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)
A unified approach to subdivision algorithms near extraordinary vertices
Computer Aided Geometric Design
Computer Aided Geometric Design
The simplest subdivision scheme for smoothing polyhedra
ACM Transactions on Graphics (TOG)
Analysis of Algorithms Generalizing B-Spline Subdivision
SIAM Journal on Numerical Analysis
SIAM Journal on Mathematical Analysis
Vector subdivision schemes and multiple wavelets
Mathematics of Computation
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
Stationary Subdivision
A Method for Analysis of C1-Continuity of Subdivision Surfaces
SIAM Journal on Numerical Analysis
Spectral Analysis of the Transition Operator and Its Applications to Smoothness Analysis of Wavelets
SIAM Journal on Matrix Analysis and Applications
Geometric Modelling, Dagstuhl, Germany, 1996
Quincunx fundamental refinable functions and Quincunx biorthogonal wavelets
Mathematics of Computation
Triangular √3-subdivision schemes: the regular case
Journal of Computational and Applied Mathematics
Composite primal/dual √3-subdivision schemes
Computer Aided Geometric Design
Analysis and application of subdivision surfaces
Analysis and application of subdivision surfaces
Convergence of multivariate non-stationary vector subdivision schemes
Applied Numerical Mathematics - Special issue: Applied scientific computing - Grid generation, approximated solutions and visualization
√2 Subdivision for quadrilateral meshes
The Visual Computer: International Journal of Computer Graphics
Designing composite triangular subdivision schemes
Computer Aided Geometric Design - Special issue: Geometric modelling and differential geometry
Computer Aided Geometric Design
Computer Aided Geometric Design
From extension of Loop's approximation scheme to interpolatory subdivisions
Computer Aided Geometric Design
Matrix-valued 4-point spline and 3-point non-spline interpolatory curve subdivision schemes
Computer Aided Geometric Design
Interpolatory quad/triangle subdivision schemes for surface design
Computer Aided Geometric Design
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Subdivision templates of numerical values are replaced by templates of matrices in this paper to allow the introduction of shape control parameters for the feasibility of achieving desirable geometric shapes at those points on the subdivision surfaces that correspond to extraordinary control vertices. Formulation of the matrix-valued subdivision surface is derived. Based on refinable bivariate spline function vectors for matrix-valued subdivisions, the notion of characteristic map introduced by Reif is extended from (scalar) surface subdivisions to matrix-valued subdivisions. The C1 - and Ck-continuity of Reif and Prautzsch for matrix-valued subdivisions are discussed. To illustrate the general theory, the smoothness of matrix-valued triangular subdivision schemes for extraordinary vertices with valences 3 and 4 is analyzed. The issue of effective choices of the shape control parameters will also be discussed in this paper.