An operator approach to tangent vector field processing

Omri Azencot, Mirela Ben-Chen, Frédéric Chazal, Maks Ovsjanikov

Research output: Contribution to journalArticlepeer-review

48 Scopus citations

Abstract

In this paper, we introduce a novel coordinate-free method for manipulating and analyzing vector fields on discrete surfaces. Unlike the commonly used representations of a vector field as an assignment of vectors to the faces of the mesh, or as real values on edges, we argue that vector fields can also be naturally viewed as operators whose domain and range are functions defined on the mesh. Although this point of view is common in differential geometry it has so far not been adopted in geometry processing applications. We recall the theoretical properties of vector fields represented as operators, and show that composition of vector fields with other functional operators is natural in this setup. This leads to the characterization of vector field properties through commutativity with other operators such as the Laplace-Beltrami and symmetry operators, as well as to a straight-forward definition of differential properties such as the Lie derivative. Finally, we demonstrate a range of applications, such as Killing vector field design, symmetric vector field estimation and joint design on multiple surfaces.

Original languageEnglish
Pages (from-to)73-82
Number of pages10
JournalComputer Graphics Forum
Volume32
Issue number5
DOIs
StatePublished - 1 Jan 2013
Externally publishedYes
Event11th Eurographics/ACM SIGGRAPH Symposium on Geometry Processing, SGP 2013 - Genova, Italy
Duration: 3 Jul 20135 Jul 2013

Keywords

  • Categories and Subject Descriptors (according to ACM CCS)
  • Computational Geometry and Object Modeling
  • I.3.5 [Computer Graphics]

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