Abstract: This paper proposes a method for surface mesh generation, by advancing from two opposite sides rather than the completed edges. By the method we solve the problem that would lead to triangulation procedure failure or quality degradation of the triangulation results incurred by poor surface corner conditions. A robust and refined triangular element formation approach is presented, which proceeds directly in three dimensions and then mapped into parametric space in order to carry out succeeding tasks in two-dimensional space, such as validity check of elements and convergence check of triangulation procedure. A simple and effective convergence check scheme is also given in the context aimed to the proposed method. Numerical experiments show that high quality triangulation results are obtained by using the method and the triangulation procedure is robust and easy on implementation.