Table Of ContentCartography and the Impact of the Quantitative Revolution
To Waldo Tobler
who developed the concept of transformation
and opened up for us so many new paths in cartography
To Jean-Claude Müller
who regularly made us realize the benefits
of the latest technologies for cartography
To Henri Reymond
who helped us put these new paths to work,
offering guidance and scientific support to our reasoning
The authors would like to thank the Laboratoire Image et Ville (UMR 7011, CNRS) and all
the people who, in one way or another, have helped in the production of this book. We would
like to mention in particular, Jean-Philippe Antoni and Hélène Haniotou who have made a
tremendous contribution to the creation of the figures in all three volumes, as well as Jimena
Martínez who created the website (http://www.geogra.uah.es/carto-thematique-hermes/).
Thematic Cartography
volume 2
Cartography and the Impact
of the Quantitative Revolution
Colette Cauvin
Francisco Escobar
Aziz Serradj
First published 2010 in Great Britain and the United States by ISTE Ltd and John Wiley & Sons, Inc.
Adapted and updated from two volumes Cartographie thématique 3 et 4 published 2008 in France by
Hermes Science/Lavoisier © LAVOISIER 2008
Apart from any fair dealing for the purposes of research or private study, or criticism or review, as
permitted under the Copyright, Designs and Patents Act 1988, this publication may only be reproduced,
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ISTE Ltd John Wiley & Sons, Inc.
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The rights of Colette Cauvin, Francisco Escobar and Aziz Serradj to be identified as the authors of this
work have been asserted by them in accordance with the Copyright, Designs and Patents Act 1988.
Library of Congress Cataloging-in-Publication Data
Cauvin, C.
Thematic cartography and transformations / Colette Cauvin, Francisco Escobar, Aziz Serradj.
p. cm.
Includes bibliographical references and index.
ISBN 978-1-84821-109-4 -- ISBN 978-1-84821-110-0 -- ISBN 978-1-84821-111-7 --
ISBN 978-1-84821-112-4
1. Cartography. 2. Visualization. I. Escobar, Francisco. II. Serradj, Aziz. III. Title.
GA108.7.C38 2010
526--dc22
2009048722
British Library Cataloguing-in-Publication Data
A CIP record for this book is available from the British Library
ISBN 978-1-84821-109-4 (Set of 3 volumes)
ISBN 978-1-84821-111-7 (Volume 2)
Printed and bound in Great Britain by CPI Antony Rowe, Chippenham and Eastbourne.
Table of Contents
General Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ix
PART I. TRANSFORMATIONS OF ATTRIBUTES [Z] AND USE OF QUANTITATIVE
METHODS: GENERALIZATION AND MODELING. . . . . . . . . . . . . . . . . . . 1
Part I. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
Chapter 1. From the Description to the Generalization of an
Attribute Variable Z . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.1. Preliminary data analysis: a crucial step. . . . . . . . . . . . . . . . . . . 8
1.1.1. From classical description to exploratory data analysis (EDA). . . 8
1.1.2. Exploratory data analysis and graphical representations. . . . . . . 11
1.1.3. Quantitative level of measurement and graphical representation. . 19
1.2. Discretization: a constraint with several choices. . . . . . . . . . . . . . 21
1.2.1. From data to the basic rules. . . . . . . . . . . . . . . . . . . . . . . . 22
1.2.2. Choice of the number of classes . . . . . . . . . . . . . . . . . . . . . 23
1.2.3. Class limits and ranges. . . . . . . . . . . . . . . . . . . . . . . . . . . 26
1.2.4. Discretization and transformation of a variable . . . . . . . . . . . . 46
1.3. Two essential requirements: choosing and assessing the methods. . . . 53
1.3.1. A logic of reasoning . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
1.3.2. Guidance for making the necessary choice. . . . . . . . . . . . . . . 56
1.3.3. Guidance and suggestions for making the decision. . . . . . . . . . 66
1.4. Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
Chapter 2. Generalization of Thematic Attributes. . . . . . . . . . . . . . . . 77
2.1. Graphical transformations of reduction and generalization. . . . . . . . 80
2.1.1. Shared characteristics and constraints of graphical processing
techniques. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
2.1.2. Techniques for quantitative variables . . . . . . . . . . . . . . . . . . 84
vi Thematic Cartography 2
2.1.3. Graphical techniques for multiple and mixed variables: taxonomic
tree, scalogram, seriated matrix . . . . . . . . . . . . . . . . . . . . . . . . . 107
