Fast and Robust Inversion-Free Shape Manipulation

Tiantian Liu, Ming Gao, Lifeng Zhu, Eftychios Sifakis, Ladislav Kavan
2016 Computer graphics forum (Print)  
Figure 1 : A band of surface vertices on a tetrahedralized bunny is constricted to a tight noose. Even with severe distortion, the resulting mesh is inversion-free, i.e., all tetrahedral elements have positive volume. 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
more » ... 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.
doi:10.1111/cgf.12806 fatcat:hnrlwz7uz5ekzeoltwmkgazeku