14 research outputs found

    Subdivide and Conquer: Adapting Non-Manifold Subdivision Surfaces to Surface-Based Representation and Reconstruction of Complex Geological Structures

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    Methods from the field of computer graphics are the foundation for the representation of geological structures in the form of geological models. However, as many of these methods have been developed for other types of applications, some of the requirements for the representation of geological features may not be considered, and the capacities and limitations of different algorithms are not always evident. In this work, we therefore review surface-based geological modelling methods from both a geological and computer graphics perspective. Specifically, we investigate the use of NURBS (non-uniform rational B-splines) and subdivision surfaces, as two main parametric surface-based modelling methods, and compare the strengths and weaknesses of the two approaches. Although NURBS surfaces have been used in geological modelling, subdivision surfaces as a standard method in the animation and gaming industries have so far received little attention—even if subdivision surfaces support arbitrary topologies and watertight boundary representation, two aspects that make them an appealing choice for complex geological modelling. It is worth mentioning that watertight models are an important basis for subsequent process simulations. Many complex geological structures require a combination of smooth and sharp edges. Investigating subdivision schemes with semi-sharp creases is therefore an important part of this paper, as semi-sharp creases characterise the resistance of a mesh structure to the subdivision procedure. Moreover, non-manifold topologies, as a challenging concept in complex geological and reservoir modelling, are explored, and the subdivision surface method, which is compatible with non-manifold topology, is described. Finally, solving inverse problems by fitting the smooth surfaces to complex geological structures is investigated with a case study. The fitted surfaces are watertight, controllable with control points, and topologically similar to the main geological structure. Also, the fitted model can reduce the cost of modelling and simulation by using a reduced number of vertices in comparison with the complex geological structure

    Modelling Orebody Structures: Block Merging Algorithms and Block Model Spatial Restructuring Strategies Given Mesh Surfaces of Geological Boundaries

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    This paper describes a framework for capturing geological structures in a 3D block model and improving its spatial fidelity given new mesh surfaces. Using surfaces that represent geological boundaries, the objectives are to identify areas where refinement is needed, increase spatial resolution to minimize surface approximation error, reduce redundancy to increase the compactness of the model and identify the geological domain on a block-by-block basis. These objectives are fulfilled by four system components which perform block-surface overlap detection, spatial structure decomposition, sub-blocks consolidation and block tagging, respectively. The main contributions are a coordinate-ascent merging algorithm and a flexible architecture for updating the spatial structure of a block model when given multiple surfaces, which emphasizes the ability to selectively retain or modify previously assigned block labels. The techniques employed include block-surface intersection analysis based on the separable axis theorem and ray-tracing for establishing the location of blocks relative to surfaces. To demonstrate the robustness and applicability of the proposed block merging strategy in a more narrow setting, it is used to reduce block fragmentation in an existing model where surfaces are not given and the minimum block size is fixed. To obtain further insight, a systematic comparison with octree subblocking subsequently illustrates the inherent constraints of dyadic hierarchical decomposition and the importance of inter-scale merging. The results show the proposed method produces merged blocks with less extreme aspect ratios and is highly amenable to parallel processing. The overall framework is applicable to orebody modelling given geological boundaries, and 3D segmentation more generally, where there is a need to delineate spatial regions using mesh surfaces within a block model.Comment: Keywords: Block merging algorithms, block model structure, spatial restructuring, mesh surfaces, subsurface modelling, geological structures, sub-blocking, boundary correction, domain identification, iterative refinement, geospatial information system. 27 page article, 26 figures, 6 tables, plus supplementary material (17 pages

    Multi-scale data storage schemes for spatial information systems

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    This thesis documents a research project that has led to the design and prototype implementation of several data storage schemes suited to the efficient multi-scale representation of integrated spatial data. Spatial information systems will benefit from having data models which allow for data to be viewed and analysed at various levels of detail, while the integration of data from different sources will lead to a more accurate representation of reality. The work has addressed two specific problems. The first concerns the design of an integrated multi-scale data model suited for use within Geographical Information Systems. This has led to the development of two data models, each of which allow for the integration of terrain data and topographic data at multiple levels of detail. The models are based on a combination of adapted versions of three previous data structures, namely, the constrained Delaunay pyramid, the line generalisation tree and the fixed grid. The second specific problem addressed in this thesis has been the development of an integrated multi-scale 3-D geological data model, for use within a Geoscientific Information System. This has resulted in a data storage scheme which enables the integration of terrain data, geological outcrop data and borehole data at various levels of detail. The thesis also presents details of prototype database implementations of each of the new data storage schemes. These implementations have served to demonstrate the feasibility and benefits of an integrated multi-scale approach. The research has also brought to light some areas that will need further research before fully functional systems are produced. The final chapter contains, in addition to conclusions made as a result of the research to date, a summary of some of these areas that require future work

