Variational Interpolation of Subsets

Johannes Wallner; Helmut Pottmann

doi:10.1007/s00365-003-0554-1

Variational Interpolation of Subsets

Johannes Wallner^*, Helmut Pottmann

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

Abstract

We consider the problem of the variational interpolation of subsets of Euclidean spaces by curves such that the L² norm of the second derivative is minimized. It is well-known that the resulting curves are cubic spline curves. We study geometric boundary conditions arising for various types of subsets such as subspaces, polyhedra, and submanifolds, and we indicate how solutions can be computed in the case of convex polyhedra.

Original language	English (US)
Pages (from-to)	233-248
Number of pages	16
Journal	Constructive Approximation
Volume	20
Issue number	2
DOIs	https://doi.org/10.1007/s00365-003-0554-1
State	Published - 2004
Externally published	Yes

Keywords

Cubic splines
Variational interpolation

ASJC Scopus subject areas

Analysis
General Mathematics
Computational Mathematics

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10.1007/s00365-003-0554-1

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title = "Variational Interpolation of Subsets",

abstract = "We consider the problem of the variational interpolation of subsets of Euclidean spaces by curves such that the L2 norm of the second derivative is minimized. It is well-known that the resulting curves are cubic spline curves. We study geometric boundary conditions arising for various types of subsets such as subspaces, polyhedra, and submanifolds, and we indicate how solutions can be computed in the case of convex polyhedra.",

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author = "Johannes Wallner and Helmut Pottmann",

year = "2004",

doi = "10.1007/s00365-003-0554-1",

language = "English (US)",

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AU - Wallner, Johannes

AU - Pottmann, Helmut

PY - 2004

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N2 - We consider the problem of the variational interpolation of subsets of Euclidean spaces by curves such that the L2 norm of the second derivative is minimized. It is well-known that the resulting curves are cubic spline curves. We study geometric boundary conditions arising for various types of subsets such as subspaces, polyhedra, and submanifolds, and we indicate how solutions can be computed in the case of convex polyhedra.

AB - We consider the problem of the variational interpolation of subsets of Euclidean spaces by curves such that the L2 norm of the second derivative is minimized. It is well-known that the resulting curves are cubic spline curves. We study geometric boundary conditions arising for various types of subsets such as subspaces, polyhedra, and submanifolds, and we indicate how solutions can be computed in the case of convex polyhedra.

KW - Cubic splines

KW - Variational interpolation

UR - http://www.scopus.com/inward/record.url?scp=1842665605&partnerID=8YFLogxK

U2 - 10.1007/s00365-003-0554-1

DO - 10.1007/s00365-003-0554-1

M3 - Article

AN - SCOPUS:1842665605

SN - 0176-4276

VL - 20

SP - 233

EP - 248

JO - Constructive Approximation

JF - Constructive Approximation

IS - 2

ER -

Variational Interpolation of Subsets

Abstract

Keywords

ASJC Scopus subject areas

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