Integrable PolyVector fields

Olga Diamanti, Amir Vaxman, Daniele Panozzo, Olga Sorkine-Hornung

Research output: Contribution to journalConference article

Abstract

We present a framework for designing curl-free tangent vector fields on discrete surfaces. Such vector fields are gradients of locallydefined scalar functions, and this property is beneficial for creating surface parameterizations, since the gradients of the parameterization coordinate functions are then exactly aligned with the designed fields. We introduce a novel definition for discrete curl between unordered sets of vectors (PolyVectors), and devise a curl-eliminating continuous optimization that is independent of the matchings between them. Our algorithm naturally places the singularities required to satisfy the user-provided alignment constraints, and our fields are the gradients of an inversion-free parameterization by design.

Original languageEnglish (US)
Article number38
JournalACM Transactions on Graphics
Volume34
Issue number4
DOIs
StatePublished - Jul 27 2015
EventACM Special Interest Group on Computer Graphics and Interactive Techniques Conference, SIGGRAPH 2015 - Los Angeles, United States
Duration: Aug 9 2015Aug 13 2015

Keywords

  • Curl-free fields
  • PolyVectors
  • Quad meshing

ASJC Scopus subject areas

  • Computer Graphics and Computer-Aided Design

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    Diamanti, O., Vaxman, A., Panozzo, D., & Sorkine-Hornung, O. (2015). Integrable PolyVector fields. ACM Transactions on Graphics, 34(4), [38]. https://doi.org/10.1145/2766906