Making the Oslo algorithm more efficient
SIAM Journal on Numerical Analysis
Knot removal for parametric B-spline curves and surfaces
Computer Aided Geometric Design
Recursive proof of Boehm's knot insertion technique
Computer-Aided Design
An introduction to wavelets
SIGGRAPH '94 Proceedings of the 21st annual conference on Computer graphics and interactive techniques
Spherical wavelets: efficiently representing functions on the sphere
SIGGRAPH '95 Proceedings of the 22nd annual conference on Computer graphics and interactive techniques
Wavelets for computer graphics: theory and applications
Wavelets for computer graphics: theory and applications
The lifting scheme: a construction of second generation wavelets
SIAM Journal on Mathematical Analysis
Hierarchical B-spline refinement
SIGGRAPH '88 Proceedings of the 15th annual conference on Computer graphics and interactive techniques
Biorthogonal nonuniform B-spline wavelets based on a discrete norm
Computer Aided Geometric Design
Wavelet-based automated river network generalization
Proceedings of the 3rd International Conference on Computing for Geospatial Research and Applications
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In this paper we present a novel approach to construct B-spline wavelets under constraints, taking advantage of the lifting scheme. Constrained B-spline wavelets allow multiresolution analysis of B-splines which fixes positions, tangents and/or high order derivatives at some user specified parameter values, thus extend the ability of B-spline wavelets: smoothing a curve while preserving user specified ''feature points''; representing several segments of a single curve at different resolution levels, leaving no awkward ''gaps''; multiresolution editing of B-spline curves under constraints. For a given B-spline order and the number of constraints, both the time and storage complexities of our algorithm are linear in the number of control points. This feature makes our algorithm extremely suitable for large scale datasets.