规则二次曲面壳密度可变的全四边形网格剖分

Graded All-quadrilateral Mesh Generation for Regular Quadric Surfaces

本文提出了一种规则二次曲面壳上密度可变的全四边形网格剖分方法。利用二次曲面壳的标准参数方程，在二次曲面块与参数平面的一个等参面之间建立一种一对一映射关系。根据白面壳上网格划分的密度要求，先在等参面上剖分网格，然后将其精确映射到二次曲面上。本方法消除了网格剖分时曲面上极点可能出现的奇异性，实现了二次曲面上的全四边形网格剖分，并可按网格划分的密度要求实现网格的疏密过渡．以球面，圆柱面为例，介绍了由二次曲面相交、相贯所产生的组合曲面上密度可变的全四边形网格的生成．本方法采用用户熟悉的二次曲面的标准参数方程形式。输入数据是用户熟悉的几何参数．通过文后的例题，可以看到本方法简单、方便，生成的单元质量好。

This paper presents a graded all-quadrilateral meshing method for regularquadric surfaces. Using the standard parametric equation of a quadric surface, A one-toone mapping is built between the quadric surface W and a isoparametric area on theparametric plane. According to the mesh density distribution. the isoparametric area isfistly meshed. then the meshes are mapped to the quadric surface. The method dispels thesingularity properly occurring at the poles of surfaces when meshing it, realizes the allquadrilateral meshing on quadric surfaces, and realizes the generation of graded meshed.Take spheres and cylinders for examples, introduces the graded all-quadrilateral mesh generation for constitute surfaces produced by several quadric surfaces. The method uses the standard parametric equation of quadric surface Which is familiar to users, and input data is the geometry parametric. The method is simple, convenient and the result meshes having good shape.