Automatic triangulation over three-dimensional parametric surfaces based on advancing front method

A new mesh generation method is proposed for creating adaptive triangle meshes over three-dimensional parametric surfaces based on the advancing front method. The method is advanced from two opposite boundaries instead of the completed edges. This method solves the problem that will lead to triangulation procedure failure or quality decrease of the surface triangulation results because of poor surface corner conditions. A robust and refined triangular element formation procedure is established, which proceeds directly in three dimensions and then the element is mapped into the parametric space in order to carry out the succeeding functions in two-dimensional space, such as validity checking and convergence checking. A simple but effective convergence checking scheme is also presented in this paper and misjudgement of the convergence points can be avoided. Numerical experiments demonstrate that the triangulation results with high quality can be obtained easily by using the method.