A bivariate C1 subdivision scheme based on cubic half-box splines

Barendrecht, P., Sabin, M. & Kosinka, J., May-2019, In : Computer aided geometric design. 71, p. 77-89 13 p.

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  • Final aut- A bivariate C1 subdivision scheme based on cubic half-box splines

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Among the bivariate subdivision schemes available, spline-based schemes, such as Catmull-Clark and Loop, are the most commonly used ones. These schemes have known continuity and can be evaluated at arbitrary parameter values. In this work, we develop a C-1 spline-based scheme based on cubic half-box splines. Although the individual surface patches are triangular, the associated control net is three-valent and thus consists in general of mostly hexagons. In addition to introducing stencils that can be applied in extraordinary regions of the mesh, we also consider boundaries. Moreover, we show that the scheme exhibits ineffective eigenvectors. Finally, we briefly consider architectural geometry and isogeometric analysis as selected applications.
Original languageEnglish
Pages (from-to)77-89
Number of pages13
JournalComputer aided geometric design
Early online date4-Apr-2019
Publication statusPublished - May-2019


  • Bivariate subdivision, Three-valent meshes, Honeycomb scheme, Eigenanalysis, LINEAR INDEPENDENCE, CATMULL-CLARK, SURFACES

ID: 79325654