各向异性网格生成及其在曲面三角化中的应用

Anisotropic Mesh Generation and Its Application to the Surface Triangulation

网格生成技术在工程分析 ,科学计算可视化等领域有着重要的意义 .为了快速进行曲面三角化 ,提出了一种二维各向异性网格生成方法 ,通过引入椭圆距离和椭圆矩阵 ,定义了三角形的外接椭圆 ,从而将 Delaunay三角化方法扩展到各向异性环境中 ,并讨论了各向异性网格的性质 .随后将各向异性网格方法应用在曲面三角化当中 ,并将曲面的第一基本形式作为参数域的椭圆矩阵 ,同时给出了曲面 Delaunay三角化的定义 ,从而成功地利用了各向异性网格方法对曲面进行三角化 .实践证明 ,不仅其速度要大大快于传统的三角化方法 ,并且该方法能统一处理各种二次曲面和裁剪 NURBS曲面 .

Meshing technology is of great importance in the areas of engineering analysis and scientific computing visualization. This paper proposes a anisotropic meshing method, In order to extends the Delaunay method to anisotropic contexts the elliptical distance and elliptical matrix is introduced and defined, and the circum\|ellipse of a triangle is also defined. And then the method is applied to the surface triangulation, which takes the first fundmental form of surface as the elliptical matrix. Consequently, the definition of surface triangulation is obtained and an algorithm is proposed. The speed of the algorithm is greatly faster than the previous methods. Our approach can uniformly copy with quadratic and trimmed NURBS surfaces.