Box splines
The simplest subdivision scheme for smoothing polyhedra
ACM Transactions on Graphics (TOG)
Edge and vertex insertion for a class of C1 subdivision surfaces
Computer Aided Geometric Design
Proceedings of the 27th annual conference on Computer graphics and interactive techniques
Using semi-regular 4-8 meshes for subdivision surfaces
Journal of Graphics Tools
Subdivision Methods for Geometric Design: A Constructive Approach
Subdivision Methods for Geometric Design: A Constructive Approach
Bezier and B-Spline Techniques
Bezier and B-Spline Techniques
Composite primal/dual √3-subdivision schemes
Computer Aided Geometric Design
Proceedings of the 2003 Eurographics/ACM SIGGRAPH symposium on Geometry processing
Interpolatory "2-Subdivision Surfaces
GMP '04 Proceedings of the Geometric Modeling and Processing 2004
√2 Subdivision for quadrilateral meshes
The Visual Computer: International Journal of Computer Graphics
Biorthogonal loop-subdivision wavelets
Computing - Geometric modelling dagstuhl 2002
A Factored Approach to Subdivision Surfaces
IEEE Computer Graphics and Applications
Designing composite triangular subdivision schemes
Computer Aided Geometric Design - Special issue: Geometric modelling and differential geometry
On subdivision schemes generalizing uniform B-spline surfaces of arbitrary degree
Computer Aided Geometric Design
Computer Aided Geometric Design
A unified framework for primal/dual quadrilateral subdivision schemes
Computer Aided Geometric Design
Biorthogonal wavelets based on gradual subdivision of quadrilateral meshes
Computer Aided Geometric Design
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This paper presents a new unified framework for subdivisions based on a $\sqrt{2}$ splitting operator, the so-called composite $\sqrt{2}$ subdivision. The composite subdivision scheme generalizes 4-direction box spline surfaces for processing irregular quadrilateral meshes and is realized through various atomic operators. Several well-known subdivisions based on both the $\sqrt{2}$ splitting operator and 1-4 splitting for quadrilateral meshes are properly included in the newly proposed unified scheme. Typical examples include the midedge and 4-8 subdivisions based on the $\sqrt{2}$ splitting operator that are now special cases of the unified scheme as the simplest dual and primal subdivisions, respectively. Variants of Catmull-Clark and Doo-Sabin subdivisions based on the 1-4 splitting operator also fall in the proposed unified framework. Furthermore, unified subdivisions as extension of tensor-product B-spline surfaces also become a subset of the proposed unified subdivision scheme. In addition, Kobbelt interpolatory subdivision can also be included into the unified framework using VV-type (vertex to vertex type) averaging operators.