A butterfly subdivision scheme for surface interpolation with tension control
ACM Transactions on Graphics (TOG)
Surface interpolation on irregular networks with normal conditions
Computer Aided Geometric Design
Efficient, fair interpolation using Catmull-Clark surfaces
SIGGRAPH '93 Proceedings of the 20th annual conference on Computer graphics and interactive techniques
Piecewise smooth surface reconstruction
SIGGRAPH '94 Proceedings of the 21st annual conference on Computer graphics and interactive techniques
Interpolating Subdivision for meshes with arbitrary topology
SIGGRAPH '96 Proceedings of the 23rd annual conference on Computer graphics and interactive techniques
Multidimensional Interpolatory Subdivision Schemes
SIAM Journal on Numerical Analysis
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
An interpolating 4-point C 2 ternary stationary subdivision scheme
Computer Aided Geometric Design
A Method for Analysis of C1-Continuity of Subdivision Surfaces
SIAM Journal on Numerical Analysis
Composite primal/dual √3-subdivision schemes
Computer Aided Geometric Design
Interpolatory "2-Subdivision Surfaces
GMP '04 Proceedings of the Geometric Modeling and Processing 2004
Exact interpolation and iterative subdivision schemes
IEEE Transactions on Signal Processing
On subdivision schemes generalizing uniform B-spline surfaces of arbitrary degree
Computer Aided Geometric Design
A unified framework for primal/dual quadrilateral subdivision schemes
Computer Aided Geometric Design
A 4-point interpolatory subdivision scheme for curve design
Computer Aided Geometric Design
Exact evaluation of limits and tangents for interpolatory subdivision surfaces at rational points
Journal of Computational and Applied Mathematics
A unified interpolatory subdivision scheme for quadrilateral meshes
ACM Transactions on Graphics (TOG)
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This paper proposes an interpolatory ternary subdivision for quadrilateral meshes that produces C2 continuous limit surfaces for regular meshes while achieves G1 continuity with bounded curvature at extraordinary vertices. The subdivision splits each quad into nine by inserting two E-vertices onto each edge and four F-vertices onto each face, and connecting them along vertical and horizontal directions respectively. The regular subdivision masks of the scheme are obtained as tensor products of the masks of the interpolatory ternary subdivision for curves while irregular geometric rules are established based on discrete Fourier transformation. For efficient practical use, an adaptive refinement algorithm is developed based on the decomposition of intermediate meshes into divisible and indivisible subsets for each refinement.