A 3D GIS MODEL BASED ON CRYSTALLOGRAPHIC PRINCIPLES DEDICATED TO SPATIAL ANALYSES IN GEOSCIENCES

3D GIS enables the integration and coherence of multiple sources of data from different providers whilst respecting and representing enduser choices in terms of geometry and topology. Current 3D GIS uses unique topological and geometrical modeling as a rule (Zlatanova, 2000 ; Coors, 2002). This feature of 3D GIS makes easier queries to compute from topological models such as the “close to close” way of relating geometric primitives of one object or its neighbor objects. However, this homogenization leads to the loss of the model specificities, leading to heavy computations for conversion of the data. Additionally, it does not compensate in an automated way for issues arising from data acquisition and modeling.

This paper proposes a model for analysis based on 3D GIS. The proposed approach allows queries to be made on one object (intra-object analysis) or a set of objects (inter-objects analysis) even if the geometrical coherence between objects is not perfect. From crystallographic principles, this model analyses the symmetric features of each object to describe its structure i.e. the way which geometric primitives are arranged together. This first abstraction, the structure, gives a global overview of the object. Complementary to topological models, it facilitates some queries such as the roof extraction of a cavity or the 3D building simplification for instance.

A second abstraction, the bounding crystalline mesh or lattice unit in the terminology of crystallography, is obtained through the analysis of symmetric elements (plans, axes or centre). The lattice unit is, in crystallography, the envelope of the smallest parallelepiped which preserves the geometric properties. It is used like a 3D Bounding Box adapted to the object shape. It allows relationships of geographical objects whatever their geometric dimension. Relationships between geographical objects follow to two principles :

• each geographical object is subject to gravity. So the emptiness is not allowed in the model. The main objective is to connect non-adjacent objects (ex. : a house which is not in contact with a DTM) or to ensure relationships between the parts of different objects (for example, connect the roof of a geological layer and these of an included cavity) ;

• if a lattice unit intersects another lattice unit, we consider these lattice units are adjacent: the intersection and the inclusion characterize small scale relationships. This last principle is formalized with proximity spaces (this mathematical theory constitutes, in topology, an axiomatization of notions of "nearness").

With the help of lattice units, two graphs are computed. The first one is an incidence graph. It describes relationships between objects and makes it possible to establish the interrelationship between them. The second graph, called a temporal graph, draws, for one object, the evolution of its relationship with its own environment.

This model has been used and validated in different applications such as 3D building simplification (Poupeau and Ruas; 2007) or in a context of coal basin affected by anthropic subsidence due to extraction (Gueguen, 2007).

References Cited

Coors, 2002, 3D GIS in networking environments, CEUS.

Gueguen Y., 2007, Etude des mouvements de surface en environnement minier à partir d'interférométrie radar et identification des origines des déformations - L'exemple du bassin Nord/Pas-de-Calais. PhD Thesis, Paris-Est - Marne-la-Vallée, 209 p.

Poupeau B., and Ruas A., 2007, A crystallographic approach to simplify 3D building, Proceedings of the 23rd ICA Conference, Moscow, Russia.

Zlatanova S., 2000, 3D GIS for urban development, PhDThesis, ITC.