Fast and Robust Inversion-Free Shape Manipulation

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Date
2016
Journal Title
Journal ISSN
Volume Title
Publisher
The Eurographics Association and John Wiley & Sons Ltd.
Abstract
We present a shape manipulation technique capable of producing deformations of 2D and 3D meshes, guaranteeing that no elements will be inverted. We achieve this by augmenting the quadratic ex-rotated elastic energy with additional convex terms that penalize the presence of inverted elements. Using a schedule of increasing penalty coefficients, we efficiently and robustly converge to an inversion free state by solving a sequence of unconstrained convex minimization problems. This process can be interpreted as a special purpose Semi-Definite Programming (SDP) solver. We demonstrate that our method outperforms solvers used in previous work, including commercial-grade SDP software (MOSEK). As an additional benefit, our method also converges to the solution via a more intuitive path, which can be used for quick preview. We demonstrate the efficacy of our scheme in a number of 2D and 3D shapes undergoing moderate to drastic deformation.
Description

        
@article{
10.1111:cgf.12806
, journal = {Computer Graphics Forum}, title = {{
Fast and Robust Inversion-Free Shape Manipulation
}}, author = {
Liu, Tiantian
and
Gao, Ming
and
Zhu, Lifeng
and
Sifakis, Eftychios
and
Kavan, Ladislav
}, year = {
2016
}, publisher = {
The Eurographics Association and John Wiley & Sons Ltd.
}, ISSN = {
1467-8659
}, DOI = {
10.1111/cgf.12806
} }
Citation