Directed Energy Deposition (DED) processes are a category of Additive Manufacturing (AM) processes that can be combined with six degrees of freedom multi-axis technologies to manufacture parts with complex internal geometries without support material, while ensuring the local distance requirements. This paper provides a numerical method to compute such a path, using both a facetized file of a part and substrates locations as inputs. Topological concepts are first described to introduce the method. The algorithm is then detailed into three steps: mesh refinement, next layer points search and connection edges computing. Application to different facetized files validates the method.