Natural neighbor extrapolation using ghost points

Tom Bobach; Gerald Farin; Dianne Hansford; Georg Umlauf

doi:10.1016/j.cad.2008.08.007

Natural neighbor extrapolation using ghost points

Tom Bobach, Gerald Farin, Dianne Hansford, Georg Umlauf

Computing and Augmented Intelligence, School of (IAFSE-SCAI)

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

13 Scopus citations

Abstract

Among locally supported scattered data schemes, natural neighbor interpolation has some unique features that makes it interesting for a range of applications. However, its restriction to the convex hull of the data sites is a limitation that has not yet been satisfyingly overcome. We use this setting to discuss some aspects of scattered data extrapolation in general, compare existing methods, and propose a framework for the extrapolation of natural neighbor interpolants on the basis of dynamic ghost points.

Original language	English (US)
Pages (from-to)	350-365
Number of pages	16
Journal	CAD Computer Aided Design
Volume	41
Issue number	5
DOIs	https://doi.org/10.1016/j.cad.2008.08.007
State	Published - May 2009

Keywords

Extrapolation
Interpolation
Natural neighbor
Scattered data

ASJC Scopus subject areas

Computer Science Applications
Computer Graphics and Computer-Aided Design
Industrial and Manufacturing Engineering

Access to Document

10.1016/j.cad.2008.08.007

Cite this

@article{afe98d6abb5c4e01bc5c4ddcecad657f,

title = "Natural neighbor extrapolation using ghost points",

abstract = "Among locally supported scattered data schemes, natural neighbor interpolation has some unique features that makes it interesting for a range of applications. However, its restriction to the convex hull of the data sites is a limitation that has not yet been satisfyingly overcome. We use this setting to discuss some aspects of scattered data extrapolation in general, compare existing methods, and propose a framework for the extrapolation of natural neighbor interpolants on the basis of dynamic ghost points.",

keywords = "Extrapolation, Interpolation, Natural neighbor, Scattered data",

author = "Tom Bobach and Gerald Farin and Dianne Hansford and Georg Umlauf",

note = "Funding Information: This work was supported by the international graduate school DFG grant 1131 on “Visualization of Large and Unstructured Data Sets — Applications in Geospatial Planning, Modeling and Engineering”. Farin and Hansford were supported by NSF grant 0306385 “Splines over Iterated Voronoi Diagrams”. The authors would like to thank P. Alfeld for his Technical Report, which initiated part of our considerations. The images have been generated by software based in parts on the CGAL library [7] . Copyright: Copyright 2009 Elsevier B.V., All rights reserved.",

year = "2009",

month = may,

doi = "10.1016/j.cad.2008.08.007",

language = "English (US)",

volume = "41",

pages = "350--365",

journal = "CAD Computer Aided Design",

issn = "0010-4485",

publisher = "Elsevier Limited",

number = "5",

}

TY - JOUR

T1 - Natural neighbor extrapolation using ghost points

AU - Bobach, Tom

AU - Farin, Gerald

AU - Hansford, Dianne

AU - Umlauf, Georg

N1 - Funding Information: This work was supported by the international graduate school DFG grant 1131 on “Visualization of Large and Unstructured Data Sets — Applications in Geospatial Planning, Modeling and Engineering”. Farin and Hansford were supported by NSF grant 0306385 “Splines over Iterated Voronoi Diagrams”. The authors would like to thank P. Alfeld for his Technical Report, which initiated part of our considerations. The images have been generated by software based in parts on the CGAL library [7] . Copyright: Copyright 2009 Elsevier B.V., All rights reserved.

PY - 2009/5

Y1 - 2009/5

N2 - Among locally supported scattered data schemes, natural neighbor interpolation has some unique features that makes it interesting for a range of applications. However, its restriction to the convex hull of the data sites is a limitation that has not yet been satisfyingly overcome. We use this setting to discuss some aspects of scattered data extrapolation in general, compare existing methods, and propose a framework for the extrapolation of natural neighbor interpolants on the basis of dynamic ghost points.

AB - Among locally supported scattered data schemes, natural neighbor interpolation has some unique features that makes it interesting for a range of applications. However, its restriction to the convex hull of the data sites is a limitation that has not yet been satisfyingly overcome. We use this setting to discuss some aspects of scattered data extrapolation in general, compare existing methods, and propose a framework for the extrapolation of natural neighbor interpolants on the basis of dynamic ghost points.

KW - Extrapolation

KW - Interpolation

KW - Natural neighbor

KW - Scattered data

UR - http://www.scopus.com/inward/record.url?scp=67349245193&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=67349245193&partnerID=8YFLogxK

U2 - 10.1016/j.cad.2008.08.007

DO - 10.1016/j.cad.2008.08.007

M3 - Article

AN - SCOPUS:67349245193

SN - 0010-4485

VL - 41

SP - 350

EP - 365

JO - CAD Computer Aided Design

JF - CAD Computer Aided Design

IS - 5

ER -

Natural neighbor extrapolation using ghost points

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this