KJENSTAD, K., 2006, On the integration of object-based models and field-based models in GIS. This is an electronic version of an article published in the International Journal of Geographical Information Science, Vol. 20, No. 5, May 2006, 491-509, available online at: http://www.informaworld.com/smpp/content~content=a747921911
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This article describes how to construct a wide range of geometry objects (called GeographicGeometry objects) in the coordinate system of an ellipsoid such as the Geographic coordinate system. Each construction process is formulated analytically and algorithmically using a combination of a set of fairly well-known mathematical methods such as ellipsoid geodesic construction functions, spherical trigonometry and iterative refinement methods. Each such geometry object may efficiently be converted to a corresponding Cartesian geometry object in any map projection coordinate system using an approximation algorithm. This property makes them particularly useful as a coordinate-system-independent geometry representation. A geographic geometry object is normally topologically equivalent to its Cartesian geometry counterpart except for some discontinuity and singularity cases.
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.
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