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陈龙, 冯文斌, 谢宇洋, 卜宁远, 汪中厚. 曲多边形四边剖分算法[J]. 计算机辅助设计与图形学学报, 2022, 34(5): 794-803. DOI: 10.3724/SP.J.1089.2022.18995
引用本文: 陈龙, 冯文斌, 谢宇洋, 卜宁远, 汪中厚. 曲多边形四边剖分算法[J]. 计算机辅助设计与图形学学报, 2022, 34(5): 794-803. DOI: 10.3724/SP.J.1089.2022.18995
Chen Long, Feng Wenbin, Xie Yuyang, Bu Ningyuan, Wang Zhonghou. Four-Sided Subdivision Algorithm of Curved Polygon[J]. Journal of Computer-Aided Design & Computer Graphics, 2022, 34(5): 794-803. DOI: 10.3724/SP.J.1089.2022.18995
Citation: Chen Long, Feng Wenbin, Xie Yuyang, Bu Ningyuan, Wang Zhonghou. Four-Sided Subdivision Algorithm of Curved Polygon[J]. Journal of Computer-Aided Design & Computer Graphics, 2022, 34(5): 794-803. DOI: 10.3724/SP.J.1089.2022.18995

曲多边形四边剖分算法

Four-Sided Subdivision Algorithm of Curved Polygon

  • 摘要: 针对当前体参数化模型构建过程中需要进行模型分割的问题,提出一种基于曲线几何特征的曲多边形四边剖分算法.首先定义轮廓曲线、内外连接线、轮廓多边形等特征,采用改进的射线法构建特征包含树;然后从特征包含树最底层叶节点开始执行一系列子域剖分操作,包括零亏格子域多边形获取及排序、可行剖分线寻找及排序、递归执行四边剖分,获得全为曲凸四边形的子域,并且尽可能避免产生尖点;最后对所有非空四边形子域进行Coons插值生成参数化曲面,辅以拉伸、扫描、旋转、放样等操作获得体参数化模型.实例部分选取了5种多孔模型,每种模型分别在轮廓变化和内外连接线变化的情况下进行剖分,结果表明所提算法能快速、准确地实现包含亏格域的复杂二维四边剖分.

     

    Abstract: Aiming at the problems of model segmentation in the current volume parametric model construction,a four-sided subdivision algorithm of curved polygons based on the geometric features of curves is proposed.Firstly,contour curves,internal and external connection lines,contour polygons and other features are defined,and the feature inclusion tree is constructed by using the improved ray method.Then,starting from the leaf nodes at the leaf level of the feature inclusion tree,a series of subdomain subdivision operations are performed,including the acquisition and sorting of polygons in the domain with zero genus,search and sorting of the feasible subdivision lines,and the recursive quadrangle subdivision,so as to obtain the four-sided subdomain which is all convex.Finally,the Coons interpolation is carried out for all four-sided subdomains to generate NURBS surfaces,and the volume parametric model is obtained by stretching,scanning,rotation and loft operations.In the example part,five kinds of models with multi holes are selected and subdivided under the condition changes of the contours or the connection lines.The results show that the algorithm can quickly and accurately realize the four-sided subdivision for complex two-dimensional models with arbitrary genus.

     

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