基于边界网格模型的T样条实体重建

第30卷第10期计算机辅助设计与图形学学报Vol.30No.10 2018年10月Journal of Computer-Aided Design & Computer Graphics Oct. 2018基于边界网格模型的T样条实体重建

柏硌, 赵罡, 王伟*, 杜孝孝, 郭马一

(北京航空航天大学机械工程及自动化学院北京100191)

(jrrt@https://www.sodocs.net/doc/e718155084.html,)

摘要: 为解决零亏格边界网格模型的T样条实体重建问题, 提出一种基于八叉树细分和渐进迭代最小二乘拟合算法的T样条实体构建算法. 首先给出一种基于体-面-边-点4层几何拓扑的T样条实体数据结构和节点矢量计算算法;

接着对边界网格进行参数化, 在单位参数立方体和网格模型之间建立参数映射关系, 并且采用MVC方法保证参数化结果的单射无自交性; 最后实现T样条实体的渐进迭代最小二乘拟合. 对sphere模型, head模型和bunny模型进行测试, 实现了基于边界网格模型的T样条实体重建, 提高了T样条实体构建的效率, 并且使得该算法在处理大规模数据时更具优势

关键词: T样条实体; 八叉树细分; 数据结构; 渐进迭代最小二乘拟合; 等几何分析

中图法分类号: TP391.41 DOI: 10.3724/SP.J.1089.2018.16983

Reconstruction of T-Spline Solid from Boundary Mesh

Bo Luo, Zhao Gang, Wang Wei*, Du Xiaoxiao, and Guo Mayi

(School of Mechanical Engineering and Automation, Beihang University, Beijing 100191)

Abstract: A T-spline solid reconstruction algorithm based on octree subdivision and least square progressive it-erative approximation (LSPIA) is proposed to solve the problem of reconstruction of T-spline solid from ge-nus-zero boundary mesh. Firstly, this paper presents a cube-face-edge-vertex based four-layer geometry topology T-spline solid data structure and its knot vector calculation algorithm. Then, the parameterization of boundary mesh is realized to build the parametric mapping between the unit cube and the boundary mesh. The MVC parameterization method is also implemented to guarantee the injective mapping and no self-intersection property of the parameterization results. Later, the least square progressive iterative approximation of T-spline solid is im-plemented. The algorithm presented in this paper has been tested in the case study, which realizes the reconstruc-tion of T-spline solid from boundary mesh. The proposed algorithm improves the efficiency of the reconstruction of T-spline solid and has the advantage in handling large amount of data.

Key words: T-spline solid; octree subdivision; data structure; least square progressive iterative approximation;

isogeometric analysis

收稿日期: 2017-11-10; 修回日期: 2018-06-07. 基金项目: 国家自然科学基金(51305016, 61572056). 柏硌(1994—), 男, 硕士研究生, 主要研究方向为CAD/CAE、计算机图形学; 赵罡(1972—), 男, 博士, 教授, 博士生导师, 主要研究方向为CAD/CAE/CAM; 王伟(1978—), 男, 博士, 副教授, 硕士生导师, 论文通讯作者, 主要研究方向为CAD/CAE; 杜孝孝(1991—), 男, 博士研究生, 主要研究方向为CAD/CAE; 郭马一(1992—), 男, 博士研究生, 主要研究方向为CAD/CAE.

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