Hugo Ledoux

Topologically consistent 3D city models obtained by extrusion

One of the simplest methods to construct a 3D city model is to extrude building footprints to obtain ‘block-shaped’ polyhedra representing buildings. Although the method is well known and easy to implement, if the 2D topological relationships between the footprints are not taken into account, the resulting 3D city models will not necessarily be topologically consistent (i.e. primitives shared by 3D buildings will be duplicated and/or intersect each others). As a result, the model will be of little use for most applications, besides visualization that is. In this article, we present a new extrusion procedure to construct topologically consistent 3D city models. It is based on the use of a constrained triangulation, is conceptually simple and offers great flexibility to create city models in different formats (e.g. CityGML or a surface-based representation). We have implemented the procedure, tested it with real-world data sets and validated it.

Transportation mode-based segmentation and classification of movement trajectories

The knowledge of the transportation mode used by humans (e.g. bicycle, on foot, car and train) is critical for travel behaviour research, transport planning and traffic management. Nowadays, new technologies such as the Global Positioning System have replaced traditional survey methods (paper diaries, telephone) because they are more accurate and problems such as under reporting are avoided. However, although the movement data collected (timestamped positions in digital form) have generally high accuracy, they do not contain the transportation mode. We present in this article a new method for segmenting movement data into single-mode segments and for classifying them according to the transportation mode used. Our fully automatic method differs from previous attempts for five reasons: (1) it relies on fuzzy concepts found in expert systems, that is membership functions and certainty factors; (2) it uses OpenStreetMap data to help the segmentation and classification process; (3) we can distinguish between 10 transportation modes (including between tram, bus and car) and propose a hierarchy; (4) it handles data with signal shortages and noise, and other real-life situations; (5) in our implementation, there is a separation between the reasoning and the knowledge, so that users can easily modify the parameters used and add new transportation modes. We have implemented the method and tested it with a 17-million point data set collected in the Netherlands and elsewhere in Europe. The accuracy of the classification with the developed prototype, determined with the comparison of the classified results with the reference data derived from manual classification, is 91.6%.

Formalisation of the level of detail in 3D city modelling

The level of detail in 3D city modelling, despite its usefulness and importance, is still an ambiguous and undefined term. It is used for the communication of how thoroughly real-world features have been acquired and modelled, as we demonstrate in this paper. Its definitions vary greatly between practitioners, standards and institutions. We fundamentally discuss the concept, and we provide a formal and consistent framework to define discrete and continuous levels of detail (LODs), by determining six metrics that constitute it, and by discussing their quantification and their relations. The resulting LODs are discretisations of functions of metrics that can be specified in an acquisition–modelling specification form that we introduce. The advantages of this approach over existing paradigms are formalisation, consistency, continuity, and finer specification of LODs. As an example of the realisation of the framework, we derive a series of 10 discrete LODs. We give a proposal for the integration of the framework within the OGC standard CityGML (through the Application Domain Extension).

An Efficient Natural Neighbour Interpolation Algorithm for Geoscientific Modelling

Although the properties of natural neighbour interpolation and its usefulness with scattered and irregularly spaced data are well-known, its implementation is still a problem in practice, especially in three and higher dimensions. We present in this paper an algorithm to implement the method in two and three dimensions, but it can be generalized to higher dimensions. Our algorithm, which uses the concept of flipping in a triangulation, has the same time complexity as the insertion of a single point in a Voronoi diagram or a Delaunay triangulation.

Simultaneous storage of primal and dual three-dimensional subdivisions

We propose a new general-purpose data structure useful for a variety of three-dimensional applications. The data structure has the characteristic of storing simultaneously the primal and dual subdivisions of a three-dimensional manifold. We argue in this paper that storing both subdivisions, for instance the Voronoi diagram and the Delaunay tetrahedralization, can be beneficial for many application domains, notably for the modelling of datasets in geosciences or for representing boundaries of real-world features. Our structure is an extension of the well-known quad-edge data structure used for representing two-dimensional manifolds. We describe the basic properties of this augmented quad-edge structure, along with the navigation operators, and we also demonstrate its usefulness with some examples of applications.

