Lifting Directional Fields to Minimal Sections
Name
3658198.pdf
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78.76 MB
Format
Adobe PDF
Checksum (MD5)
3dcfb09efbe14bbb285cd2cba122f870
Author(s)
Palmer, David
Chern, Albert
Solomon, Justin
Date Issued
July 19, 2024
Journal
ACM Transactions on Graphics
Publisher
ACM
Citation
Palmer, David, Chern, Albert and Solomon, Justin. 2024. "Lifting Directional Fields to Minimal Sections." ACM Transactions on Graphics, 43 (4).
Version
Final published version
Abstract
Directional fields, including unit vector, line, and cross fields, are essential tools in the geometry processing toolkit. The topology of directional fields is characterized by their singularities. While singularities play an important role in downstream applications such as meshing, existing methods for computing directional fields either require them to be specified in advance, ignore them altogether, or treat them as zeros of a relaxed field. While fields are ill-defined at their singularities, the graphs of directional fields with singularities are well-defined surfaces in a circle bundle. By lifting optimization of fields to optimization over their graphs, we can exploit a natural convex relaxation to a minimal section problem over the space of currents in the bundle. This relaxation treats singularities as first-class citizens, expressing the relationship between fields and singularities as an explicit boundary condition. As curvature frustrates finite element discretization of the bundle, we devise a hybrid spectral method for representing and optimizing minimal sections. Our method supports field optimization on both flat and curved domains and enables more precise control over singularity placement.
MIT Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory
Terms of Use
Creative Commons Attribution-NoDerivs License
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1145/3658198
