PH-CPF: Planar Hexagonal Meshing Using Coordinate Power Fields

Kacper Pluta, Michal Edelstein, Amir Vaxman, Mirela Ben-Chen

Research output: Contribution to journalArticlepeer-review

Abstract / Description of output

We present a new approach for computing planar hexagonal meshes that approximate a given surface, represented as a triangle mesh. Our method is based on two novel technical contributions. First, we introduce Coordinate Power Fields, which are a pair of tangent vector fields on the surface that fulfill a certain continuity constraint. We prove that the fulfillment of this constraint guarantees the existence of a seamless parameterization with quantized rotational jumps, which we then use to regularly remesh the surface. We additionally propose an optimization framework for finding Coordinate Power Fields, which also fulfill additional constraints, such as alignment, sizing and bijectivity. Second, we build upon this framework to address a challenging meshing problem: planar hexagonal meshing. To this end, we suggest a combination of conjugacy, scaling and alignment constraints, which together lead to planarizable hexagons. We demonstrate our approach on a variety of surfaces, automatically generating planar hexagonal meshes on complicated meshes, which were not achievable with existing methods.
Original languageEnglish
Article number156
Number of pages19
JournalACM Transactions on Graphics
Issue number4
Early online date19 Jul 2021
Publication statusPublished - 1 Aug 2021
EventACM SIGGRAPH 2021 - Online
Duration: 9 Aug 202113 Aug 2021

Keywords / Materials (for Non-textual outputs)

  • tangent vector fields
  • geoemtry processing
  • parameterization
  • planar hexagonal meshing


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