Piecewise smooth subdivision surfaces with normal control
Proceedings of the 27th annual conference on Computer graphics and interactive techniques
Proceedings of the conference on Visualization '01
A cascadic geometric filtering approach to subdivision
Computer Aided Geometric Design
Mesh optimization using global error with application to geometry simplification
Graphical Models - Special issue: Processing on large polygonal meshes
Eigenanalysis and Continuity of Non-Uniform Doo-Sabin Surfaces
PG '99 Proceedings of the 7th Pacific Conference on Computer Graphics and Applications
Composite primal/dual √3-subdivision schemes
Computer Aided Geometric Design
Non-linear subdivision using local spherical coordinates
Computer Aided Geometric Design
Subdivision scheme tuning around extraordinary vertices
Computer Aided Geometric Design
Designing composite triangular subdivision schemes
Computer Aided Geometric Design - Special issue: Geometric modelling and differential geometry
Interpolatory ternary subdivision surfaces
Computer Aided Geometric Design
Edge subdivision schemes and the construction of smooth vector fields
ACM SIGGRAPH 2006 Papers
Matrix-valued subdivision schemes for generating surfaces with extraordinary vertices
Computer Aided Geometric Design
Jet subdivision schemes on the k-regular complex
Computer Aided Geometric Design
Interpolatory √3 subdivision with harmonic interpolation
AFRIGRAPH '07 Proceedings of the 5th international conference on Computer graphics, virtual reality, visualisation and interaction in Africa
From extension of Loop's approximation scheme to interpolatory subdivisions
Computer Aided Geometric Design
Technical Section: Ternary butterfly subdivision
Computers and Graphics
Numerical Checking of C1 for Arbitrary Degree Quadrilateral Subdivision Schemes
Proceedings of the 13th IMA International Conference on Mathematics of Surfaces XIII
Matrix-valued subdivision schemes for generating surfaces with extraordinary vertices
Computer Aided Geometric Design
Designing composite triangular subdivision schemes
Computer Aided Geometric Design - Special issue: Geometric modelling and differential geometry
Interpolatory ternary subdivision surfaces
Computer Aided Geometric Design
Jet subdivision schemes on the k-regular complex
Computer Aided Geometric Design
Subdivision surfaces for CAD-an overview
Computer-Aided Design
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
Manifold-based surfaces with boundaries
Computer Aided Geometric Design
An interpolatory subdivision scheme for triangular meshes and progressive transmission
VSMM'06 Proceedings of the 12th international conference on Interactive Technologies and Sociotechnical Systems
A unified framework for primal/dual quadrilateral subdivision schemes
Computer Aided Geometric Design
Beyond Catmull–Clark? A Survey of Advances in Subdivision Surface Methods
Computer Graphics Forum
A generalized surface subdivision scheme of arbitrary order with a tension parameter
Computer-Aided Design
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A sufficient condition for C1-continuity of subdivision surfaces was proposed by Reif [Comput. Aided Geom. Design, 12 (1995), pp. 153--174.] and extended to a more general setting in [D. Zorin, Constr. Approx., accepted for publication]. In both cases, the analysis of C1-continuity is reduced to establishing injectivity and regularity of a characteristic map. In all known proofs of C1-continuity, explicit representation of the limit surface on an annular region was used to establish regularity, and a variety of relatively complex techniques were used to establish injectivity. We propose a new approach to this problem: we show that for a general class of subdivision schemes, regularity can be inferred from the properties of a sufficiently close linear approximation, and injectivity can be verified by computing the index of a curve. An additional advantage of our approach is that it allows us to prove C1-continuity for all valences of vertices, rather than for an arbitrarily large but finite number of valences. As an application, we use our method to analyze C1-continuity of most stationary subdivision schemes known to us, including interpolating butterfly and modified butterfly schemes, as well as the Kobbelt's interpolating scheme for quadrilateral meshes.