NDLI: Biorthogonal wavelets for subdivision volumes

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Biorthogonal wavelets for subdivision volumes

Content Provider	ACM Digital Library
Author	Bertram, Martin
Abstract	We present a biorthogonal wavelet construction based on Catmull-Clark-style subdivision volumes. Our wavelet transform is the three-dimensional extension of a previously developed construction of subdivision-surface wavelets that was used for multiresolution modeling of large-scale isosurfaces. Subdivision surfaces provide a flexible modeling tool for surfaces of arbitrary topology and for functions defined thereon. Wavelet representations add the ability to compactly represent large-scale geometries at multiple levels of detail. Our wavelet construction based on subdivision volumes extends these concepts to trivariate geometries, such as time-varying surfaces, free-form deformations, and solid models with non-uniform material properties. The domains of the repre-sented trivariate functions are defined by lattices composed of arbitrary polyhedral cells. These are recursively subdivided based on stationary rules converging to piecewise smooth limit-geometries. Sharp features and boundaries, defined by specific polygons, edges, and vertices of a lattice are explicitly represented using modified subdivision rules. Our wavelet transform provides the ability to reverse the subdivision process after a lattice has been re-shaped at a very fine level of detail, for example using an automatic fitting method. During this coarsening process all geometric detail is compactly stored in form of wavelet coefficients from which it can be reconstructed without loss.
Starting Page	72
Ending Page	82
Page Count	11
File Format	PDF
ISBN	1581135068
DOI	10.1145/566282.566296
Language	English
Publisher	Association for Computing Machinery (ACM)
Publisher Date	2002-06-17
Publisher Place	New York
Access Restriction	Subscribed
Subject Keyword	Geometry compression Subdivision surfaces Subdivision volumes Multiresolution modeling B-spline wavelets Hierarchical b-splines Arbitrary topology
Content Type	Text
Resource Type	Article

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