A butterfly subdivision scheme for surface interpolation with tension control
ACM Transactions on Graphics (TOG)
Ten lectures on wavelets
Sobolev characterization of solutions of dilation equations
SIAM Journal on Mathematical Analysis
Convergence, error estimation and some properties of four-point interpolation subdivision scheme
Computer Aided Geometric Design
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
An interpolating 4-point C 2 ternary stationary subdivision scheme
Computer Aided Geometric Design
Subdivision Methods for Geometric Design: A Constructive Approach
Subdivision Methods for Geometric Design: A Constructive Approach
Composite primal/dual √3-subdivision schemes
Computer Aided Geometric Design
Deducing interpolating subdivision schemes from approximating subdivision schemes
ACM SIGGRAPH Asia 2008 papers
Polynomial reproduction by symmetric subdivision schemes
Journal of Approximation Theory
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
Subdivision Surfaces
Education: PolyMeCo-An integrated environment for polygonal mesh analysis and comparison
Computers and Graphics
NURBS with extraordinary points: high-degree, non-uniform, rational subdivision schemes
ACM SIGGRAPH 2009 papers
Numerical Checking of C1 for Arbitrary Degree Quadrilateral Subdivision Schemes
Proceedings of the 13th IMA International Conference on Mathematics of Surfaces XIII
Interpolatory ternary subdivision surfaces
Computer Aided Geometric Design
A generalized curve subdivision scheme of arbitrary order with a tension parameter
Computer Aided Geometric Design
Analyzing midpoint subdivision
Computer Aided Geometric Design
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
Beyond Catmull–Clark? A Survey of Advances in Subdivision Surface Methods
Computer Graphics Forum
A Theoretical Development for the Computer Generation and Display of Piecewise Polynomial Surfaces
IEEE Transactions on Pattern Analysis and Machine Intelligence
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For approximating subdivision schemes, there are several unified frameworks for effectively constructing subdivision surfaces generalizing splines of an arbitrary degree. In this article, we present a similar unified framework for interpolatory subdivision schemes. We first decompose the 2n-point interpolatory curve subdivision scheme into repeated local operations. By extending the repeated local operations to quadrilateral meshes, an efficient algorithm can be further derived for interpolatory surface subdivision. Depending on the number n of repeated local operations, the continuity of the limit curve or surface can be of an arbitrary order CL, except in the surface case at a limited number of extraordinary vertices where C1 continuity with bounded curvature is obtained. Boundary rules built upon repeated local operations are also presented.