Selective knot insertion for symmetric, non-uniform refine and smooth B-spline subdivision

Authors:
Thomas J. Cashman;Neil A. Dodgson;Malcolm A. Sabin
Affiliations:
Computer Laboratory, University of Cambridge, CB3 0FD, England, UK;Computer Laboratory, University of Cambridge, CB3 0FD, England, UK;Numerical Geometry Ltd, 19 John Amner Close, Ely, Cambridge CB6 1DT, England, UK
Venue:
Computer Aided Geometric Design
Year:
2009

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Abstract

NURBS surfaces can be non-uniform and defined for any degree, but existing subdivision surfaces are either uniform or of fixed degree. The resulting incompatibility forms a barrier to the adoption of subdivision for CAD applications. Motivated by the search for NURBS-compatible subdivision schemes, we present a non-uniform subdivision algorithm for B-splines in the spirit of the uniform Lane-Riesenfeld 'refine and smooth' algorithm. In contrast to previous approaches, our algorithm is independent of index direction (symmetric), and also allows a selection of knot intervals to remain unaltered by the subdivision process. B-splines containing multiple knots, an important non-uniform design tool, can therefore be subdivided without increasing knot multiplicity.