基于曲面拟合的复杂自由曲面网格划分

Grid generation on complex free-form surface based on surface fitting

为了实现复杂自由曲面的建筑网格划分,将复杂自由曲面拟合成1个曲面,并利用映射法进行网格划分。首先提出基于非均匀有理B样条(NURBS)的线面求交和基于NURBS的面面求交2种方法,获得复杂自由曲面的N×M点云;将N×M点云作为控制点构造NURBS曲面,然后把修剪后的NURBS曲面边界按给定数目或给定长度划分,连接参数域上的边界节点后得到参数域网格,将其映射回空间曲面。对边界处网格进行投影处理以减少曲面拟合出现的边界褶皱及内缩问题。采用加密点阵技术减小曲面拟合的误差。研究结果表明:与多曲面网格划分方法相比,采用曲面拟合及映射法能够得到线条流畅、大小基本一致的网格,具有良好的建筑美学效果。

In order to obtain architectural mesh of complex free-form surface,the complex free-form surface was fitted into one surface and then grids were generated using mapping method.First,two methods called NURBS based on ray-surface intersection and NURBS based on plane-surface intersection were proposed to obtain the N×M point cloud of complex free-form surface.Secondly,a NURBS surface was constructed using the N×M point cloud as control points,then the boundaries of trimmed NURBS surface were divided by a given number or a given length,and the boundary nodes of the parametric domain were connected to get parametric domain grids.After that,the grids were mapped onto the free-form surface.Lastly,the grids near the boundaries were projected onto original surfaces to reduce boundary fold and shrinkage caused by surface fitting.To reduce the error of surface fitting,the number of point cloud was increased.The results show that compared with the method which respectively generates grids on multiple trimmed surfaces,the proposed methods produce fluent and uniform grids,with good architectural aesthetics.