The M2Disco (Multiresolution, Discrete and Combinatorial Models) research team aims at proposing new combinatorial, discrete and multiresolution models to analyse and manage various types of data such as images, 3D volumes and 3D meshes, represented as Digital Sur- faces (ie subset of Zn). One of their project called PALSE foam requires the computation of the shortest path between two points on a manifold. We are proposing the study of two algorithm for computing such a dis- tance, but also providing metric embedding inside a Discrete Exterior Calculus structure (DEC). We performs various tests regarding the two algorithms, but also con rm through experience DEC's operators con- vergence using suitable metric. This work is the base of both a research project named CoMeDiC (Convergent Metrics for Digital Calculus) and Ph.D. project.