Propagation of positional error in 3D GIS: estimation of the solar irradiation of building roofs

While error propagation in GIS is a topic that has received a lot of attention, it has not been researched with 3D GIS data. We extend error propagation to 3D city models using a Monte Carlo simulation on a use case of annual solar irradiation estimation of building rooftops for assessing the efficiency of installing solar panels. Besides investigating the extension of the theory of error propagation in GIS from 2D to 3D, this paper presents the following contributions. We (1) introduce varying XY/Z accuracy levels of the geometry to reflect actual acquisition outcomes; (2) run experiments on multiple accuracy classes (121 in total); (3) implement an uncertainty engine for simulating acquisition positional errors to procedurally modelled (synthetic) buildings; (4) perform the uncertainty propagation analysis on multiple levels of detail (LODs); and (5) implement Solar3Dcity – a CityGML-compliant software for estimating the solar irradiation of roofs, which we use in our experiments. The results show that in the case of the city of Delft in the Netherlands, a 0.3/0.6 m positional uncertainty yields an error of 68 kWh/m2/year (10%) in solar irradiation estimation. Furthermore, the results indicate that the planar and vertical uncertainties have a different influence on the estimations, and that the results are comparable between LODs. In the experiments we use procedural models, implying that analyses are carried out in a controlled environment where results can be validated. Our uncertainty propagation method and the framework are applicable to other 3D GIS operations and/or use cases. We released Solar3Dcity as open-source software to support related research efforts in the future.

Modelling three-dimensional geoscientific fields with the Voronoi diagram and its dual

Fields as found in the geosciences have properties that are not usually found in other disciplines: the phenomena studied are often three‐dimensional (3D), 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 geographical information system (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 tetrahedralisation (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 Voronoi‐based spatial model is demonstrated with a series of potential applications.

A Voronoi-Based Map Algebra

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.

On the validation of solids represented with the international standards for geographic information

The international standards for geographic information provide unambiguous definitions of geometric primitives, with the aim of fostering exchange and interoperability in the geographical information system (GIS) community. In two dimensions, the standards are wellaccepted and there are algorithms (and implementations of these) to validate primitives, i.e. given a polygon, they ensure that it respects the standardised definition (and if it does not a reason is given to the user). However, while there exists an equivalent definition in three dimensions (for solids), it is ignored by most researchers and by software vendors. Several different definitions are indeed used, and none is compliant with the standards: e.g. solids are often defined as 2-manifold objects only, while in fact they can be non-manifold objects. Exchanging and converting datasets from one format/platform to another is thus highly problematic. I present in this paper a methodology to validate solids according to the international standards. It is hierarchical and permits us to validate the primitives of all dimensionalities. To understand and study the topological relationships between the different parts of a solid (the shells) the concept of Nef polyhedron is used. The methodology has been implemented in a prototype, and I report on the main engineering decisions that were made and on its use for the validation of real-world three-dimensional datasets.

Automatic conversion of IFC datasets to geometrically and semantically correct CityGML LOD3 buildings

Although the international standard CityGML has five levels of detail (LODs), the vast majority of available models are the coarse ones (up to LOD2, i.e. block-shaped buildings with roofs). LOD3 and LOD4 models, which contain architectural details such as balconies, windows and rooms, rarely exist because, unlike coarser LODs, their construction requires several datasets that must be acquired with different technologies, and often extensive manual work is needed. In this article we investigate an alternative to obtaining CityGML LOD3 models: the automatic conversion from already existing architectural models (stored in the IFC format). Existing conversion algorithms mostly focus on the semantic mappings and convert all the geometries, which yields CityGML models having poor usability in practice (spatial analysis, for instance, is not possible). We present a conversion algorithm that accurately applies the correct semantics from IFC models and that constructs valid CityGML LOD3 buildings by performing a series of geometric operations in 3D. We have implemented our algorithm and we demonstrate its effectiveness with several real-world datasets. We also propose specific improvements to both standards to foster their integration in the future.