Variational Barycentric Coordinates
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3618403.pdf
Size
46.11 MB
Format
Adobe PDF
Checksum (MD5)
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Author(s)
Dodik, Ana
Stein, Oded
Sitzmann, Vincent
Solomon, Justin
Date Issued
December 4, 2023
Journal
ACM Transactions on Graphics
Publisher
ACM
Citation
Dodik, Ana, Stein, Oded, Sitzmann, Vincent and Solomon, Justin. 2023. "Variational Barycentric Coordinates." ACM Transactions on Graphics, 42 (6).
Version
Final published version
Abstract
We propose a variational technique to optimize for generalized barycentric coordinates that offers additional control compared to existing models. Prior work represents barycentric coordinates using meshes or closed-form formulae, in practice limiting the choice of objective function. In contrast, we directly parameterize the continuous function that maps any coordinate in a polytope's interior to its barycentric coordinates using a neural field. This formulation is enabled by our theoretical characterization of barycentric coordinates, which allows us to construct neural fields that parameterize the entire function class of valid coordinates. We demonstrate the flexibility of our model using a variety of objective functions, including multiple smoothness and deformation-aware energies; as a side contribution, we also present mathematically-justified means of measuring and minimizing objectives like total variation on discontinuous neural fields. We offer a practical acceleration strategy, present a thorough validation of our algorithm, and demonstrate several applications.
MIT Department
Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory
Terms of Use
Creative Commons Attribution-Noncommercial-Share Alike
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1145/3618403
