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.

@InProceedings{SWMKS14,
  author       = "Setaluri, Rajsekhar and Wang, Yu and Mitchell, Nathan and Kavan, Ladislav and Sifakis, Eftychios",
  title        = "Fast Grid-Based Nonlinear Elasticity for 2D Deformations",
  booktitle    = "Proceedings of the Symposium on Computer Animation",
  year         = "2014",
  projecturl   = "http://www.seas.upenn.edu/~ladislav/setaluri14fast/setaluri14fast.html",
  url          = "http://graphics.cs.wisc.edu/Papers/2014/SWMKS14"
}