In the presented paper, an approach for the direct triangulation of 3D surfaces described by STL meshes has been introduced. Although the STL mesh is a valid fully conforming triangulation, its special designation for rapid prototyping makes it very specific. The actual discretization consists of several phases. Firstly, a boundary representation of the object is constructed from the STL file using feature recognition approach. It has been shown that this is an ambiguous task which cannot be generally fully automated. A successful completion of this procedure often requires user intervention in a framework of an interactive environment. In the next phase, a smooth (limit) surface is reconstructed over the original STL mesh using a subdivision technique yielding the differentiable limit surface. An interpolating subdivision based on the slightly modified Butterfly scheme has been adopted. The modifications make the limit surface smoother in situations where the original strategy seems to be not enough flexible, which is often the case of STL meshes containing elements of large aspect ratio spanning the whole extent of the surface in a particular direction. Furthermore, for surfaces with curvature only in one direction, the enhancement of the underlying STL mesh has been proposed in order to better recover the shape of the original surface. Finally, the limit surface is subjected to a triangulation based on the advancing front technique constrained directly to the limit surface. The vitality of the proposed approach has been demonstrated on few examples. The further research is focused primarily on additional improvement of the construction of the boundary representation in order to enable as much as possible automated processing of complex STL models.