“Optimal transport-based polar interpolation of directional fields” by Solomon and Vaxman

  • ©Justin M. Solomon and Amir Vaxman




    Optimal transport-based polar interpolation of directional fields

Session/Category Title:   Transport: Parallel and Optimal



    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.


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