基于曲面展开的自由曲面网格划分  

Grid generation on free-form surface based on surface flattening

作　　者：潘炜[1] 吴慧[2] 李铁瑞[1] 高博青[1] 

机构地区：[1]浙江大学建筑工程学院,浙江杭州310058 [2]浙江财经大学城乡规划与管理学院,浙江杭州310018

出　　处：《浙江大学学报（工学版）》2016年第10期1973-1979,共7页Journal of Zhejiang University：Engineering Science

基　　金：国家自然科学基金资助项目(51378457);浙江省自然科学基金资助项目(LY15E080017)

摘　　要：为了实现自由曲面的网格划分,提出基于曲面展开和映射思想的网格划分方法.自由曲面参数域的2个方向分别等分,将等分点映射回空间曲面以在曲面上形成矩形点阵,则曲面的展开等效为矩形点阵的映射展开,以参数域对角线所对应的空间曲面对角线为展开基线,按照展开前、后面积变化最小的基本原则,对自由曲面由中心逐层向外展开.该种展开方式能够很好地反映曲面的形状、走向及面积分布;展开的点阵通过拟合形成有边界的二维平面,将二维平面从中心点等角度分成6部分,考虑不同的边界情形,依次对每部分采用线推进方法逐层生成三角形网格,最终实现完整平面的网格生成.该种平面网格划分方式更具操作性,效果更流畅;二维平面的网格根据拓扑不变性,映射回自由曲面形成空间曲面网格.该方法生成的网格线条流畅、大小均匀,有较好的适用性.A method based on surface flattening and mapping theory was proposed in order to realize grid generation on free-form surface.The parametric domain of free-form surface was divided into the given number in both directions,and these discrete points were mapped back to free-form surface so as to generate rectangular lattices on the surface.Surface flattening can be realized by making efforts to flat the rectangular lattices.The diagonal line on the free-form surface was regarded as the base line.The surface was flatted starting from the center point,from inside to outside,based on the rule of minimum area variation.The provided flattening method can reflect the shape,trend and area distribution of free-form surface well.Then the flatted rectangular lattices were fitted into a two-dimensional surface.The twodimensional surface was divided into 6parts from the center point with the same angle.Considering the different boundary conditions,the line advancing method was adopted to generate triangular grids for each part.Grid generation was realized for the whole two-dimensional surface.The two-dimensional grids were mapped back to the free form surface based on the constant topology.The proposed method can apply to many different cases,and the grids generated by the method have advantages of fluent lines and uniform sizes.

关 键 词：自由曲面 曲面展开 曲面拟合 空间映射 网格生成 

分 类 号：TU311[建筑科学—结构工程]