad mesh of control points, a basis function is constructed for each control point. Then the surface is defined by the weighted combination of all the control points using their associated basis functions. This surface is a piecewise bi-cubic rational parametric polynomial surface. It is an extension to uniform B-spline surfaces in the sense that its definition is an analogy of the B-spline surface, and it produces a uniform bi-cubic B-spline surface if the control mesh is a regular quad mesh. Examples are also included to show that the new method can be used to construct surface on irregular meshes effectively.

关 键 词：不规则网格 B样条曲面 基函数 分片双三次有理参数多项式曲面 

分 类 号：TP391[自动化与计算机技术—计算机应用技术]