Computer Aided Geometric Design
Another knot insertion algorithm for B-spline curves
Computer Aided Geometric Design
Subdivision surfaces in character animation
Proceedings of the 25th annual conference on Computer graphics and interactive techniques
Subdivision Methods for Geometric Design: A Constructive Approach
Subdivision Methods for Geometric Design: A Constructive Approach
Two blossoming proofs of the Lane-Riesenfeld algorithm
Computing - Special issue on Geometric Modeling (Dagstuhl 2005)
Non-uniform B-spline subdivision using refine and smooth
Proceedings of the 12th IMA international conference on Mathematics of surfaces XII
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 Theoretical Development for the Computer Generation and Display of Piecewise Polynomial Surfaces
IEEE Transactions on Pattern Analysis and Machine Intelligence
A symmetric, non-uniform, refine and smooth subdivision algorithm for general degree B-splines
Computer Aided Geometric Design
Selective knot insertion for symmetric, non-uniform refine and smooth B-spline subdivision
Computer Aided Geometric Design
NURBS with extraordinary points: high-degree, non-uniform, rational subdivision schemes
ACM SIGGRAPH 2009 papers
Adjustable speed surface subdivision
Computer Aided Geometric Design
Dinus: Double insertion, nonuniform, stationary subdivision surfaces
ACM Transactions on Graphics (TOG)
L-system specification of knot-insertion rules for non-uniform B-spline subdivision
Computer Aided Geometric Design
Cubic subdivision schemes with double knots
Computer Aided Geometric Design
Non-uniform non-tensor product local interpolatory subdivision surfaces
Computer Aided Geometric Design
A unified interpolatory subdivision scheme for quadrilateral meshes
ACM Transactions on Graphics (TOG)
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We present an efficient algorithm for subdividing non-uniform B-splines of arbitrary degree in a manner similar to the Lane-Riesenfeld subdivision algorithm for uniform B-splines of arbitrary degree. Our algorithm consists of doubling the control points followed by d rounds of non-uniform averaging similar to the d rounds of uniform averaging in the Lane-Riesenfeld algorithm for uniform B-splines of degree d. However, unlike the Lane-Riesenfeld algorithm which follows most directly from the continuous convolution formula for the uniform B-spline basis functions, our algorithm follows naturally from blossoming. We show that our knot insertion method is simpler and more efficient than previous knot insertion algorithms for non-uniform B-splines.