Setaluri, RajsekharWang, YuMitchell, NathanKavan, LadislavSifakis, EftychiosVladlen Koltun and Eftychios Sifakis2014-12-162014-12-162014978-3-905674-61-31727-5288https://doi.org/10.2312/sca.20141124https://diglib.eg.org/handle/10.2312/sca.20141124.067-076We 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.I.3.7 [Computer Graphics]Computational Geometry and Object ModelingPhysically based modeling