Linear Subspace Design for Real-Time Shape Deformation

Yu Wang
University of Pennsylvania
Alec Jacobson
Columbia University and ETH Zurich
Jernej Barbič
University of Southern California
Ladislav Kavan
University of Pennsylvania

Our linear subspaces are very fast to compute. This enables the users to add (or remove) control handles very quickly, allowing them to realize their creative intent in a single interactive session.


We propose a novel method to design linear deformation subspaces, combining both linear blend skinning and generalized barycentric coordinates under a unified framework. Deformation subspaces play a key role in cutting down the time complexity of variational shape deformation methods and physics-based animation (reduced-order physics). Our subspaces feature many desirable properties: interpolation, smoothness, shape-awareness, locality, and constant and linear precision. We achieve these by minimizing a novel quadratic deformation energy, carefully constructed via a discrete Laplacian that induces linear precision on the boundary of the domain. The main advantage of our method is speed. The bases of our subspaces are found as solutions of sparse linear systems, which can be computed interactively even for generously tessellated domains. This allows the user to seamlessly switch between applying transformations at handles and editing the subspace by adding, removing or relocating control handles. The combination of fast computation and good properties means that designing the right subspace is now just as creative as manipulating handles. This paradigm shift in handle-based deformation opens new opportunities to explore the space of shape deformations.


Yu Wang, Alec Jacobson, Jernej Barbič, Ladislav Kavan. Linear Subspace Design for Real-Time Shape Deformation. ACM Transactions on Graphics 34(4) (SIGGRAPH 2015).    


Code (coming soon)

Demo (coming soon)


We would like to thank Keenan Crane, Mathieu Desbrun, Yotam Gingold, Eitan Grinspun, Maks Ovsjanikov, Eftychios Sifakis, Olga Sorkine-Hornung, Lifeng Zhu, and Denis Zorin for illuminating discussions. Harmony Li narrated the accompanying video. We thank Scott Schaefer for providing the wooden gingerbread man image from "Image Deformation Using Moving Least Squares". This research was sponsored by the National Science Foundation (IIS-1350330, CAREER-1055035, IIS-1422869) and the Sloan Foundation. The Columbia Computer Graphics Group is supported by the NSF, Intel, The Walt Disney Company, and Autodesk.