    Un Modèle de Vue Spatiale pour une Représentation Flexible de Données Géographiques

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    The objective of this study is to provide a dynamic spatial view model to Geographical Information Systems. The notion of spatial view allows independent external interpretations of a database schema i.e. the representation of geographical data according to different point of views and in function of objectives which may be distinct from those of the database schema. As no view definition has been offered for spatial data, this research proposes the definition of a view formalism for spatial databases.The model we develop is defined as an extension of the classic database view. Spatial views model both alphanumeric and spatial data. A spatial view is defined an ordered set of spatial view atoms. Each atom is a set of database relations, a set of conventional spatial and non spatial database operators. Manipulations of views allow the derivation of new views according to specific needs. They are realized with a set of identified operators. The spatial view model integrates structured and cognitive spatial representations. The proposal defines a model and operations that allow the decomposition and representation of navigation knowledge. The spatial view allows a displacement action to be situated within its geographical context through complementary abstraction levels that accept partial knowledge. It associates the description of a route with related multidimensional spaces including significant symbolic landmarks and textual descriptions. Continuity of route representation is ensured by the graph concept applied to spatial views and spatial collage spatially materialized by connections. A route trace in each spatial view spaces is described by a section. Graph operators allow abstraction level changes within the route representation.The spatial view concept provides a relative flexibility to compose a land representation adapted to user needs. From the external modeling point of view, the spatial view concept enables representation of different, numerous database schema interpretations which are inevitable in GIS applications. By extension, it facilitates schema evolution by allowing external representations which do not directly affect the original database schema. For geographic applications, spatial views gives an original solution for database consultation and manipulation tasksL'objectif de cette étude est la définition d'un modèle de vue spatiale dynamique adapté aux Systèmes d'Information Géographiques. La notion de vue spatiale proposée permet une relative indépendance dans l'interprétation d'un schéma de base de données spatiales à savoir la représentation de données géographiques selon différents points de vues et en fonction d'objectifs distincts de ceux du schéma d'origine. Les mécanismes classiques de vue, dans le domaine des bases de données, n'intégrant pas la composante spatiale, cette recherche propose la définition d'un formalisme de vue adapté aux bases de données spatiales.Le modèle proposé est défini comme une extension de la vue classique telle qu'elle est identifiée par les bases de données. Le modèle de vue spatiale intègre la représentation de données spatiales et non spatiales. Une vue spatiale est un ensemble ordonné d'atomes de vue spatiale. Chaque atome de vue spatiale est construit à partir de relations et d'opérateurs spatiaux et non spatiaux. Un ensemble d'opérateurs de manipulation de vues spatiales est défini. Ces opérateurs permettent la manipulation et la dérivation de nouvelles vues spatiales.La vue spatiale autorise la représentation de modèles spatiaux structurés et cognitifs. La proposition définit un modèle et les opérations qui permettent la décomposition et la représentation d'un processus de déplacement. Le modèle de vue spatiale permet de situer la représentation d'un déplacement dans son contexte géographique à partir de niveaux d'abstraction complémentaires qui intègrent des connaissances partielles. Il associe la description d'un processus de déplacement dans un contexte d'espaces multi-dimensionels. La continuité de la représentation d'un déplacement est assurée par l'application de constructeurs de graphe appliqués au cadre de la vue spatiale à travers des concepts de collages et de connexions de vues spatiales. L'application d'opérateurs de graphe permet des changements de niveau d'abstraction dans la représentation des processus navigationnels.La vue spatiale apporte une flexibilité aux utilisateurs dans la représentation de données géographiques. Du point de vue de la modélisation, la vue spatiale permet la représentation de différentes interprétations utilisateurs d'une base de données spatiales. Par extension, la vue spatiale facilite l'évolution du schéma des bases de données spatiales. Elle constitue une forme originale de manipulation et de consultation d'applications géographiques
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