A matrix approach to the analysis of recursively generated B-spline surfaces
Computer-Aided Design
Conditions for tangent plane continuity over recursively generated B-spline surfaces
ACM Transactions on Graphics (TOG)
Cubic recursive division with bounded curvature
Curves and surfaces
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
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
The simplest subdivision scheme for smoothing polyhedra
ACM Transactions on Graphics (TOG)
Analysis of Algorithms Generalizing B-Spline Subdivision
SIAM Journal on Numerical Analysis
Subdivision surfaces in character animation
Proceedings of the 25th annual conference on Computer graphics and interactive techniques
Interactive multi-resolution modeling on arbitrary meshes
Proceedings of the 25th annual conference on Computer graphics and interactive techniques
Non-uniform recursive subdivision surfaces
Proceedings of the 25th annual conference on Computer graphics and interactive techniques
Exact evaluation of Catmull-Clark subdivision surfaces at arbitrary parameter values
Proceedings of the 25th annual conference on Computer graphics and interactive techniques
Edge and vertex insertion for a class of C1 subdivision surfaces
Computer Aided Geometric Design
Stationary Subdivision
Subdivision Methods for Geometric Design: A Constructive Approach
Subdivision Methods for Geometric Design: A Constructive Approach
A Method for Analysis of C1-Continuity of Subdivision Surfaces
SIAM Journal on Numerical Analysis
Dynamic Catmull-Clark Subdivision Surfaces
IEEE Transactions on Visualization and Computer Graphics
Analysis and application of subdivision surfaces
Analysis and application of subdivision surfaces
Stationary subdivision and multiresolution surface representations
Stationary subdivision and multiresolution surface representations
Non-uniform recursive Doo-Sabin surfaces
Computer-Aided Design
Beyond Catmull–Clark? A Survey of Advances in Subdivision Surface Methods
Computer Graphics Forum
Cubic subdivision schemes with double knots
Computer Aided Geometric Design
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In computer graphics and computer-aided geometric design, more and more subdivision schemes are being extensively used for free-form surfaces of arbitrary topology. The convergence and continuity analyses of uniform subdivision surfaces have been performed very well, but it is very difficult to prove the convergence and the continuity properties of non-uniform recursive subdivision surfaces (NURSSes, for short) because the subdivision matrix varies at each iteration step. This restricts widespread use of NURSSes, although NURSSes have a lot of advantages over uniform subdivision surfaces. In this paper, the concept of equivalent knot spacing is presented. A new technique for eigenanalysis, convergence and continuity analyses of non-uniform Doo-Sabin surfaces is proposed. Also, an interesting and important fact is found that the subdivision process of non-uniform Doo-Sabin surfaces may diverge sometime.