Fast and Robust Inversion-Free Shape Manipulation

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• 作者：Tiantian Liu ; Ming Gao ; Lifeng Zhu ; Eftychios Sifakis and Ladislav Kavan
• 刊名：Computer Graphics Forum
• 出版年：2016
• 出版时间：May 2016
• 年：2016
• 卷：35
• 期：2
• 页码：1-11
• 全文大小：900K
• ISSN：1467-8659

文摘

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.