Conditions for tangent plane continuity over recursively generated B-spline surfaces
ACM Transactions on Graphics (TOG)
A butterfly subdivision scheme for surface interpolation with tension control
ACM Transactions on Graphics (TOG)
P.L. homeomorphic manifolds are equivalent by elementary shellings
European Journal of Combinatorics
Efficient, fair interpolation using Catmull-Clark surfaces
SIGGRAPH '93 Proceedings of the 20th annual conference on Computer graphics and interactive techniques
Box splines
A unified approach to subdivision algorithms near extraordinary vertices
Computer Aided Geometric Design
A variational approach to subdivision
Computer Aided Geometric Design
The simplest subdivision scheme for smoothing polyhedra
ACM Transactions on Graphics (TOG)
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
Using semi-regular 4-8 meshes for subdivision surfaces
Journal of Graphics Tools
Graph Grammars and Their Application to Computer Science: 4th International Workshop, Bremen, Germany, March 5-9, 1990 Proceedings
Subdivision Methods for Geometric Design: A Constructive Approach
Subdivision Methods for Geometric Design: A Constructive Approach
Polyhedra Operators for Mesh Refinement
GMP '02 Proceedings of the Geometric Modeling and Processing — Theory and Applications (GMP'02)
Composite primal/dual √3-subdivision schemes
Computer Aided Geometric Design
Stationary subdivision and multiresolution surface representations
Stationary subdivision and multiresolution surface representations
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 generative classification of mesh refinement rules with lattice transformations
Computer Aided Geometric Design
Composite 2 subdivision surfaces
Computer Aided Geometric Design
Designing composite triangular subdivision schemes
Computer Aided Geometric Design - Special issue: Geometric modelling and differential geometry
L-system specification of knot-insertion rules for non-uniform B-spline subdivision
Computer Aided Geometric Design
Composite √2 subdivision surfaces
GMP'06 Proceedings of the 4th international conference on Geometric Modeling and Processing
An overview of procedures for refining triangulations
ICCSA'12 Proceedings of the 12th international conference on Computational Science and Its Applications - Volume Part I
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In this paper we develop a new description for subdivision surfaces based on a graph grammar formalism. Subdivision schemes are specified by a context sensitive grammar in which production rules represent topological and geometrical transformations to the surface's control mesh. This methodology can be used for all known subdivision surface schemes. Moreover, it gives an effective representation that allows simple implementation and is suitable for adaptive computations.