icon.jpgFast Grid-Based Nonlinear Elasticity for 2D Deformations
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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.Symposium on Computer Animation, 2014.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.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.Rajsekhar Setaluri
http://pages.cs.wisc.edu/~rajasekh/
University of Wisconsin-Madison
Yu Wang
http://www.cis.upenn.edu/~wangyu9/
University of Pennsylvania
Nathan Mitchell
University of Wisconsin-Madison
Ladislav Kavan
http://www.seas.upenn.edu/~ladislav/
University of Pennsylvania
Eftychios Sifakis
http://pages.cs.wisc.edu/~sifakis/
University of Wisconsin-Madison