A butterfly subdivision scheme for surface interpolation with tension control
ACM Transactions on Graphics (TOG)
A unified approach to subdivision algorithms near extraordinary vertices
Computer Aided Geometric Design
Interpolating Subdivision for meshes with arbitrary topology
SIGGRAPH '96 Proceedings of the 23rd annual conference on Computer graphics and interactive techniques
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
Piecewise smooth subdivision surfaces with normal control
Proceedings of the 27th annual conference on Computer graphics and interactive techniques
A Method for Analysis of C1-Continuity of Subdivision Surfaces
SIAM Journal on Numerical Analysis
On subdivision schemes generalizing uniform B-spline surfaces of arbitrary degree
Computer Aided Geometric Design
Computer Aided Geometric Design
CHARMS: a simple framework for adaptive simulation
Proceedings of the 29th annual conference on Computer graphics and interactive techniques
Graphical Models - Pacific graphics 2001
Computer Aided Geometric Design
Composite primal/dual √3-subdivision schemes
Computer Aided Geometric Design
Proceedings of the 2003 Eurographics/ACM SIGGRAPH symposium on Geometry processing
A generative classification of mesh refinement rules with lattice transformations
Computer Aided Geometric Design
Generalized B-Spline Subdivision-Surface Wavelets for Geometry Compression
IEEE Transactions on Visualization and Computer Graphics
Subdivision scheme tuning around extraordinary vertices
Computer Aided Geometric Design
Shape characterization of subdivision surfaces: case studies
Computer Aided Geometric Design
Combining 4- and 3-direction subdivision
ACM Transactions on Graphics (TOG)
On C2 triangle/quad subdivision
ACM Transactions on Graphics (TOG)
Smooth subdivision of tetrahedral meshes
Proceedings of the 2004 Eurographics/ACM SIGGRAPH symposium on Geometry processing
Proceedings of the 2005 ACM symposium on Solid and physical modeling
Analysis and tuning of subdivision algorithms
Proceedings of the 21st spring conference on Computer graphics
Interpolatory ternary subdivision surfaces
Computer Aided Geometric Design
Parametrizations for triangular Gk spline surfaces of low degree
ACM Transactions on Graphics (TOG)
Composite 2 subdivision surfaces
Computer Aided Geometric Design
Non-uniform subdivision for B-splines of arbitrary degree
Computer Aided Geometric Design
A symmetric, non-uniform, refine and smooth subdivision algorithm for general degree B-splines
Computer Aided Geometric Design
Selective knot insertion for symmetric, non-uniform refine and smooth B-spline subdivision
Computer Aided Geometric Design
NURBS with extraordinary points: high-degree, non-uniform, rational subdivision schemes
ACM SIGGRAPH 2009 papers
Cyclic plain-weaving on polygonal mesh surfaces with graph rotation systems
ACM SIGGRAPH 2009 papers
Deriving Box-Spline Subdivision Schemes
Proceedings of the 13th IMA International Conference on Mathematics of Surfaces XIII
Interpolatory ternary subdivision surfaces
Computer Aided Geometric Design
Subdivision surfaces for CAD-an overview
Computer-Aided Design
Variations on the four-point subdivision scheme
Computer Aided Geometric Design
Lens-shaped surfaces and C 2 subdivision
Computing - Geometric Modelling, Dagstuhl 2008
Analyzing midpoint subdivision
Computer Aided Geometric Design
Non-uniform recursive Doo-Sabin surfaces
Computer-Aided Design
An approach for embedding regular analytic shapes with subdivision surfaces
CGI'06 Proceedings of the 24th international conference on Advances in Computer Graphics
An introduction to guided and polar surfacing
MMCS'08 Proceedings of the 7th international conference on Mathematical Methods for Curves and Surfaces
An heuristic analysis of the classification of bivariate subdivision schemes
IMA'05 Proceedings of the 11th IMA international conference on Mathematics of Surfaces
Insight for practical subdivision modeling with discrete gauss-bonnet theorem
GMP'06 Proceedings of the 4th international conference on Geometric Modeling and Processing
Composite √2 subdivision surfaces
GMP'06 Proceedings of the 4th international conference on Geometric Modeling and Processing
On subdivision schemes generalizing uniform B-spline surfaces of arbitrary degree
Computer Aided Geometric Design
A subdivision scheme for surfaces of revolution
Computer Aided Geometric Design
Beyond Catmull–Clark? A Survey of Advances in Subdivision Surface Methods
Computer Graphics Forum
Compressed random-access trees for spatially coherent data
EGSR'07 Proceedings of the 18th Eurographics conference on Rendering Techniques
A unified interpolatory subdivision scheme for quadrilateral meshes
ACM Transactions on Graphics (TOG)
A generalized surface subdivision scheme of arbitrary order with a tension parameter
Computer-Aided Design
| Hi-index | 0.00 |
Quadrilateral subdivision schemes come in primal and dual varieties, splitting faces or respectively vertices. The scheme of Catmull-Clark is an example of the former, while the Doo-Sabin scheme exemplifies the latter. In this paper we consider the construction of an increasing sequence of alternating primal/dual quadrilateral subdivision schemes based on a simple averaging approach. Beginning with a vertex split step we successively construct variants of Doo-Sabin and Catmull-Clark schemes followed by novel schemes generalizing B-splines of bidegree up to nine. We prove the schemes to be C^1 at irregular surface points, and analyze the behavior of the schemes as the number of averaging steps increases. We discuss a number of implementation issues common to all quadrilateral schemes. In particular we show how both primal and dual quadrilateral schemes can be implemented in the same code, opening up new possibilities for more flexible geometric modeling applications and p-versions of the Subdivision Element Method. Additionally we describe a simple algorithm for adaptive subdivision of dual schemes.