2.2. From mathematical structuring to standardized cartographic results . . 118
2.2.1. A factorial method for quantitative variables . . . . . . . . . . . . . 121
2.2.2. Methods for frequencies and mixed variables . . . . . . . . . . . . . 129
2.3. From mathematical classifications to the interpretation of the results . 137
2.3.1. Principles and review of classifications. . . . . . . . . . . . . . . . . 137
2.3.2. Representations and hierarchical classifications. . . . . . . . . . . . 140
2.3.3. Non-hierarchical classifications . . . . . . . . . . . . . . . . . . . . . 145
2.4. Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147
Chapter 3. Modeling Thematic Attributes: Generalizable Cartographic
Choices. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149
3.1. Thematic models based on the concept of regression . . . . . . . . . . . 150
3.1.1. Common characteristics to regression models and to their
representations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150
3.1.2. Basic model: simple regression. . . . . . . . . . . . . . . . . . . . . . 156
3.1.3. From statistical logic to thematic logic . . . . . . . . . . . . . . . . . 164
3.2. Models incorporating space via calculations . . . . . . . . . . . . . . . . 181
3.2.1. A model linked to the concept of regression: trend surfaces. . . . . 181
3.2.2. A model integrating spatial component via distance: the potential
model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191
3.3. Models incorporating space by construction and by calculations . . . . 197
3.3.1. A model of spatial interaction: the isochronous gravity model . . . 197
3.3.2. A model based on the DAI – cellular automata – a method of
simulating the evolution of geographic space . . . . . . . . . . . . . . . . . 208
3.4. Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213
Part I. Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 215
PART II. NEW CARTOGRAPHIC TRANSFORMATIONS AND 3D
REPRESENTATIONS. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 219
Part II. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 221
Chapter 4. Cartographic Transformations of Position . . . . . . . . . . . . . 223
4.1. Cartographic transformations of position: aims and characteristics. . . 224
4.1.1. Double objectives. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 227
4.1.2. Characteristics. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 229
4.2. Thematic CTPs of weight . . . . . . . . . . . . . . . . . . . . . . . . . . . 233
4.2.1. Characteristics and classification criteria. . . . . . . . . . . . . . . . 235
4.2.2. Area cartograms: design and applications . . . . . . . . . . . . . . . 237
Table of Contents vii
4.3. Thematic CTPs of links and directions. . . . . . . . . . . . . . . . . . . . 252
4.3.1. Unipolar thematic CTPs of links and directions. . . . . . . . . . . . 253
4.3.2. Multi-polar thematic CTPs of connections. . . . . . . . . . . . . . . 263
4.4. Differential CTPs or CTPs of comparison. . . . . . . . . . . . . . . . . . 267
4.4.1. Steps of bidimensional regression . . . . . . . . . . . . . . . . . . . . 268
4.4.2. Results and contributions of bidimensional regression. . . . . . . . 272
4.5. Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 276
Chapter 5. Taking a Third Dimension into Account, Transformation
of Display . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 277
5.1. From perception of relief to the diversity of “3D” products . . . . . . . 280
5.1.1. Vision and perception in 3D: understanding and grasping
depth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 281
5.1.2. Conventional 3D cartographic representations. . . . . . . . . . . . . 282
5.1.3. Diversity and classification of 3D images . . . . . . . . . . . . . . . 290
5.2. Basic principles of representations with a third dimension. . . . . . . . 296
5.2.1. A constraint: the use of projection. . . . . . . . . . . . . . . . . . . . 296
5.2.2. Basic parameters of 3D representations. . . . . . . . . . . . . . . . . 299
5.2.3. Specific principles depending on the continuity property . . . . . . 310
5.3. DTMs as examples of possibilities of DSMs . . . . . . . . . . . . . . . . 318
5.3.1. From the first digital attempts to establishing the vocabulary. . . . 319
5.3.2. Modern DTMs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 321
5.3.3. Derived data and associated cartography. . . . . . . . . . . . . . . . 333
5.4. A new way: true 3D. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 339
5.4.1. The true 3D: basic principles. . . . . . . . . . . . . . . . . . . . . . . 340
