Single-knot wavelets for non-uniform B-splines

doi:10.1016/j.cagd.2005.04.008

Computer Aided Geometric Design

Volume 22, Issue 9, December 2005, Pages 849-864

https://doi.org/10.1016/j.cagd.2005.04.008 Get rights and content

Abstract

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.

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Single-knot wavelets for non-uniform B-splines

Abstract

Comput. Graph. Image Process.

Computer Aided Geometric Design

Appl. Comput. Harmonic Anal.

Discrete spline filters for multiresolution and wavelets of l2

SIAM J. Math. Anal.

Biorthogonal loop-subdivision wavelets

Computing

Generalized b-spline subdivision-surface wavelets for geometry compression

IEEE Trans. Vis. Comput. Graph.

Inserting new knots into b-spline curves

Computer-Aided Design

An Introduction to Wavelets

Wavelets on a bounded interval

Ten Lectures on Wavelets

Wavelets on irregular point sets

Philos. Trans. A Roy. Soc. London

Discrete spline filters for multiresolution and wavelets of $l_{2}$