On Linear Variational Surface Deformation Methods

IEEE Transactions on Visualization and Computer Graphics, Vol. 14(1), 2008
Interactive Shape Modeling and Deformation, EUROGRAPHICS 2009
Mario Botsch, Olga Sorkine-Hornung

Surface-based deformation benchmark.

Several deformation examples chosen to test linear surface-based deformation methods and to reveal their strengths and limitations. A reference non-linear deformation method (PriMo) was chosen for comparison purposes (bottom row).


This survey reviews the recent advances in linear variational mesh deformation techniques. These methods were developed for editing detailed high-resolution meshes, like those produced by scanning real-world objects. The challenge of manipulating such complex surfaces is three-fold: the deformation technique has to be sufficiently fast, robust, and intuitive and easy to control to be useful for interactive applications. An intuitive, and thus predictable, deformation tool should provide physically plausible and aesthetically pleasing surface deformations, which in particular requires its geometric details to be preserved. The methods we survey generally formulate surface deformation as a global variational optimization problem that addresses the differential properties of the edited surface. Efficiency and robustness are achieved by linearizing the underlying objective functional, such that the global optimization amounts to solving a sparse linear system of equations. We review the different deformation energies and detail preservation techniques that were proposed in the recent years, together with the various techniques to rectify the linearization artifacts. Our goal is to provide the reader with a systematic classification and comparative description of the different techniques, revealing the strengths and weaknesses of each approach in common editing scenarios.



We wish to thank Leif Kobbelt and Daniel Cohen-Or for encouraging us to prepare this survey and for co-authoring numerous papers recited here. We are also grateful to them, and to Marc Alexa, Markus Gross, Denis Zorin, Max Wardetzky, Klaus Hildebrandt for the various discussions that helped to improve this manuscript. We also thank the anonymous reviewers for their valuable comments and suggestions. The results in Fig. 7 of the survey are courtesy of Tiberiu Popa and Alla Sheffer.