5.4.2. Examples and usefulness of true 3D representations . . . . . . . . . 344
5.5. Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 348
Part II. Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 351
General conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 353
Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 355
Software used. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 389
Appendices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 391
Appendix 1. Table of standardized normal distribution . . . . . . . . . . . . 393
Appendix 2. Critical values of Bravais-Pearson’s correlation
coefficient R. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 394
Appendix 3. Critical values of Student’s t . . . . . . . . . . . . . . . . . . . . 395
viii Thematic Cartography 2
Appendix 4a. Critical values of Fisher-Snedecor’s F, significance
level 0.05. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 396
Appendix 4b. Critical values of Fisher-Snedecor’s F, significance
level 0.01 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 397
List of Authors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 399
Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 401
General Introduction
In the first volume of this book on thematic cartography we established the
essential elements of making a map and advocated the concept of transformation,
introduced by W. Tobler [TOB 61]. A map is thought of as a result of a
transformation process. The cartographic reasoning associated with this idea can be
adapted for the production of any type of map, regardless of its aim or the study
phase for which a given map is intended. In order to be able to make the necessary
decisions, a cartographer needs to keep in mind all the different stages of the
mapmaking process.
Nevertheless, only those transformations that are indispensable in making a map
were described and explained previously. We now turn to the more inventive
transformations, to which the second volume is devoted. This volume consists of
two large parts, and aims to show the contributions of different manners of
processing the attributes, and those representations which are difficult to create
without the help of a computer.
The first part concerns the stage T2b, which was not discussed in the first
volume of this book. Thus, in this part we address the processing of the attributes
[Z] and the role of quantitative methods in cartography. Indeed, whilst for a long
time cartographers have been superimposing and juxtaposing variables (often
making the maps illegible), the inclusion of statistical tools in order to process data
before representing them produced a fundamental revolution in the discipline. From
now on, maps visualize the results of data processing, which summarize the
available information or stress a particular feature of the studied phenomenon.
Depending on the phase in the study for which the map is required, and also
depending on whether the map is needed for a preliminary exploration or for a
verification of a proposed assumption, the data processing can be very basic or very
complex. It ranges from simple structuring of a single variable to combining k
x Thematic Cartography 2
variables or creating a model, which may or may not incorporate the geographic
space explicitly.
The second part puts forward the transformations connecting the coordinates
[XYZ]. The principles of these transformations have been known for a long time, but
their application was difficult, if not impossible, without a computer. This part
examines the techniques which were long known but later renewed thanks to the
computing revolution. These include cartographic transformations of position on the
one hand, and 3D representations on the other. The former are more often
encountered under the name of anamorphosis. These are original models, often
revealing the underlying structure, which is not visible directly. The latter (3D
representations) are characterized by the presence of a variable which is expressed
vertically. These representations comprise several distinct categories with different
meanings: 2.5D, 3D and virtual reality.
It is certain that this second volume will leave unanswered some questions about
the future and the new opportunities in cartography. Therefore, the goal of the last
volume will be to describe the contributions of new technologies. Although
cartographers should always be open to these, it is important to judge them critically
in order not to end up with aberrant maps and not to make ill-advised decisions.
