基于气泡吸附的自由曲面三角形网格生成方法  

Automatic grid generation on free-form surface based on bubble-like adsorption

作　　者：王奇胜[1] 高博青[1] 李铁瑞[1] 吴慧 Wang Qisheng1, Gao Boqing1,Li Tierui1, Wu Hui2(1 College of Civil Engineering and Architecture, Zhejiang University, Hangzhou 310058, China; 2 Public Administration College, Zhejiang University of Finance ＆ Economics, Hangzhou 310018, Chin)

机构地区：[1]浙江大学建筑工程学院,浙江杭州310058 [2]浙江财经大学公共管理学院,浙江杭州310018

出　　处：《华中科技大学学报（自然科学版）》2018年第3期98-102,共5页Journal of Huazhong University of Science and Technology(Natural Science Edition)

基　　金：国家自然科学基金资助项目(51678521,51778558);浙江省自然科学基金资助项目(LY15E080017)

摘　　要：为了满足自由曲面网格结构对网格均匀性的要求,提出了一种自由曲面的三角形网格自动生成方法——空间气泡法.首先,按一定规则在曲面上布置适量的网格点;然后,将网格点模拟为大小相同的弹性气泡,引入气泡间的相互作用力,得到各气泡的运动控制方程,并利用Velocity-Verlet算法求得气泡系统的平衡状态;接着,通过求气泡中心点的三维Voronoi图与曲面的交线得到曲面上的Voronoi图;最后,对曲面Voronoi图做对偶变化并删去冗余边,得到曲面上的Delaunay图,即所求的三角形网格.算例表明：该方法自动化程度高,适用范围广,生成的网格规整、均匀,为网格结构的设计提供了便利.To meet the grid uniformity of the free-form surface grid structure,an automatic triangular grid generation method was presented for free-form surfaces,named spatial bubble-like method.Firstly,a moderate amount of grid points were decorated on a given surface according to certain rules.Secondly,the grid points were regarded as elastic bubbles with the same size and the interaction forces were introduced between the bubbles.The motion control equations of bubbles were established,and the equilibrium state of the bubble system was acquired by Velocity-Verlet algorithm.Thirdly,the Voronoi diagram on the surface was obtained by calculating the intersection between the surface and the three-dimensional Voronoi diagram of the centers of bubbles.Finally,the Delaunay triangulation on the surface was determined based on the dual change of the Voronoi diagram and elimination of redundant edges.The case study indicates that this method is of high automation level,wide applicable scope and good grid uniformity,and provides the convenience for the design of grid structures.

关 键 词：自由曲面 网格结构 网格生成 气泡法 Delaunay法 

分 类 号：TU311.41[建筑科学—结构工程]