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_Spatial Data Modelling for 3D GIS_, Alias Abdul-Rahman · Morakot Pilouk This book is based on research works done by the authors at the University of Glasgow, Scotland, United Kingdom and the International Institute for GeoInformation Science and Earth Observation (ITC), The Netherlands in 2000 and 1996 respectively. We were motivated to write the book when we began a joint research work in 1992 for our postgraduate theses on Digital Terrain Modelling (DTM) data structuring and eventually DTM software development based on triangular irregular network (TIN) data structure. We realized then that many aspects needed to be addressed especially if an advanced geo information system (GIS) such as 3D GIS system was to be realized. We would like to thank our former supervisors, Dr Jane Drummond of University of Glasgow and Dr Klaus Tempfli of ITC. Various helps received from friends and colleagues at both institutions are also acknowledged. Special thanks go to Mohamad Hasif Nasaruddin, a postgraduate student at the Dept of Geoinformatics, Faculty of Geoinformation Science and Engineering, Universiti Teknologi Malaysia (UTM), Johor, Malaysia for his patient in formatting the manuscript. This book aims to introduce a framework for spatial data modelling for 3D GIS and it is specifically written for GIS postgraduate level courses. Postgraduate students, researchers, and professionals in Geo Information (GI) science community may find this book useful and it may provide some insights in various spatial data modeling problems. We hope that this book will serve as one of the useful resources in 3D GIS or 3D geoinformation research. Alias Abdul-Rahman (UTM, Johor, Malaysia) Morakot Pilouk (ESRI, Redlands, CA, USA) 2007 Contents: 1 Introduction 1.1 Why Does 3D GIS Matter? 1.2 The Needs for 3D GIS 1.3 The Need for 3D Spatial Data Modeling 1.4 Problems Associated with Spatial Modelling for 3D GIS 1.5 Previous Work 1.6 Background to the 3D GIS Problem 2 An Overview of 3D GIS Development 2.1 GIS Functions 2.2 3D GIS 2.3 Recent Progress Made on 3D GIS 2.4 Commercially Available Systems and 3D GIS 2.4.1 ArcView 3D Analyst 2.4.2 Imagine VirtualGIS 2.4.3 GeoMedia Terrain 2.4.4 PAMAP GIS Topographer 2.5 Why is 3D GIS Difficult to Realise? 2.6 Discussion 3 2D and 3D Spatial Data Representations 3.1 Introduction 3.2 Classes of Object Representations 3.2.1 Grid 3.2.2 Shape Model 3.2.3 Facet Model 3.2.4 Boundary Representation (B-rep) 3.2.5 3D Array 3.2.6 Octree 3.2.7 Constructive Solid Geometry (CSG) 3.2.8 3D TIN (Tetrahedral network, TEN) 3.3 GIS Applicability of the Representations 3.4 The Selection Criteria 3.4.1 Representation of Object Primitives 3.4.2 Topology of Spatial Objects: Simplexes and Complexes 3.5 Vector and Raster Representations 3.6 Summary 4 The Fundamentals of Geo-Spatial Modelling 4.1 Spatial Data 4.2 Spatial Data Modeling 4.3 Models and Their Importance for Geoinformation 4.4 Components of Geo-spatial Model 4.5 Phases in Geo-spatial Modeling 4.6 Conceptual Design of a Geo-spatial Model 4.6.1 Definition of Space 4.6.2 Abstraction of Space 4.6.3 Abstraction of Real World Object 4.6.4 Object and Spatial Extent 4.6.5 Spatial Relations 4.6.6 Application of Spatial Relations 4.6.7 Representation of Spatial Objects and Relationships 4.6.8 Spatial Data Models in GIS 4.7 Logical Design of Geo-spatial Model 4.7.1 Relational Approach 4.7.2 Object-oriented Approach 4.8 Summary 5 The Conceptual Design 5.1 TIN-based (2.5D) Data Model 5.2 Properties of the TIN-based Data Model 5.3 TEN-based Data Model 5.4 Generalized n-dimensional Integrated Data Model 5.4.1 The Definitions 5.5 Single-theme and Multi-theme 5.6 Euler’s Characteristics 5.6.1 Euler’s Equality 5.6.2 The Generalized Euler Equality REFERENCES AND BIBLIOGRAPHY: Manacher, GK, Zobrist, AL (1979) Neither the greedy nor the Delaunay triangulation of a planar point set approximates the optimal triangulation. 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