We introduce the term shape resolution, which adds to the existing definitions of screen and touch resolution. We propose a framework, based on a geometric model (Non-Uniform Rational B-splines), which defines a metric for shape resolution in ten features. We illustrate it by comparing the current related work of shape changing devices. We then propose the concept of Morphees that are self-actuated flexible mobile devices adapting their shapes on their own to the context of use in order to offer better affordances. For instance, when a game is launched, the mobile device morphs into a console-like shape by curling two opposite edges to be better grasped with two hands. We then create preliminary prototypes of Morphees in order to explore six different building strategies using advanced shape changing materials (dielectric electro active polymers and shape memory alloys). By comparing the shape resolution of our prototypes, we generate insights to help designers toward creating high shape resolution Morphees.