In this paper we tackle the problem of mapping a surface acquired from a real object onto a piece of the plane, taking into account the topological and geometrical properties of the surface, as well as the speci-ficity of low-resolution acquisitions. We first describe the general background of surfaces unfolding and cutting. We then introduce the cutting process used to manage the topological constraint of the one-to-one mapping, with some speedup improvements. Specific geometrical constraints linked to the low resolution context are detailed, and some experimental results on real and synthetic data are finally presented.