A framework for evaluating 3D topological relations based on a vector data model
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A framework for evaluating 3D topological relations based on a vector data model Alberto Belussi1 · Sara Migliorini1
· Mauro Negri2
Received: 6 December 2018 / Revised: 20 December 2019 / Accepted: 24 April 2020 / © Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract 3D topological relations are commonly used for testing or imposing the existence of desired properties between objects of a dataset, such as a city model. Currently available GIS systems usually provide a limited 3D support which usually includes a set of 3D spatial data types together with few operations and predicates, while limited or no support is generally provided for 3D topological relations. Therefore, an important problem to face is how such relations can be actually implemented by using the constructs already provided by the available systems. In this paper, we introduce a generic 3D vector model which includes an abstract and formal description of the 3D spatial data types and of the related basic operations and predicates that are commonly provided by GIS systems. Based on this model, we formally demonstrate how these limited sets of operations and predicates can be combined with 2D topological relations for implementing 3D topological relations. Keywords 3D topological relations · Topological relation implementation · Spatial constraint validation · Vector model
1 Introduction In recent years many 3D modeling techniques have been applied for describing urban environments in different application contexts and with different goals. In particular, among other approaches, the OGC Standard CityGML [9] and its UML data model have been used for the representation of buildings located inside a common urban environment, requiring the explicit description of the spatial relations existing between each building and the environment and between buildings themselves. This new scenario exploits 3D technologies in a new and challenging way, since it forces the designers of 3D solutions to deal with relationships among solids or solids and other geometries (like, surfaces or curves), while in the recent past 3D modeling techniques were Sara Migliorini
[email protected] 1
Department of Computer Science, University of Verona, Verona, Italy
2
Department of Electronics, Information and Bioengineering, Politecnico of Milan, Milan, Italy
Geoinformatica
applied only for the representation of a single construction particularly valuable in terms of the cultural heritage of a city or country, like an ancient church or palace. In the latter case the goal of the 3D technique was mainly to produce a 3D visualization of the construction that was as close as possible to its actual appearance in the reality. This approach places less emphasis on the overall correctness of the represented spatial objects, in particular as regards to the spatial relations between them and their parts or between them and the environment. However, as soon as we switch from a single construction context to a metropolitan area of hundreds or thousands
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