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中文摘要：
针对映射法的曲面网格生成容易产生畸变而导致网格质量较差的问题,提出一种基于黎曼度量,结合前沿推进技术（AFT）和Delaunay三角划分（DT）方法的曲面网格生成算法。该算法在黎曼度量的基础上,用改进的前沿推进技术生成参数域内的背景网格;且在对参数域内背景网格进行加密时,为了抵消映射过程中的畸变,采用插入三角形外接椭圆圆心的方法代替传统Delaunay插点内核,并给出了椭圆圆心定位以及判断节点是否在椭圆内的方法。该算法通过黎曼度量的引入以及合理的背景网格充分地考虑了映射畸变和算法效率,实例表明,算法易于实施,稳定性好且生成的网格质量较高。
英文摘要：
With the aim to solve the problem of shape distortion when generating the finite element mesh of parametric surfaces, mapping method was used. But mapping method could generate distortion elements which lead to poor quality meshes easily. Based on the Riemannian metric, a combined advancing front technique （AFT） and Delaunay triangulation（DT） method were applied. In this algorithm, Riemannian metric was considered, and background grids of parametric space were generated by improved AFT. When background grids of parametric space were refined to counteract mapping distortion, the traditional Delaunay incremental insertion kernel was replaced by inserting the center of triangle circumscribed ellipse, and the algorithm for locating ellipse center and judging whether nodes within ellipse. The mapping distortion and algorithm efficiency were considered by the algorithm by introducing Riemannian metric and reasonable background mesh. Examples show that the new method is easy to implement. The mesh which has good stability and high quality can be generated.
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