Fast Grid-Based Nonlinear Elasticity for 2D Deformations

We present a deformation technique that constructs 2D warps by using spline curves to specify the starting and target shapes of selected key contours. We generate a two-dimensional deformation map from these contours by simulating a non-linear elastic membrane deforming in accordance with user-specified constraints. Although we support and demonstrate elastic models inspired by physical membranes, we highlight a custom material model for this specific application, which combines the benefits of harmonic interpolation and area-preserving deformations. Our warps are represented via a standard Cartesian lattice and leverage the regularity of this description to enable efficient computation. Specifically, our method resolves the targeting constraints imposed along arbitrarily shaped contours with sub-grid cell precision, without requiring an explicit remeshing of the warp lattice around the constraint curve. We describe how to obtain a well-conditioned discretization of our membrane model even under elaborate constraints and strict area preservation demands, and present a multigrid solver for the efficient numerical solution of the deformation problem.

Rajsekhar Setaluri, Yu Wang, Nathan Mitchell, Ladislav Kavan, Eftychios Sifakis. Fast Grid-Based Nonlinear Elasticity for 2D Deformations. Symposium on Computer Animation, 2014.  

We are grateful to Perry Kivolowitz for motivating this work and providing crucial feedback. We thank Peter Kaufmann and Christian Schueller for sharing their source code and expertise; Tiantian Liu and Nathan Marshak for help with the accompanying video. This research is supported in part by NSF IIS-1253598, NSF CNS-1218432, NSF IIS-1350330, and US Army TARDEC.