Canonical möbius subdivision

Amir Vaxman, Christian Müller, Ofir Weber

Research output: Contribution to journalArticlepeer-review


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
Article number227
JournalACM Transactions on Graphics
Issue number6
StatePublished - Nov 2018


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

All Science Journal Classification (ASJC) codes

  • Computer Graphics and Computer-Aided Design


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