Scattered data fitting on surfaces using projected Powell-Sabin splines

Oleg Davydov; L.L. Schumaker; R. Martin; M. Sabin; J. Winkler

Scattered data fitting on surfaces using projected Powell-Sabin splines

Oleg Davydov, L.L. Schumaker, R. Martin (Editor), M. Sabin (Editor), J. Winkler (Editor)

Mathematics And Statistics

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution book

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Abstract

We present C1 methods for either interpolating data or for fitting scattered data associated with a smooth function on a two-dimensional smooth manifold Ω embedded into R3. The methods are based on a local bivariate Powell-Sabin interpolation scheme, and make use of local projections on the tangent planes. The data fitting method is a two-stage method. We illustrate the performance of the algorithms with some numerical examples, which, in particular, confirm the O(h3) order of convergence as the data becomes dense

Original language	English
Title of host publication	Proceedings of the 12th IMA international conference on Mathematics of surfaces XII
Publisher	Springer-Verlag
Pages	138-153
Number of pages	16
ISBN (Print)	978-3-540-73842-8
Publication status	Published - 2007

Keywords

powell-sabine splines
scattered data fitting
statistics

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Man1Submitted manuscript, 576 KB

Cite this

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title = "Scattered data fitting on surfaces using projected Powell-Sabin splines",

abstract = "We present C1 methods for either interpolating data or for fitting scattered data associated with a smooth function on a two-dimensional smooth manifold Ω embedded into R3. The methods are based on a local bivariate Powell-Sabin interpolation scheme, and make use of local projections on the tangent planes. The data fitting method is a two-stage method. We illustrate the performance of the algorithms with some numerical examples, which, in particular, confirm the O(h3) order of convergence as the data becomes dense",

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T1 - Scattered data fitting on surfaces using projected Powell-Sabin splines

AU - Davydov, Oleg

AU - Schumaker, L.L.

A2 - Martin, R.

A2 - Sabin, M.

A2 - Winkler, J.

PY - 2007

Y1 - 2007

N2 - We present C1 methods for either interpolating data or for fitting scattered data associated with a smooth function on a two-dimensional smooth manifold Ω embedded into R3. The methods are based on a local bivariate Powell-Sabin interpolation scheme, and make use of local projections on the tangent planes. The data fitting method is a two-stage method. We illustrate the performance of the algorithms with some numerical examples, which, in particular, confirm the O(h3) order of convergence as the data becomes dense

AB - We present C1 methods for either interpolating data or for fitting scattered data associated with a smooth function on a two-dimensional smooth manifold Ω embedded into R3. The methods are based on a local bivariate Powell-Sabin interpolation scheme, and make use of local projections on the tangent planes. The data fitting method is a two-stage method. We illustrate the performance of the algorithms with some numerical examples, which, in particular, confirm the O(h3) order of convergence as the data becomes dense

KW - powell-sabine splines

KW - scattered data fitting

KW - statistics

UR - http://portal.acm.org/citation.cfm?id=1770882

UR - http://personal.strath.ac.uk/oleg.davydov/man1.pdf

M3 - Conference contribution book

SN - 978-3-540-73842-8

SP - 138

EP - 153

BT - Proceedings of the 12th IMA international conference on Mathematics of surfaces XII

PB - Springer-Verlag

ER -

Scattered data fitting on surfaces using projected Powell-Sabin splines

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Keywords

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