Computer Aided Geometric Design - Special issue: Topics in CAGD
Ten lectures on wavelets
An introduction to wavelets
Discrete spline filters for multiresolutions and wavelets of l2
SIAM Journal on Mathematical Analysis
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
Multiresolution analysis for surfaces of arbitrary topological type
ACM Transactions on Graphics (TOG)
Wavelets for computer graphics: theory and applications
Wavelets for computer graphics: theory and applications
Hierarchical B-spline refinement
SIGGRAPH '88 Proceedings of the 15th annual conference on Computer graphics and interactive techniques
Tutorials on Multiresolution in Geometric Modelling: Summer School Lectures Notes
Tutorials on Multiresolution in Geometric Modelling: Summer School Lectures Notes
Generalized B-Spline Subdivision-Surface Wavelets for Geometry Compression
IEEE Transactions on Visualization and Computer Graphics
Biorthogonal loop-subdivision wavelets
Computing - Geometric modelling dagstuhl 2002
Biorthogonal nonuniform B-spline wavelets based on a discrete norm
Computer Aided Geometric Design
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We propose a flexible and efficient wavelet construction for non-uniform B-spline curves and surfaces. The method allows to remove knots in arbitrary order minimizing the displacement of control points when a knot is re-inserted. Geometric detail subtracted from a shape by knot removal is represented by an associated wavelet coefficient replacing one of the control points at a coarser level of detail. From the hierarchy of wavelet coefficients, perfect reconstruction of the original shape is obtained. Both knot removal and insertion have local impact. Wavelet synthesis and analysis are both computed in linear time, based on the lifting scheme for biorthogonal wavelets. The method is perfectly suited for multiresolution surface editing, progressive transmission, and compression of spline curves and surfaces.