Real-Time Symmetry-Preserving Deformation

• Published in: Computer graphics forum Vol. 33; no. 7; pp. 229 - 238
• Main Authors: Wu, Xiaokun, Wand, Michael, Hildebrandt, Klaus, Kohli, Pushmeet, Seidel, Hans-Peter
• Format: Journal Article
• Language: English
• Published: Oxford Blackwell Publishing Ltd 01.10.2014
• Subjects: Analysis; and object representations; Categories and Subject Descriptors (according to ACM CCS); Computer graphics; Deformation; Editing; I.3.5 [Computer Graphics]: Computational Geometry and Object Modeling-Curve; I.3.5 [Computer Graphics]: Computational Geometry and Object Modeling—Curve, surface, solid, and object representations; Optimization; solid; Studies; surface; Symmetry; Topological manifolds
• ISSN: 0167-7055; 1467-8659
• DOI: 10.1111/cgf.12491

In this paper, we address the problem of structure‐aware shape deformation: We specifically consider deformations that preserve symmetries of the shape being edited. While this is an elegant approach for obtaining plausible shape variations from minimal assumptions, a straightforward optimization is numerically expensive and poorly conditioned. Our paper introduces an explicit construction of bases of linear spaces of shape deformations that exactly preserve symmetries for any user‐defined level of detail. This permits the construction of low‐dimensional spaces of low‐frequency deformations that preserve the symmetries. We obtain substantial speed‐ups over alternative approaches for symmetry‐preserving shape editing due to (i) the sub‐space approach, which permits low‐res editing, (ii) the removal of redundant, symmetric information, and (iii) the simplification of the numerical formulation due to hard‐coded symmetry preservation. We demonstrate the utility in practice by applying our framework to symmetry‐preserving co‐rotated iterative Laplace surface editing of models with complex symmetry structure, including partial and nested symmetry.