Fast Grid-Based Nonlinear Elasticity for 2D Deformations

Rajsekhar Setaluri
University of Wisconsin-Madison
Yu Wang
University of Pennsylvania
Nathan Mitchell
University of Wisconsin-Madison
Ladislav Kavan
University of Pennsylvania

Eftychios Sifakis
University of Wisconsin-Madison

Image warp of a flexible, yet incompressible, elastic sphere pinched between two fingers. The effect was created by providing spatially-varying compression resistance values to make the sphere significantly more area-preserving than its compressible background.


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.

accompanying video


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

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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.