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Interpolation by Low Rank Spline Surfaces Jüttler, Bert
Description
It has been observed recently that tensor-product spline surfaces with low rank coefficients provide advantages for efficient numerical integration, which is important in the context of matrix assembly in isogeometric analysis. By exploiting the low-rank structure one may efficiently perform multivariate integration by a executing a sequence of univariate quadrature operations. This fact has motivated us to study the problem of creating such surfaces from given boundary curves. On the one hand, we reconsider the classical constructions, which include Coons surfaces. We analyze the rank of the resulting parameterizations. On the other hand, we propose a new coordinate-wise rank-2 interpolation algorithm and discuss its extension to the case of parametric boundary curves. Here we discuss the properties of the new construction, which include a permanence principle and the reproduction of bilinear surfaces. Special attention is paid to the property of affine invariance. This is joint work with Dominik Mokri\(\v{s}\).
Item Metadata
Title |
Interpolation by Low Rank Spline Surfaces
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Creator | |
Publisher |
Banff International Research Station for Mathematical Innovation and Discovery
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Date Issued |
2016-08-09T11:47
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Description |
It has been observed recently that tensor-product spline surfaces
with low rank coefficients provide advantages for efficient
numerical integration, which is important in the context of matrix
assembly in isogeometric analysis. By exploiting the
low-rank structure one may efficiently perform multivariate
integration by a executing a sequence of univariate quadrature
operations. This fact has motivated us to study the problem of
creating such surfaces from given boundary curves.
On the one hand, we reconsider the classical constructions, which
include Coons surfaces. We analyze the rank of the
resulting parameterizations. On the other hand, we propose a new
coordinate-wise rank-2 interpolation algorithm and discuss its
extension to the case of parametric boundary curves. Here we discuss
the properties of the new construction, which include a permanence
principle and the reproduction of bilinear surfaces. Special
attention is paid to the property of affine invariance.
This is joint work with Dominik Mokri\(\v{s}\).
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Extent |
45 minutes
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Subject | |
Type | |
File Format |
video/mp4
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Language |
eng
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Notes |
Author affiliation: JKU Linz
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Series | |
Date Available |
2017-02-08
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Provider |
Vancouver : University of British Columbia Library
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Rights |
Attribution-NonCommercial-NoDerivatives 4.0 International
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DOI |
10.14288/1.0342689
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URI | |
Affiliation | |
Peer Review Status |
Unreviewed
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Scholarly Level |
Faculty
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Rights URI | |
Aggregated Source Repository |
DSpace
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Item Media
Item Citations and Data
Rights
Attribution-NonCommercial-NoDerivatives 4.0 International