Smoothness of stationary subdivision on irregular meshes

Research output: Contribution to journalArticlepeer-review


We derive necessary and sufficient conditions for tangent plane and Ck-continuity of stationary subdivision schemes near extraordinary vertices. Our criteria generalize most previously known conditions. We introduce a new approach to analysis of subdivision surfaces based on the idea of the universal surface. Any subdivision surface can be locally represented as a projection of the universal surface, which is uniquely defined by the subdivision scheme. This approach provides us with a more intuitive geometric understanding of subdivision near extraordinary vertices.

Original languageEnglish (US)
Pages (from-to)359-397
Number of pages39
JournalConstructive Approximation
Issue number3
StatePublished - 2000


  • Arbitrary meshes
  • Stationary subdivision
  • Subdivision surfaces

ASJC Scopus subject areas

  • Analysis
  • General Mathematics
  • Computational Mathematics


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