Modified multiquadric methods for scattered data interpolation over a sphere

Helmut Pottmann; Matthias Eck

doi:10.1016/0167-8396(90)90039-T

Modified multiquadric methods for scattered data interpolation over a sphere

Helmut Pottmann^*, Matthias Eck

^*Corresponding author for this work

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

30 Scopus citations

Abstract

Given arbitrary points on a sphere and associated real values, we address the problem of constructing a smooth function defined over the sphere which interpolates the given data. Several methods which are appropriate modifications of Hardy's planar multiquadric method are described and compared: the restriction of trivariate multiquadric interpolation to the sphere, spherical multiquadric interpolation due to Hardy and Goepfert and a scheme called 'elliptic multiquadric interpolation'. Following Franke's ideas, localized versions of these global techniques can be derived.

Original language	English (US)
Pages (from-to)	313-321
Number of pages	9
Journal	Computer Aided Geometric Design
Volume	7
Issue number	1-4
DOIs	https://doi.org/10.1016/0167-8396(90)90039-T
State	Published - Jun 1990
Externally published	Yes

Keywords

Interpolation
multiquadric surfaces
scattered data fitting
spherical domain

ASJC Scopus subject areas

Modeling and Simulation
Automotive Engineering
Aerospace Engineering
Computer Graphics and Computer-Aided Design

Access to Document

10.1016/0167-8396(90)90039-T

Cite this

@article{891375e8c72741aa92c73cb1c48bc028,

title = "Modified multiquadric methods for scattered data interpolation over a sphere",

abstract = "Given arbitrary points on a sphere and associated real values, we address the problem of constructing a smooth function defined over the sphere which interpolates the given data. Several methods which are appropriate modifications of Hardy's planar multiquadric method are described and compared: the restriction of trivariate multiquadric interpolation to the sphere, spherical multiquadric interpolation due to Hardy and Goepfert and a scheme called 'elliptic multiquadric interpolation'. Following Franke's ideas, localized versions of these global techniques can be derived.",

keywords = "Interpolation, multiquadric surfaces, scattered data fitting, spherical domain",

author = "Helmut Pottmann and Matthias Eck",

year = "1990",

month = jun,

doi = "10.1016/0167-8396(90)90039-T",

language = "English (US)",

volume = "7",

pages = "313--321",

journal = "Computer Aided Geometric Design",

issn = "0167-8396",

publisher = "Elsevier B.V.",

number = "1-4",

}

TY - JOUR

T1 - Modified multiquadric methods for scattered data interpolation over a sphere

AU - Pottmann, Helmut

AU - Eck, Matthias

PY - 1990/6

Y1 - 1990/6

N2 - Given arbitrary points on a sphere and associated real values, we address the problem of constructing a smooth function defined over the sphere which interpolates the given data. Several methods which are appropriate modifications of Hardy's planar multiquadric method are described and compared: the restriction of trivariate multiquadric interpolation to the sphere, spherical multiquadric interpolation due to Hardy and Goepfert and a scheme called 'elliptic multiquadric interpolation'. Following Franke's ideas, localized versions of these global techniques can be derived.

AB - Given arbitrary points on a sphere and associated real values, we address the problem of constructing a smooth function defined over the sphere which interpolates the given data. Several methods which are appropriate modifications of Hardy's planar multiquadric method are described and compared: the restriction of trivariate multiquadric interpolation to the sphere, spherical multiquadric interpolation due to Hardy and Goepfert and a scheme called 'elliptic multiquadric interpolation'. Following Franke's ideas, localized versions of these global techniques can be derived.

KW - Interpolation

KW - multiquadric surfaces

KW - scattered data fitting

KW - spherical domain

UR - http://www.scopus.com/inward/record.url?scp=0025442431&partnerID=8YFLogxK

U2 - 10.1016/0167-8396(90)90039-T

DO - 10.1016/0167-8396(90)90039-T

M3 - Article

AN - SCOPUS:0025442431

SN - 0167-8396

VL - 7

SP - 313

EP - 321

JO - Computer Aided Geometric Design

JF - Computer Aided Geometric Design

IS - 1-4

ER -

Modified multiquadric methods for scattered data interpolation over a sphere

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this