Continuous Deformations by Isometry Preserving Shape Integration

We introduce a novel continuous surface deformation method which relies on a time-dependent vector field over a triangular mesh. For every time step the piecewise linear vector field is obtained by leastsquares minimization of the metric distortion induced by integration subject to boundary conditions. As an integral part of the approach, we introduce a new measure to describe local metric distortion which is invariant to the particular triangulation of the surface and which can incorporate smoothness of the field. Neither of these properties are met by previous work. A GPU implementation of the proposed algorithm enables fast deformations. The resulting deformations have lower metric distortions than deformations by existing (linear or non-linear) methods. This is shown for a number of representative test data sets.