Efficient, fair interpolation using Catmull-Clark surfaces
SIGGRAPH '93 Proceedings of the 20th annual conference on Computer graphics and interactive techniques
A unified approach to subdivision algorithms near extraordinary vertices
Computer Aided Geometric Design
Scalar- and planar-valued curve fitting using splines under tension
Communications of the ACM
Subdivision Methods for Geometric Design: A Constructive Approach
Subdivision Methods for Geometric Design: A Constructive Approach
Proceedings of the conference on Visualization '01
Polynomial generation and quasi-interlpolation in stationary non-uniform subdivision
Computer Aided Geometric Design
Local control of bias and tension in beta-splines
SIGGRAPH '83 Proceedings of the 10th annual conference on Computer graphics and interactive techniques
Optimization techniques for approximation with subdivision surfaces
SM '04 Proceedings of the ninth ACM symposium on Solid modeling and applications
ScrewBender: Smoothing Piecewise Helical Motions
IEEE Computer Graphics and Applications
On subdivision schemes generalizing uniform B-spline surfaces of arbitrary degree
Computer Aided Geometric Design
A 4-point interpolatory subdivision scheme for curve design
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
3D ball skinning using PDEs for generation of smooth tubular surfaces
Computer-Aided Design
Steady affine motions and morphs
ACM Transactions on Graphics (TOG)
A parametric feature-based approach to reconstructing traditional filigree jewelry
Computer-Aided Design
SMI 2012: Full Curvature-based offset distance: Implementations and applications
Computers and Graphics
Interproximate curve subdivision
Journal of Computational and Applied Mathematics
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Both the 4-point and the uniform cubic B-spline subdivisions double the number of vertices of a closed-loop polygon ^kP and produce sequences of vertices f"j and b"j respectively. We study the J-spline subdivision scheme J"s, introduced by Maillot and Stam, which blends these two methods to produce vertices of the form v"j=(1-s)f"j+sb"j. Iterative applications of J"s yield a family of limit curves, the shape of which is parameterized by s. They include four-point subdivision curves (J"0), uniform cubic B-spline curves (J"1), and uniform quintic B-spline curves (J"1"."5). We show that the limit curve is at least C^1 when -1.7@?s@?5.8, C^2 when 0