Shape deformation from metric ’s transport

We exploit the possibility of deforming a solid volume, or a surface as well, by assigning a target metric. As well known, an elastic solid may change its shape under two different kinds of actions: one are the loadings, the other one are the distortions, aka, the pre-strains. Actually, a distortion prescribes the target metric sought by the solid, and the metric effectively realized is the one that minimize the distance, measured through an elastic energy, between the target metric and the actual one. The challenge of our work is to use the metric information taken from a pair of configurations X¯, X of a given body Bx, to deform a different body By, so that its deformation be as similar as possible to the one suffered by Bx. In particular, we assess the metric change between the two configurations X¯, X of the template Bx; then, we use this information to build a target metric for By, exploiting the notion of distortions: given a source configuration Y¯, we find a target configuration Y by minimizing an appropriate elastic energy. The proposed method is very effective in deforming solids as well as surfaces, and in reproducing similar deformations even when applied to different bodies.