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DOI:
Journal of Software:2009.20(6):1673-1684

不规则网格上的曲面设计方法
何军,张彩明,杨兴强
(山东大学 计算机科学与技术学院,山东 济南 250101;山东大学 计算机科学与技术学院,山东 济南 250101;山东经济学院 计算机科学与技术学院,山东 济南 250014)
Constructing Surface on Irregular Meshes
HE Jun,ZHANG Cai-Ming,YANG Xing-Qiang
()
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Received:January 01, 2008    Revised:May 19, 2008
> 中文摘要: 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.
Abstract: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.
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基金项目:Supported by the National Natural Science Foundation of China under Grant Nos.60603077, 60633030 (国家自然科学基金); the National Basic Research Program of China under Grant No.2006CB303102 (国家重点基础研究发展计划(973)) Supported by the National Natural Science Foundation of China under Grant Nos.60603077, 60633030 (国家自然科学基金); the National Basic Research Program of China under Grant No.2006CB303102 (国家重点基础研究发展计划(973))
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何军,张彩明,杨兴强.不规则网格上的曲面设计方法.软件学报,2009,20(6):1673-1684

HE Jun,ZHANG Cai-Ming,YANG Xing-Qiang.Constructing Surface on Irregular Meshes.Journal of Software,2009,20(6):1673-1684