Event‐based topology for dynamic planar areal objects

Jiang, Jixiang; Worboys, Michael

doi:10.1080/13658810802577247

Cited by 48 publications

(54 citation statements)

References 13 publications

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“…Section 7 contains the main result, showing that bipartite relations are the same as evolutions. This result, Theorem 13, shows that any bipartite relation can be factorized into atomic relations, and the connections with another factorization result, obtained by Jiang and Worboys [JW09], are explained in Section 8. Finally in Section 9 we present some conclusions and suggestions for further work.…”

Section: Overviewmentioning

confidence: 99%

“…If however the regions exist on a sphere, there is no 3 intrinsic reason to prefer one node of the tree above any other. The work by Jiang and Worboys [JW09] used rooted trees, and concentrated on planar regions. Apart from Egenhofer's spherical topological relations [Ege05], there is relatively little work on qualitative distinctions which can be made on the sphere but not in the plane.…”

Section: Static Aspectmentioning

confidence: 99%

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Relations between adjacency trees

Stell¹,

Worboys²

2011

Theoretical Computer Science

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Adjacency trees can model the nesting structure of spatial regions. In many applications it is necessary to model foreground and background regions which exhibit changes over time such as splitting, where one region divides into two. For example, the qualitative description of the development of wildfires would use the foreground for areas on fire and the background for areas not on fire. Such dynamic behaviour can be modelled by a particular kind of relation between the nodes of two adjacency trees representing the initial and final configurations of the regions at two times. These relations, which we call bipartite, correspond to having an arbitrary relation between the foreground regions at the two times and an arbitrary relation between the background regions at the two times. We show that all bipartite relations between trees arise from sequences of atomic relations between trees. There are just four types of these atomic relations (in addition to one representing no change): inserts, splits, merges and deletes.

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Section: Overviewmentioning

confidence: 99%

Section: Static Aspectmentioning

confidence: 99%

Relations between adjacency trees

Stell¹,

Worboys²

2011

Theoretical Computer Science

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“…This could establish what kinds of spatio-temporal change are possible from particular rules. There will be close connections between the behaviour of the split and merge rules for bigraphs and the splitting and merging studied in [9,15]. There are also many possible application problems for spatiotemporal analysis described in the literature cited in the introduction.…”

Section: Conclusion and Further Workmentioning

confidence: 99%

“…We can imagine spatio-temporal scenarios between regions, such as one moving to encircle another, or two regions moving further apart to allow a third to pass between them. The most basic scenarios of single regions splitting and merging have been rigorously analysed in [9,15], but it is not clear whether more complex behaviours can be treated in a similar way. In order to study such behaviour it is necessary to have a formal framework that is capable of modelling spatio-temporal change without pre-judging the kinds of higher level events and process that will be significant.…”

Section: Introductionmentioning

confidence: 99%

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Spatio-temporal Evolution as Bigraph Dynamics

Stell

Mondo

Thibaud

et al. 2011

Spatial Information Theory

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Abstract. We present a novel approach to modelling the evolution of spatial entities over time by using bigraphs. We use the links in a bigraph to represent the sharing of a common ancestor and the places in a bigraph to represent spatial nesting as usual. We provide bigraphical reaction rules that are able to model situations such as two crowds of people merging together while still keeping track of the resulting crowd's historical links.

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Representation: Time

Peuquet

2017

International Encyclopedia of Geography

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Interest in representing temporal as well as spatial information in digital form coincided with the availability of large volumes of spatiotemporal data via advancing geosensing technology as well as accumulation of digital data from archival sources. A historical review is given, including entity‐based, location‐based, time‐based, and combined representational approaches and a framework for spatiotemporal query. The importance of going beyond representation of strictly observational data to include process is discussed, as well as issues and challenges unique to representation of the temporal dimension.

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Event‐based topology for dynamic planar areal objects

Cited by 48 publications

References 13 publications

Relations between adjacency trees

Relations between adjacency trees

Spatio-temporal Evolution as Bigraph Dynamics

Representation: Time

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