Surface Mesh Generation in Parametric Space Using a Riemannian Surface Definition

抄録

In order to solve the problem of generating distortion elements in the mapping from parameter space to real space, and the boundary coincidence of the mesh generated by the software quality, an approach for parametric surface mesh generation based on Riemannian metric, combined with Delaunay triangulation and AFT is proposed. In our algorithm, the boundary curves are discretized based on the proximity and curvature of the curves in the model after derivation the correlation of curve length between parametric space and real space. Background meshes of parametric space were generated by using improved AFT, and could improve the efficient of the algorithm and control element sizing and metric values. When background mesh of parametric space were refined, to counteract mapping distortion, the traditional Delaunay incremental insertion kernel is replaced by inserting the center of triangle circumscribed ellipse, and the algorithm for locating ellipse center and judging whether nodes within ellipse. In this paper, the details of the surface mesh generated by the algorithm are introduced in detail. The algorithm proposed in this paper has the characteristics of reliable algorithm, high mesh generation efficiency and mesh quality. Finally, the reliability of the proposed algorithm is verified by an example of surface mesh generation.