Canonical Möbius subdivision

Amir Vaxman, Christian Müller, Ofir Weber

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

4 Scopus citations

Abstract

We present a novel framework for creating Möbius-invariant subdivision operators with a simple conversion of existing linear subdivision operators. By doing so, we create a wide variety of subdivision surfaces that have properties derived from Möbius geometry; namely, reproducing spheres, circular arcs, and Möbius regularity. Our method is based on establishing a canonical form for each 1-ring in the mesh, representing the class of all 1-rings that are Möbius equivalent to that 1-ring. We perform a chosen linear subdivision operation on these canonical forms, and blend the positions contributed from adjacent 1-rings, using two novel Möbius-invariant operators, into new face and edge points. The generality of the method allows for easy coarse-to-fine mesh editing with diverse polygonal patterns, and with exact reproduction of circular and spherical features. Our operators are in closed-form and their computation is as local as the computation of the linear operators they correspond to, allowing for efficient subdivision mesh editing and optimization.

Original languageEnglish
Title of host publicationSIGGRAPH Asia 2018 Technical Papers, SIGGRAPH Asia 2018
PublisherAssociation for Computing Machinery, Inc
ISBN (Electronic)9781450360081
DOIs
StatePublished - 4 Dec 2018
EventSIGGRAPH Asia 2018 Technical Papers - International Conference on Computer Graphics and Interactive Techniques, SIGGRAPH Asia 2018 - Tokyo, Japan
Duration: 4 Dec 20187 Dec 2018

Publication series

NameSIGGRAPH Asia 2018 Technical Papers, SIGGRAPH Asia 2018

Conference

ConferenceSIGGRAPH Asia 2018 Technical Papers - International Conference on Computer Graphics and Interactive Techniques, SIGGRAPH Asia 2018
Country/TerritoryJapan
CityTokyo
Period4/12/187/12/18

Bibliographical note

Publisher Copyright:
© 2018 Association for Computing Machinery.

Keywords

  • Architectural geometry
  • Conformal transformations
  • Mesh subdivision
  • Möbius transformations
  • Regular meshes

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