Fast Grid-Based Nonlinear Elasticity for 2D Deformations

Abstract
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.
Description

        
@inproceedings{
:10.2312/sca.20141124
https::/diglib.eg.org/handle/10.2312/sca.20141124.067-076
, booktitle = {
Eurographics/ ACM SIGGRAPH Symposium on Computer Animation
}, editor = {
Vladlen Koltun and Eftychios Sifakis
}, title = {{
Fast Grid-Based Nonlinear Elasticity for 2D Deformations
}}, author = {
Setaluri, Rajsekhar
and
Wang, Yu
and
Mitchell, Nathan
and
Kavan, Ladislav
and
Sifakis, Eftychios
}, year = {
2014
}, publisher = {
The Eurographics Association
}, ISSN = {
1727-5288
}, ISBN = {
978-3-905674-61-3
}, DOI = {
/10.2312/sca.20141124
https://diglib.eg.org/handle/10.2312/sca.20141124.067-076
} }
Citation