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Fast and Robust Inversion-Free Shape Manipulation.

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Title: Fast and Robust Inversion-Free Shape Manipulation.
Authors: Liu, Tiantian1, Gao, Ming2, Zhu, Lifeng1,3, Sifakis, Eftychios2, Kavan, Ladislav1,4
Source: Computer Graphics Forum. May2016, Vol. 35 Issue 2, p1-11. 11p.
Subjects: Computer graphics research, Computer art, Digital image processing, Graphic arts, Data visualization
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. [ABSTRACT FROM AUTHOR]
Copyright of Computer Graphics Forum is the property of Wiley-Blackwell and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: 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. [ABSTRACT FROM AUTHOR]
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  Data: <i>Copyright of Computer Graphics Forum is the property of Wiley-Blackwell and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Value: 10.1111/cgf.12806
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        Text: English
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        PageCount: 11
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      – SubjectFull: Digital image processing
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              Text: May2016
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