Computer Aided Geometric Design
Blossoming and knot insertion algorithms for B-spline curves
Computer Aided Geometric Design
Lindenmayer systems, fractals and plants
Lindenmayer systems, fractals and plants
Another knot insertion algorithm for B-spline curves
Computer Aided Geometric Design
An extension of Chaiken's algorithm to B-spline curves with knots in geometric progression
CVGIP: Graphical Models and Image Processing
Non-uniform recursive subdivision surfaces
Proceedings of the 25th annual conference on Computer graphics and interactive techniques
Proceedings of the 2003 Eurographics/ACM SIGGRAPH symposium on Geometry processing
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
Selective knot insertion for symmetric, non-uniform refine and smooth B-spline subdivision
Computer Aided Geometric Design
Rates of convergence of control polygons
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
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Subdivision schemes are based on a hierarchy of knot grids in parameter space. A univariate grid hierarchy is regular if all knots are equidistant on each level, and irregular otherwise. We use L-systems to design a wide class of systematically described irregular grid hierarchies. Furthermore, we give sufficient conditions on the L-system which guarantee that the subdivision scheme, based on the non-uniform B-spline of degree d defined on the initial knot grid, is uniformly convergent. If n is the number of symbols in the alphabet of the L-system, this subdivision scheme is defined with a finite set of masks (at most n^d^+^1) which does not depend on the subdivision step. We provide an implementation of such schemes which is available as a worksheet for Sage software.