Orthogonal Decomposition of Non-Uniform Bspline Spaces using Wavelets

We take advantage of ideas of an orthogonal wavelet complement to produce multiresolution orthogonal decomposition of nonuniformBspline (NUB) spaces. The editing of NUB curves and surfaces can be handled at different levels of resolutions. ApplyingMultiresolution decomposition to possiblyC1 discontinuous surfaces, one can preservethe general shape on one hand and local features on the other of the free-formmodels, 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 problemis 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-formsurfaces.