Journal
COMPUTER GRAPHICS FORUM
Volume 35, Issue 2, Pages 1-11Publisher
WILEY
DOI: 10.1111/cgf.12806
Keywords
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Funding
- NSF [IIS-1350330, IIS-1253598, IIS-1407282]
- National Science Foundation of China (NSFC) [61502096]
- Natural Science Foundation of Jiangsu Province [BK20150634]
- Direct For Computer & Info Scie & Enginr
- Div Of Information & Intelligent Systems [1622360, 1407282] Funding Source: National Science Foundation
- Direct For Computer & Info Scie & Enginr
- Div Of Information & Intelligent Systems [1253598] Funding Source: National Science Foundation
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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.
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