Shape Space Spectra
SIGGRAPH North America 2025
Best Paper Award

Abstract

We introduce the first eigenanalysis method for continuously parameterized shape families. Given a parametric shape, our method constructs spatial neural fields that represent eigenfunctions across the entire shape space. It is agnostic to the specific shape representation, requiring only an inside/outside indicator function that depends on shape parameters.

Eigenfunctions are computed by minimizing a variational principle over nested spaces with orthogonality constraints. Since eigenvalues may swap dominance at points of multiplicity, we jointly train multiple eigenfunctions while dynamically reordering them based on their eigenvalues at each step. Through causal gradient filtering , this reordering is reflected in backpropagation.

Our method enables applications to operate over shape space, providing a single ROM that encapsulates vibration modes for all shapes, including previously unseen ones. Since our eigenanalysis is differentiable with respect to shape parameters, it facilitates eigenfunction-aware shape optimization. We evaluate our approach on shape optimization for sound synthesis and locomotion, as well as reduced-order modeling for elastodynamic simulation.

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BibTeX

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@article{chang2025shapespacespectra,
  title = {Shape Space Spectra},
  author = {Yue Chang and Otman Benchekroun and Maurizio M. Chiaramonte and Peter Yichen Chen and Eitan Grinspun},
  year = {2025},
  journal = {ACM Transactions on Graphics}
}

Acknowledgements

We thank Max Wardetzky for valuable discussions about the Min-Max Theorem and the spectral properties of the Laplace operator. We are also grateful to Mengfei Liu for narrating the video and to Vishnu Nittoor for proofreading the paper. We thank Abhishek Madan, David Levin, Jonathan Panuelos, Silvia Sellán, and Zhecheng Wang for their helpful feedback on the title. We would also like to thank our lab system administrator, John Hancock, and our financial officer, Xuan Dam, for their invaluable administrative support in making this research possible. This work was supported by the Natural Sciences and Engineering Research Council of Canada (NSERC), grant RGPIN-2021-03733.