A template-based approach for the specification of 3D topological constraints

Several different models have been defined in literature for the definition of 3D scenes that include a geometrical representation of objects together with a semantical classification of them. Such semantical characterization encapsulates important details about the object properties and behavior and often includes spatial relations that are defined only implicitly or through natural language, such as \u201can external access shall be in touch with the building only when it is classified as a direct access\u201d. The problem of ensuring the coherence between geometric and semantic information is well known in literature. Many attempts exist which try to extent the OCL to allow the representation of spatial integrity constraints in an UML model. However, this approach requires a deep knowledge of the OCL formalism and the implementation of ad-hoc procedures to validate the constraints specified at conceptual level. Therefore, a new approach is needed that helps designers to define complex OCL constraints and at the same time allows the automatic generation of the code to test them on a given dataset. The aim of this paper is to propose a set of predefined templates to express on the classes of an UML data model, a family of 3D spatial integrity constraints based on topological relations; all this without requiring the knowledge of any formal language by domain experts and supporting their automatic translation into validation procedures

Snap Rounding with Restore: an Algorithm for Producing Robust Geometric Datasets

This paper presents a new algorithm called Snap Rounding with Restore (SRR), which aims to make ge- ometric datasets robust and to increase the quality of geometric approximation and the preservation of topological structure. It is based on the well-known Snap Rounding algorithm, but improves it by eliminat- ing from the snap rounded arrangement the configurations in which the distance between a vertex and a non-incident edge is smaller than half-the-width of a pixel of the rounding grid. Therefore, the goal of SRR is exactly the same as the goal of another algorithm, Iterated Snap Rounding (ISR), and of its evolution, Iterated Snap Rounding with Bounded Drift (ISRBD). However, SRR produces an output with a quality of approximation that is on average better than ISRBD, both under the viewpoint of the distance from the original segments and of the conservation of their topological structure. The paper also reports some cases where ISRBD, notwithstanding the bounded drift, produces strong topological modifications while SRR does not. A statistical analysis on a large collection of input datasets confirms these differences. It follows that the proposed Snap Rounding with Restore algorithm is suitable for applications that require both robustness, a guaranteed geometric approximation and a good topological approximation

Establishing Robustness of a Spatial Dataset in a Tolerance-Based Vector Model

Spatial data are usually described through a vector model in which geometries are rep- resented by a set of coordinates embedded into an Euclidean space. The use of a finite representation, instead of the real numbers theoretically required, causes many robustness problems which are well-known in literature. Such problems are made even worst in a distributed context, where data is exchanged between different systems and several perturbations can be introduced in the data representation. In this context, a spatial dataset is said to be robust if the evaluation of the spatial relations existing among its objects can be performed in different systems, producing always the same result.In order to discuss the robustness of a spatial dataset, two implementation models have to be distinguished, since they determine different ways to evaluate the relations existing among geometric objects: the identity and the tolerance model. The robustness of a dataset in the identity model has been widely discussed in [Belussi et al., 2012, Belussi et al., 2013, Belussi et al., 2015a] and some algorithms of the Snap Rounding (SR) family [Hobby, 1999, Halperin and Packer, 2002, Packer, 2008, Belussi et al., 2015b] can be successfully applied in such context. Conversely, this problem has been less explored in the tolerance model. The aim of this paper is to propose an algorithm inspired by the ones of SR family for establishing or restoring the robustness of a vector dataset in the tolerance model. The main ideas are to introduce an additional operation which spreads instead of snapping geometries, in order to preserve the original relation between them, and to use a tolerance region for such operation instead of a single snapping location. Finally, some experiments on real-world datasets are presented, which confirms how the proposed algorithm can establish the robustness of a dataset

Robustness of Spatial Relation Evaluation

In the last few years the amount of spatial data available through the network has increased both in volume and in heterogeneity, so that dealing with this huge amount of information has become an interesting new research challenge. In particular, spatial data is usually represented through a vector model upon which several spatial relations have been defined. Such relations represent the basic tools for querying spatial data and their robust evaluation in a distributed heterogeneous environment is an important issue to consider, in order to allow an effective usage of this kind of data. Among all possible spatial relations, this report considers the topological ones, since they are the most widely available in existing systems and represent the building blocks for the implementation of other spatial relations. The conditions and the operations needed to make a dataset robust w.r.t. topological interpretations strictly depends on the adopted evaluation model. In particular, this report considers an environment where two different eval- uation models for topological relations exist, one in which equality is based on identity of geometric primitives, and the other one where a tolerance in equality evaluation is introduced. Given such premises, the report proposes a set of rules for guaranteeing the robustness in both models, and discusses the applicability of available algorithms of the Snap Rounding family, in order to preserve robustness in case of perturbations

Evaluation of Topological Relations in a Discrete Vector Model

A spatial object is characterized not only by its geometric extents, but also by the spatial relations existing with its surrounding objects. An important kind of spatial relations is represented by topological relations. Many models have been defined in literature for formalizing the semantics of topological relations between spatial objects in the Euclidean 2D and 3D space [6, 3, 2]. Nevertheless, when these relations are evaluated in available systems many robustness problems can arise, which are essentially related to the discrete representations adopted by such systems. Moreover, in a Spatial Data Infrastructure (SDI) the perturbations introduced by the exchange of data between different systems can increase the robustness problems. The aim of this report is to define an implementation of topological relations with reference to a discrete vector model commonly adopted by today\u2019s systems

Establishing Robustness of a Spatial Dataset in a Tolerance-Based Vector Model

Spatial data are usually described through a vector model in which geometries are represented by a set of coordinates embedded into an Euclidean space. The use of a finite representation, instead of the real numbers theoretically required, causes many robustness problems which are well known in the literature. Such problems are made even worse in a distributed context, where data is exchanged between different systems and several perturbations can be introduced in the data representation. In order to discuss the robustness of a spatial dataset, two implementation models have to be distinguished: the identity and the tolerance model. The robustness of a dataset in the identity model has been widely discussed in the literature and some algorithms of the Snap Rounding (SR) family can be successfully applied in such contexts. Conversely, this problem has been less explored in the tolerance model. The aim of this article is to propose an algorithm inspired by those of the SR family for establishing or restoring the robustness of a vector dataset in the tolerance model. The main ideas are to introduce an additional operation which spreads instead of snapping geometries, in order to preserve the original relation between them, and to use a tolerance region for such an operation instead of a single snapping location. Finally, some experiments on real-world datasets are presented, confirming how the proposed algorithm can establish the robustness of a dataset

Spatial Integrity Constraints in 3D City Models: from Conceptual Definition to SQL Implementation

Several different models have been defined in literature for the definition of 3D city models, from CityGML to Inspire (Annex 3 - Buildings). Such models include a geometrical representation of features together with a semantical classification of them. The semantical characterization of objects encapsulates important meaning and spatial relations which are defined only implicitly or through natural language, such as buildings shall be disjoint or in touch, or a window surface shall be contained in the building boundary. The problem of ensuring the coherence between geometric and semantic information is well known in literature. Many attempts exist which try to extent the OCL language in order to represent spatial constraints for an UML model. However, this approach requires a deep knowledge of the OCL language and the implementation of ad-hoc procedures for the validation of constraints defined at conceptual level. The aim of this paper is the development of a set of templates for expressing spatial 3D constraints between features which does not require any particular knowledge of a formal language. Moreover, the constraints instantiated from these templates can be automatically translated into validation SQL queries, without the need for ad-hoc implementations

Distributive join: a new algorithm for joining relations

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