Triangulation of a domain is a discretization process in which a selection of triples pertaining to one of the various possible collections of three distinct elements of a set within the domain is found such that every triple can be used as a triangular facet to model that domain. The ideal triangulation process should render a domain decomposition into a triangular grid which should be simple to generate, comfortable to use and computationally efficient. To select a triangular grid exhibiting these properties is far from being an easy task. In short, what is sought of in this problem is a triangulation schemme which may lead to Delaunay triangles. In the present paper a computerized triangulation method accomplished through three refinement phases is resented. During the first phase the set is pre-processed to organize the candidate triples. In the second phase an initial temptative triangular grid is formed. Finally, this temptative grid is automatically refined by optimizing the triangular facets so that each triangle exhibits the greatest minimum internal angle. This innovative algorithm. although based on well known ideas. can be used advantegeously to discretize 2D convex and non-convex sets and also 3D smooth surfaces for any given set of discrete surface.