Roland Billen

3D spatial relationships model: a useful concept for 3D cadastre?

This paper contains some reflections about using 3D topology, and more generally some 3D concepts related to 3D cadastre. Firstly, we develop some conceptual views about 3D modelling and more specifically about the definition of 3D spatial objects. Secondly, we present a new framework for representing spatial relationships. The framework has different “complexity” levels and allows mixing simple and complex spatial relationships. Therefore, it is possible to consider different levels when querying spatial objects. Finally, some examples are presented in R 3 that demonstrate the applicability of the framework for cadastral objects.

Modeling and computing ternary projective relations between regions

Current spatial database systems offer limited querying capabilities beyond binary topological relations. This paper introduces a model for projective relations between regions to support other qualitative spatial queries. The relations are ternary because they are based on the collinearity invariant of three points under projective geometry. The model is built on a partition of the plane into separate zones that are obtained from projective properties of two reference objects: then, by considering the empty/nonempty intersections of a primary object with these zones, the model is able to distinguish between 34 different projective relations. Then, the paper proposes original algorithms for computing the relations under the assumption that regions of the plane are stored as vector polygons in a spatial database. These algorithms run in optimal O(nlogn) time

Dynamic and Mobile GIS: Investigating Changes in Space and Time

With the widespread use of PDAs, wireless internet, Internet-based GIS, and 3G and 4G telecommunications, the technology supporting mobile GIS is rapidly gaining popularity and effectiveness. This book addresses Web GIS, mobile GIS, and the modeling, processing, and representation of dynamic events, as well as current demands to update GIS representations. Providing a comprehensive overview of this emerging technology, this book highlights innovations, new ways of modeling both spatial objects and dynamic processes affecting them, and advances in visualization. Featuring contributions from established GIS workers, it begins with an introduction of extant technology and previews future developments. The book examines challenges to security and privacy and presents practical solutions to these problems while focusing on modeling approaches and exploring the need to display an appropriate level of information in a mobile environment. Concluding with a study of mobility, the book also contains practical examples of applications of mobile devices for disaster management and environmental monitoring. Dynamic and Mobile GIS: Investigating Changes in Space and Time offers detailed cases of successful applications and identifies the current cutting-edge aspects of mobile and dynamic GIS. The book also looks to the future, investigating important research directions and potential challenges.

The Dimensional Model: A Framework to Distinguish Spatial Relationships

A unique characteristic of GIS as compared to other information systems, is their capacity to manage spatial relationships, such as connections or interrelations among objects in the geometric domain. A number of frameworks use topology as a basic mechanism to define spatial relationships. The OpenGIS consortium has adopted one of them, i.e. the 9-intersection model. In this paper, a new framework for representing spatial relationships — the Dimensional model — is introduced. The model was first developed for convex spatial objects and is now extended to topological n-manifolds. It is based on two major concepts, i.e. the dimensional elements of spatial objects and the dimensional relationships, i.e. the relationships existing between dimensional elements. The model addresses a substantial group of spatial relationships and provides a flexible framework to consider either generalised or specialised types of associations.

A Model for Ternary Projective Relations between Regions

Current spatial database systems offer limited querying capabilities beyond topological relations. This paper introduces a model for projective relations between regions to support other qualitative spatial queries. The relations are ternary because they are based on the collinearity invariant of three points under projective geometry. The model is built on a partition of the plane in five regions that are obtained from projective properties of two reference objects: then, by considering the empty/non empty intersections of a primary object with these five regions, the model is able to distinguish between 31 different projective relations.

A Reasoning System of Ternary Projective Relations

This paper introduces a reasoning system based on a previously developed model for ternary projective relations between spatial objects. The model applies to spatial objects of the kind point and region is based on basic projective invariants and takes into account the size and shape of the three objects that are involved in a relation. The reasoning system proposes a set of permutation and composition rules, which allow the inference of unknown relations from given ones.

Projective relations in a 3d environment

This paper presents a model for positional relations among bodies of arbitrary shape in three dimensions. It is based on an existing model for projective relations among regions in two dimensions. The motivation is to provide a formal qualitative spatial relations model for emerging 3D applications. Two sets of relations are defined: ternary projective relations based on the concept of collinearity between a primary object and two reference objects and quaternary projective relations based on the concept of coplanarity between a primary object and three reference objects. Four sets of JEPD relations are defined for points and bodies in R3.

Semantics of collinearity among regions

Collinearity is a basic arrangement of regions in the plane. We investigate the semantics of collinearity in various possible meanings for three regions and we combine these concepts to obtain definitions for four and more regions. The aim of the paper is to support the formalization of projective properties for modelling geographic information and qualitative spatial reasoning. Exploring the semantics of collinearity will enable us to shed light on elementary projective properties from which all the others can be inferred. Collinearity is also used to find a qualitative classification of the arrangement of many regions in the plane.

Introducing a Reasoning System Based on Ternary Projective Relations

This paper introduces a reasoning system based on ternary projective relations between spatial objects. The model applies to spatial objects of the kind point and region, is based on basic projective invariants and takes into account the size and shape of the three objects that are involved in a relation. The reasoning system uses permutation and composition properties, which allow the inference of unknown relations from given ones.

A model for ternary projective relations between regions

Current spatial database systems offer limited querying capabilities beyond topological relations. This paper introduces a model for projective relations between regions to support other qualitative spatial queries. The relations are ternary because they are based on the collinearity invariant of three points under projective geometry. The model is built on a partition of the plane in five regions that are obtained from projective properties of two reference objects: then, by considering the empty/non empty intersections of a primary object with these five regions, the model is able to distinguish between 31 different projective relations.Current spatial database systems offer limited querying capabilities beyond topological relations. This paper introduces a model for projective relations between regions to support other qualitative spatial queries. The relations are ternary because they are based on the collinearity invariant of three points under projective geometry. The model is built on a partition of the plane in five regions that are obtained from projective properties of two reference objects: then, by considering the empty/non empty intersections of a primary object with these five regions, the model is able to distinguish between 31 different projective relations.