STM images of multidomain epitaxial graphene on Pt(111) have been combined with a geometrical model to investigate the origin of the coincidence Moiré superstructures. We show that there is a relation between the appearance of a particular Moiré periodicity and the minimization of the absolute value of the strain between the graphene and the substrate for the different orientations between both atomic lattices. This model predicts all the stable epitaxial graphene structures that can be grown on transition metal surfaces, and we have made use of it for reproducing previously published data from different authors. Its validity suggests that minimization of the strain within the coincident graphene unit-cell due to a strong local interaction is the driving force in the formation of Moiré superstructures.