Surface Deformations Driven by Vector-Valued 1-Forms

We formulate the problem of surface deformations as the integration in the least square sense of a discrete vector-valued 1-forms obtained as the result of applying smooth stretching and rotation fields to the discrete differential of the 0-form defined by the vertex coordinates of a polygon mesh graph. Simple algorithms result from this formulation, which reduces to the solution of sparse linear systems. The method handles large angle rotations in one step and is invariant to rotations, translations, and scaling. We also introduce the integration of 1-forms along spanning trees as a heuristic to speed up the convergence of iterative solvers.