6,615 research outputs found
Unstructured spline spaces for isogeometric analysis based on spline manifolds
Based on spline manifolds we introduce and study a mathematical framework for
analysis-suitable unstructured B-spline spaces. In this setting the parameter
domain has a manifold structure, which allows for the definition of function
spaces that have a tensor-product structure locally, but not globally. This
includes configurations such as B-splines over multi-patch domains with
extraordinary points, analysis-suitable unstructured T-splines, or more general
constructions. Within this framework, we generalize the concept of
dual-compatible B-splines, which was originally developed for structured
T-splines. This allows us to prove the key properties that are needed for
isogeometric analysis, such as linear independence and optimal approximation
properties for -refined meshes
Splines and Wavelets on Geophysically Relevant Manifolds
Analysis on the unit sphere found many applications in
seismology, weather prediction, astrophysics, signal analysis, crystallography,
computer vision, computerized tomography, neuroscience, and statistics.
In the last two decades, the importance of these and other applications
triggered the development of various tools such as splines and wavelet bases
suitable for the unit spheres , and the
rotation group . Present paper is a summary of some of results of the
author and his collaborators on generalized (average) variational splines and
localized frames (wavelets) on compact Riemannian manifolds. The results are
illustrated by applications to Radon-type transforms on and
.Comment: The final publication is available at http://www.springerlink.co
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