On the hyperfield or field-of-field concept

Abstract

This article introduces the concept of hyperfield as a recursive field-of-field structure using a Unified Modelling Language (UML) modelling approach in two different variants, the hyperfield instance and hyperfield template models. The recursive property defines a hyperfield of degree n as a representation of a relation between n locations in space, and where the normal field and constant value are special cases. Fields exposing vector space algebra may be used in the construction of a hyperfield of degree n. Inherent properties such as interpolation, dual appearance, fixed points and dual domain are discussed. There is also a description on how to implement the model in a generic programming language environment.

Keywords:

• hyperfield
• field
• GIS
• UML

Acknowledgements

I thank Kjetil Reiten Myhra of Kongsberg Defence Systems for allowing the publication of results from an internal development project. Several colleagues have made their valuable contributions in discussions during the development project. I am particularly appreciative of the helpful comments of Dr. Tor Lønnestad from Telemark University College, and our discussions connected to draft versions of this article.