Isotropic umbrella based triangulation of regular parametric surfaces

In this paper we propose an advancing front method for generating an isotropic triangular mesh on a regular parametric surface. Starting from a point on the surface, the method computes a set of points in the intersection curve between the surface and the sphere centered at that point with a prescribed radius. From this set we select the vertices of a cell composed by triangles approximately equilateral. The mesh grows repeating the described computation with boundary vertices of the cell as starting points. Compared to methods proposed by other authors, the current method may be considered as an improvement, since it is more efficient and flexible. Furthermore, the resulting mesh is closer to being isotropic. Additionally, we obtain a sufficient condition ensuring that a surface triangulation is of Delaunay type.