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Acknowledgements Acknowledgements This thesis is submitted for the degree of Cand Scient at the Department of Informatics University of Oslo 1 The work has b een carried out at the Division of Information Technology at SINTEF SI Department of Industrial Mathematics I would like to thank all the sta of the division for the stimulating environment they have supplied b oth professionally and so cially Without mentioning your names you should all know how thankful I am for your friendship and the answers you have provided to all my questions I would like to thank my sup ervisors Erlend Arge and Morten Dhlen for their inspiring guidance in general and the advices given on mathematical issues in particular I am esp ecially grateful to them for giving me sucient freedom to ensure the creativity of the work A sp ecial thank to Bjrn Skjellaug at the Department for Co op erative Systems who has b een an informal advisor on the data mo deling asp ects of my work He has also guided me in the art of writing scientic rep orts and generously encouraged me when I needed it at most To David Skogan and Olav Mork Bjrnas I have very much appreciated our vivid dis cussions and your comments to selected parts of the thesis At last but not least I want to express my sincere gratitude for the p ersonal supp ort given by my wife Hilde Bro dahl and the patience she has showed during the work She has also b een of great help in pro of reading of the thesis and in giving a helping hand in other editorial pro cesses Oslo November Gunnar Misund SI Center for Industrial Research Oslo is part of the SINTEF Group which employs ab out research scientists ii MULTIMODELS AND METAMAP TOWARDS AN AUGMENTED MAP CONCEPT Contents Acknowledgments i Introduction ix Prologue I CARTOGRAPHY AND GIS Outline Cartography Representing the Earth The Paper Map Mo del Generalization Cartographic information Generalizing top ographic information Generalizing thematic information Cartographic generalization Geographic Information Systems Managing Spatiotemp oral Information Computer Aided Cartography Automated Generalization Map Mo dels in GIS Topographic mo dels Thematic mo dels GIS standards An Augmented Map Concept Challenges Augmenting the Paper Map Mo del Summary iv II MULTIMODELS Outline The Multiple Nature of Geographic Information Examples of Multiple Geographic Information Text Parametric curves Functions Multiple Mo deling Vector approaches Tessellation approaches Topological approaches Temporal reasoning Integrated Mo deling The Multimo del The Multimo del Concept Digital Mo dels Denitions Mo del arithmetics Approximation and renement Digital Multimo dels Asp ects of Multimo dels Some Categories of Multimo dels Explicit Multimo del Multiedition mo dels Multiscale mo dels MULTIMOD A generic ob ject mo del Examples of Multimo dels Designing Multimo dels Piecewise Linear Curves Piecewise Linear Surfaces Summary III METAMAP Outline Integration of Geographic Information Strategies in spatial information integration Topology as information integration MULTIMODELS AND METAMAP TOWARDS AN AUGMENTED MAP CONCEPT v Metamap The Conceptual Mo del Geographic entities Geographic duality The Metamap element Topographic elements Thematic elements Topological structures Map top ology Primary top ology Secondary top ology Tertiary top ology The Metamap Ob ject mo del Metamap as an augmented map concept MINIMAP Towards an Implementation Metamap mo deling MINIMAP Geographic elements Topographic elements Thematic elements Topological structures Ob ject mo del Summary IV CONCLUSIONS AND IMPLEMENTATIONS Results Future Research Epilogue A MULTIMOD A Simple Multimo del Library A The generic library A Customizing MULTIMOD B MINIMAP A Simple Metamap Library B The library B Examples vi MULTIMODELS AND METAMAP TOWARDS AN AUGMENTED MAP CONCEPT List of Figures Contour map Crossing contours meter tolerance corresp onding to ca Crossing contours meter tolerance corresp onding to ca Dislo cation causing oshore road Primitive sea chart Roman road map TOmap Transfer of information Simplication Combination Deformation Generalization of text Generalization of pattern A Geographic Information System Textual description as thematic timevarying information Initial map Generalized edition Propagation of change in initial mo del Description of tidal variation in three resolution Delta vectors Adding initial vector and dierences Change in initial vector and the comp onent 1 Data reduction of delta mo del Pseudoscaleless structure Quadtree Simp el temp oral mo deling .
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