Smoothness of Subdivision Surfaces with Boundary

Henning Biermann, Sara Grundel, Denis Zorin

Research output: Contribution to journalArticlepeer-review


Subdivision rules for meshes with boundary are essential for practical applications of subdivision surfaces. These rules have to result in piecewise C-continuous boundary limit curves and ensure C-continuity of the surface itself. Extending the theory of Zorin (Constr Approx 16(3):359–397, 2000), we present in this paper general necessary and sufficient conditions for C-continuity of subdivision schemes for surfaces with boundary, and specialize these to practically applicable sufficient conditions for C1-continuity. We use these conditions to show that certain boundary rules for Loop and Catmull–Clark are in fact C1 continuous.

Original languageEnglish (US)
Pages (from-to)1-29
Number of pages29
JournalConstructive Approximation
Issue number1
StatePublished - Aug 1 2015


  • Boundary rules
  • C-analysis
  • Catmull–Clark
  • Characteristic maps
  • Loop
  • Subdivision algorithms

ASJC Scopus subject areas

  • Analysis
  • General Mathematics
  • Computational Mathematics


Dive into the research topics of 'Smoothness of Subdivision Surfaces with Boundary'. Together they form a unique fingerprint.

Cite this