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Spherical Harmonics, Splines, and Wavelets

Definitoric Constituents, Strategic Perspectives, Specific Applicability and Applications
  • Willi FreedenEmail author
  • Michael Schreiner
Living reference work entry
Part of the Springer Reference Naturwissenschaften book series (SRN)

Zusammenfassung

Dieser Beitrag stellt eine geodätisch relevante Sammlung von besonders wertvollem Material in den diversen Approximationsgebieten dar, die mit Kugelfunktionen, Splines und Wavelets involviert sind, und zwar in einem konsistenten und vereinheitlichtem Gefüge. Das Ziel der Arbeit besteht darin vorzugsweise Geodäten zu überzeugen, dass sphärisch orientierte Approximation ein reiches mathematisches Füllhorn bereitstellt, welches viel für eine breite Palette von Anwendungen zu bieten hat. Geomathematisch spiegelt es sowohl die approximative Erdfigur als auch die typische Satellitengeometrie eines tief fliegenden Erdorbiters wider. Unser wesentliches Interesse liegt in den Charakteristiken der Rekonstruktion und Dekomposition der verschiedenen Datentypen auf Sphären und der natürlich in der geodätischen Praxis auftretenden mannigfaltigen Observablen. Ein weiteres Anliegen ist, eine Zusatzbibliothek für Interessenten in lokal sowie global geprägter sphärischer Approximationstheorie verfügbar zu machen.

Keywords

Spherical harmonics Spherical splines Spherical wavelets Philosophies Definitions Strategies Applicabilities Applications 

Abstract

This contribution substantially represents a geodetically relevant collection of particularly valuable material in the diverse approximation areas involving spherical harmonics, splines, and wavelets, thereby establishing a consistent and unified setup. The goal of the work is to preferably convince members from geodesy that spherically oriented approximation provides a rich mathematical cornucopia that has much to offer to a large palette of applications. Geomathematically it reflects both the approximate shape of the Earth’s surface and the typical satellite geometry of a low Earth orbiter (LEO). Our essential interest is in reconstruction and decomposition characteristics corresponding to different types of data on spheres and various observables naturally occurring in geodetic practice. Another objective is to provide an addition to the library of any individual interested in geodetically reflected local as well as global spherical approximation theory.

Notes

Acknowledgements

This contribution represents a synopsis of ideas and concepts presented in the textbook “Spherical Sampling”, Geosystem Mathematics, Birkhäuser, Basel [90]. For more mathematical details and algorithmic aspects the interested reader is referred to the contents of this work.

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Copyright information

© Springer-Verlag GmbH Deutschland, ein Teil von Springer Nature 2018

Authors and Affiliations

  1. 1.Mathematics DepartmentUniversity of KaiserslauternKaiserslauternGermany
  2. 2.Institute for Computational EngineeringUniversity of Applied Sciences of Technology NTBBuchsSwitzerland

Section editors and affiliations

  • Willi Freeden
    • 1
  1. 1.Geomathematics GroupUniversity of KaiserslauternKaiserslauternGermany

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