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Orthogonal Decomposition of Non‐Uniform Bspline Spaces using Wavelets
Author(s) -
Kazinnik Roman,
Elber Gershon
Publication year - 1997
Publication title -
computer graphics forum
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.578
H-Index - 120
eISSN - 1467-8659
pISSN - 0167-7055
DOI - 10.1111/1467-8659.00139
Subject(s) - multiresolution analysis , wavelet , decomposition , interpolation (computer graphics) , tensor product , representation (politics) , basis (linear algebra) , computation , classification of discontinuities , orthogonality , mathematics , basis function , computer science , geometry , algorithm , pure mathematics , wavelet transform , computer graphics (images) , mathematical analysis , computer vision , wavelet packet decomposition , animation , ecology , politics , political science , law , biology
We take advantage of ideas of an orthogonal wavelet complement to produce multiresolution orthogonal decomposition of nonuniform Bspline (NUB) spaces. The editing of NUB curves and surfaces can be handled at different levels of resolutions. Applying Multiresolution decomposition to possibly C 1 discontinuous surfaces, one can preserve the general shape on one hand and local features on the other of the free‐form models, including geometric discontinuities. The Multiresolution decomposition of the NUB tensor product surface is computed via the symbolic computation of inner products of Bspline basis functions. To find a closed form representation for the inner product of the Bspline basis functions, an equivalent interpolation problem is solved. As an example for the strength of the Multiresolution decomposition, a tool demonstrating the Multiresolution editing capabilities of NUB surfaces was developed and is presented as part of this work, allowing interactive 3D editing of NUB free‐form surfaces.