Subspace Condensation: Full Space Adaptivity for Subspace Deformations
Proceedings of ACM SIGGRAPH 2015

Yun Teng
Mark Meyer
Tony DeRose
Theodore Kim
        University of California, Santa Barbara
Pixar Animation Studios
Pixar Animation Studios
University of California, Santa Barbara

Above: Far left: The simulation runs at 16 FPS, entirely within the subspace, 67X faster than a full space simulation over the entire mesh. Middle left: Novel wall collisions begin, activating full space tets, shown in red in the inset. The simulation still runs at 2.1 FPS, a 7.7X speedup. Middle right: Collisions produce a deformation far outside the basis, and 49% of the tets are simulated in full space. The step runs at 0.5 FPS; still a 1.9X speedup. Far right: The collisions are removed, and the 67X speedup returns.


Subspace deformable body simulations can be very fast, but can behave unrealistically when behaviors outside the prescribed subspace, such as novel external collisions, are encountered. We address this limitation by presenting a fast, flexible new method that allows full space computation to be activated in the neighborhood of novel events while the rest of the body still computes in a subspace. We achieve this using a method we call subspace condensation, a variant on the classic static condensation precomputation. However, instead of a precomputation, we use the speed of subspace methods to perform the condensation at every frame. This approach allows the full space regions to be specified arbitrarily at runtime, and forms a natural two-way coupling with the subspace regions. While condensation is usually only applicable to linear materials, the speed of our technique enables its application to non-linear materials as well. We show the effectiveness of our approach by applying it to a variety of articulated character scenarios.

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Supplemental Videos:
    Fullspace simulation
Full vs. subspace condensation(large influence radius)
Full vs. subspace condensation(small influence radius)
        Subspace-only Simulation
Visualization (large influence radius)
Visualization (small influence radius)
    Subspace condensation
Subspace-only simulation
    Subspace condensation
Subspace-only simulation

This material is based upon work supported by a National Science Foundation CAREER award (IIS-1253948). Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation.