Optimal Transport-Based Polar Interpolation of Directional Fields

Justin Solomon, Amir Vaxman

Research output: Contribution to journalArticlepeer-review

Abstract / Description of output

We propose an algorithm that interpolates between vector and frame fields on triangulated surfaces, designed to complement field design methods in geometry processing and simulation. Our algorithm is based on a polar construction, leveraging a conservation law from the Hopf-Poincaré theorem to match singular points using ideas from optimal transport; the remaining detail of the field is interpolated using straightforward machinery. Our model is designed with topology in mind, sliding singular points along the surface rather than having them appear and disappear, and it caters to all surface topologies, including boundary and generator loops.
Original languageEnglish
Article number88
Number of pages13
JournalACM Transactions on Graphics
Issue number4
Publication statusPublished - 1 Jul 2019
EventSIGGRAPH 2019 - Los Angeles, United States
Duration: 28 Jul 20191 Aug 2019

Keywords / Materials (for Non-textual outputs)

  • frame fields
  • optimal transport


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