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SIAM Journal on Mathematical Analysis
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Unlifted Loop Subdivision Wavelets
PG '04 Proceedings of the Computer Graphics and Applications, 12th Pacific Conference
Biorthogonal loop-subdivision wavelets
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Generalized hierarchical NURBS for interactive shape modification
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Technical Section: Smooth reverse subdivision
Computers and Graphics
Image-assisted modeling from sketches
Proceedings of Graphics Interface 2010
Freeform-based form feature modeling using a hierarchical & multi-resolution NURBS method
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Technical Section: Multiresolutions numerically from subdivisions
Computers and Graphics
Smooth reverse Loop and Catmull-Clark subdivision
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A discrete approach to multiresolution curves and surfaces
Transactions on Computational Science VI
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Proceedings of Graphics Interface 2013
Special Section on Graphics Interface: Atlas of connectivity maps
Computers and Graphics
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We present a novel method for determining local multiresolution filters for a broad range of subdivision schemes. Our approach is based on constraining the wavelet coefficients such that the coefficients at even vertices can be computed from the coefficients of neighboring odd vertices. This constraint leads to an initial set of decomposition filters. To increase the quality of these initial filters, we use an optimization that reduces the size of the wavelet coefficients. The resulting multiresolution filters yield a biorthogonal wavelet system whose construction is similar to the lifting scheme. This approach is demonstrated in depth for cubic B-spline curves and Loop subdivision surfaces. Our filters are shown to perform comparably with existing filters.