任意四边形网格上G1／C2连续B样条曲面的构造  

Construction of G^1/C^2 continuous B-spline surfaces over arbitrary quadrilateral network

作　　者：蒋跃华[1] 李根[1] 陈志杨[2] 张三元[1] 叶修梓[1] 

机构地区：[1]浙江大学计算机科学与技术学院,CAD＆CG国家重点实验室,浙江杭州310027 [2]浙江工业大学软件学院,浙江杭州310014

出　　处：《浙江大学学报（工学版）》2008年第12期2068-2073,共6页Journal of Zhejiang University：Engineering Science

基　　金：国家自然科学基金资助项目(60473106,60333010);国家“863”高技术研究发展计划资助项目(2007AA01Z311,2007AA04Z1A5);高等学校博士学科点基金资助项目(20060335114)

摘　　要：针对经过四边形划分的点云或网格模型,提出了在呈任意拓扑四边形的网格上构造光滑拼接曲面片的算法.首先生成原始模型上的四边形曲线网格,且对每个四边形区域,由边界曲线和内部数据点拟合生成B样条曲面,在得到G0连续的曲面片网格后,采用了一种跨界导矢矫正方法,使相连的两张曲面片在正则边界上保持C2连续,非正则边界上保持近似的G1连续.实验表明,该算法速度快,适用性强,对四边形网格的拓扑结构没有限制;在重建的曲面片具有较好的连续性,同时保持了模型的几何特征,能满足工程实际需要.For the point cloud or mesh model with quad-partition, an algorithm of constructing smooth joining B-spline surfaces over arbitrary quadrilateral network was developed. Firstly, a curve network was constructed over the quad-partitioned model. Then for each quadrilateral patch, a B-spline surface was fitted from four boundary curves, and internal data points. After obtaining GO continuous surface patches network, a method of modifying the cross-boundary derivatives was proposed to make two adjacent surfaces to be C2 continuous along regular edges or G1 continuous along irregular edges. Applications showed that the presented algorithm is efficient and practical, and it has no restriction on the topology structure of the quadrilateral network; the reconstructed surfaces not only have good continuity but also capture the geometric details of the model and can satisfy the engineering requirements.

关 键 词：逆向工程 B样条曲面拟合 多个曲面片 光滑拼接 连续性 相容性 

分 类 号：TP391[自动化与计算机技术—计算机应用技术]