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.
Abstract
We propose a method to design linear deformation subspaces, unifying
linear blend skinning and generalized barycentric coordinates.
Deformation subspaces cut 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 both constant and linear precision. We achieve these by minimizing
a quadratic deformation energy, built via a discrete Laplacian
inducing linear precision on the domain boundary. Our main
advantage is speed: subspace bases are solutions to a sparse linear
system, computed interactively even for generously tessellated
domains. Users may 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.
Publication
Yu Wang, Alec Jacobson, Jernej Barbic, Ladislav Kavan. Linear Subspace Design for Real-Time Shape Deformation. ACM Transaction on Graphics 34(4) [Proceedings of SIGGRAPH], 2015.
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Acknowledgements
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.
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.