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Modelling threedimensional geoscientific fields with the voronoi diagram and its dual
 International Journal of Geographical Information Science
"... Fields as found in the geosciences have properties that are not usually found in other disciplines: the phenomena studied are often threedimensional, they tend to change continuously over time, and the collection of samples to study the phenomena is problematic, which often results in highly aniso ..."
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Cited by 6 (2 self)
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Fields as found in the geosciences have properties that are not usually found in other disciplines: the phenomena studied are often threedimensional, they tend to change continuously over time, and the collection of samples to study the phenomena is problematic, which often results in highly anisotropic distributions of samples. In the GIS community, raster structures (voxels or octrees) are the most popular solutions, but, as we show in this paper, they have shortcomings for modelling and analysing 3D geoscientific fields. As an alternative to using rasters, we propose a new spatial model based on the Voronoi diagram (VD) and its dual the Delaunay tetrahedralization (DT), and argue that they have many advantages over other tessellations. We discuss the main properties of the 3D VD/DT, present some GIS operations that are greatly simplified when the VD/DT is used, and, to analyse two or more fields, we also present a variant of the map algebra framework where all the operations are performed directly on VDs. The usefulness of this Voronoibased spatial model is demonstrated with a series of potential applications.
A Voronoibased map algebra
 In Progress in Spatial Data Handling–12th International Symposium on Spatial Data Handling
, 2006
"... Although the map algebra framework is very popular within the GIS community for modelling fields, the fact that it is solely based on raster structures has been severely criticised. Instead of representing fields with a regular tessellation, we propose in this paper using the Voronoi diagram (VD), ..."
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Cited by 5 (1 self)
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Although the map algebra framework is very popular within the GIS community for modelling fields, the fact that it is solely based on raster structures has been severely criticised. Instead of representing fields with a regular tessellation, we propose in this paper using the Voronoi diagram (VD), and argue that it has many advantages over other tessellations. We also present a variant of map algebra where all the operations are performed directly on VDs. Our solution is valid in two and three dimensions, and permits us to circumvent the gridding and resampling processes that must be performed with map algebra. 1 Introduction and Related Work The representation and modelling of geographical data can be done with two contrasting approaches: the object and the field models (Peuquet, 1984; Couclelis, 1992; Goodchild, 1992). The former model considers the space as being ‘empty ’ and populated with discrete entities (e.g. a house or a road)
Research Article Featurebased cartographic modelling
"... Cartographic modelling operations provide powerful tools for analysing and manipulating geographic data in the raster data model. This research extends these operations to the vector data model. It first discusses how the spatial scopes of analysis can be defined for point, line, and polygon feature ..."
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Cartographic modelling operations provide powerful tools for analysing and manipulating geographic data in the raster data model. This research extends these operations to the vector data model. It first discusses how the spatial scopes of analysis can be defined for point, line, and polygon features analogous to the raster cell. Then it introduces the local, focal, and zonal operations available for vector features, followed by providing a prototype syntax that might guide the implementation of these operations. Through example applications, this research also demonstrates the usefulness of these operations by comparing them with traditional vector spatial analysis.
FieldGML: An Alternative Representation For Fields∗
, 2008
"... While we can affirm that the representation, storage and exchange of twodimensional objects (vector data) in GIS is solved (at least if we consider the de facto standards shapefile and GML), the same cannot be said for fields. Among the GIS community, most people assume that fields are synonymous ..."
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While we can affirm that the representation, storage and exchange of twodimensional objects (vector data) in GIS is solved (at least if we consider the de facto standards shapefile and GML), the same cannot be said for fields. Among the GIS community, most people assume that fields are synonymous with raster structures, and thus only representations for these are being used in practice (many formats exist) and have been standardised. In this paper, I present a new GMLbased representation for fields in 2D and 3D, one that permits us to represent not only rasters, but also fields in any other forms. This is achieved by storing the original samples of the field, alongside the interpolation method used to reconstruct the field. The solution, called FieldGML, is based on current standards, is flexible, extensible and is also more appropriate than raster structures to model the kind of datasets found in GISrelated applications. 1
Research Article Towards a General Field model and its order in GIS
"... Geospatial data modelling is dominated by the distinction between continuousfield and discreteobject conceptualizations. However, the boundary between them is not always clear, and the field view is more fundamental in some respects than the object view. By viewing a set of objects as an object fie ..."
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Geospatial data modelling is dominated by the distinction between continuousfield and discreteobject conceptualizations. However, the boundary between them is not always clear, and the field view is more fundamental in some respects than the object view. By viewing a set of objects as an object field and unifying it with conventional field models, a new concept, the General Field (GField) model, is proposed. In this paper, the properties of GField models, including domain, range, and categorization, are discussed. As a summary, a descriptive framework for GField models is proposed. Then, some common geospatial operations in geographic information systems are reconsidered from the GField perspective. The geospatial operations are classified into orderincreasing operations and nonorderincreasing operations, depending on changes induced in the GField’s order. Generally, the order can be viewed as an indicator of the level of information extraction of geospatial data. It is thus possible to integrate the concept of order with a geoworkflow management system to support geographic semantics.