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
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
Designing composite triangular subdivision schemes
Computer Aided Geometric Design - Special issue: Geometric modelling and differential geometry
Efficient wavelet construction with Catmull–Clark subdivision
The Visual Computer: International Journal of Computer Graphics
A Factored Approach to Subdivision Surfaces
IEEE Computer Graphics and Applications
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
A Theoretical Development for the Computer Generation and Display of Piecewise Polynomial Surfaces
IEEE Transactions on Pattern Analysis and Machine Intelligence
Integration of CAD and boundary element analysis through subdivision methods
Computers and Industrial Engineering
Geometric calibration of projector imagery on curved screen based-on subdivision mesh
GMP'08 Proceedings of the 5th international conference on Advances in geometric modeling and processing
A generalized surface subdivision scheme of arbitrary order with a tension parameter
Computer-Aided Design
| Hi-index | 0.00 |
This paper presents a new unified framework for subdivisions based on a 2 splitting operator, the so-called composite 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 2 splitting operator and based on 1-4 splitting operator for quadrilateral meshes are properly included in the newly proposed unified scheme. Typical examples include the midedge and 4-8 subdivisions based on the 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.