application of entities methodology and rules for

APPLICATION OF ENTITIES METHODOLOGY AND RULES FOR DESIGNING OF ANIMATED CARTOGRAPHIC

ANAMORPHOSES

Dariusz Dukaczewski and Anna Markowska

PhD Dariusz Dukaczewski IGiK – Institute of Geodesy and Cartography ul. Modzelewskiego 27, 02-679 Warsaw, Poland tel.: +48 22 3291970, fax: +48 22 3291950 e-mail: [email protected]

PhD Anna Markowska IGiK – Institute of Geodesy and Cartography ul. Modzelewskiego 27, 02-679 Warsaw, Poland tel.: +48 22 3291990, fax: +48 22 3291950 e-mail: [email protected]

Abstract The authors analysed currently distinguished types of animated cartographic anamorphoses and proposed its classifi-cation based on 7 criteria: mathematical bases, transformed object, methods of transformation, continuity, graphic presentation, grid transformation and location of the main distortion point. The analysis of possibilities of usage of static and dynamic visual variables during process of designing of main types of animated cartographic anamorphoses allowed to formulate the tables of rules, inspired by research on entities methodology for designing spatiotemporal maps (Dukaczewski 2019). The analyses of properties of distinguished types of anamorphoses and other methods of cartographic presentation allowed to propose the rules of its potential combined usage. The authors proposed the method facilitating the design of animated cartographic anamorphoses. The analysis on utility of these maps, employing the statistical solutions and coefficients (Markowska 2018), allowed to carry out an evaluation of its effectiveness of transfer of information and utility for didactic purposes.

Keywords: Animated cartographic anamorphoses, Entities methodology of designing of spatiotemporal maps, carto-graphic anamorphoses classification, Static and dynamic visual variables

INTRODUCTION

Although first animated cartographic anamorphoses have appeared in the middle of the eighties of the XX century (Dukaczewski 2019), the majority of them was created during the last decade. In this period the first complex animated cartographic anamorphoses (employing more than one cartographic presentation method) were published. The number of animated cartographic anamorphoses, available at different websites is growing dramatically, but part of them made by non-cartographers is full of errors. There is no doubt, that designing the animated cartographic anamorphoses is a complex process, demanding very good knowledge of cartographic methodology. In the case of these maps the method-ology has still some gaps. Despite the growing interest in producing static or dynamic cartographic anamorphoses and unquestioned methodological development, it should be stressed that till now there is no common terminology and coherent classification of these maps (Monmonier 2015, Markowska 2019). This situation makes hard to analyze and discuss the properties of different types of anamorphoses, the possibilities and limitations of application of static and dynamic visual variables during process of its designing, as well as potentialities of its combined usage with others methods of cartographic presentation. Thus, it is relatively difficult to assess the effectiveness of transfer of information by these maps. This situation implies the need for an attempt to complete the identified gaps in methodology, to propose a method facilitating the design of animated cartographic anamorphoses and to analyse the utility of these maps, em-ploying the statistical solutions and coefficients.

Proceedings Vol. 1, 8th International Conference on Cartography and GIS, 2020, Nessebar, Bulgaria ISSN: 1314-0604, Eds: Bandrova T., Konečný M., Marinova S.

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OBJECTIVES, APPROACH AND METHODS

The first aim of this research was to analyse and to synthesize the currently distinguished types of animated cartograph-ic anamorphoses and to propose its classification. The next stage was an analysis of possibilities of usage of static and dynamic visual variables during process of designing of distinguished main types of animated cartographic anamorpho-ses. This allowed achieve the second aim of research - to formulate the tables of rules, inspired by author’s research on entities methodology for designing spatiotemporal maps (Dukaczewski 2019). The analyses of properties of distin-guished main types of anamorphoses and other methods of cartographic presentation allowed to propose the rules of its potential combined usage. Thus, it was possible to formulate the proposition of method facilitating the design of ani-mated cartographic anamorphoses. The analysis on utility of these maps, employing the statistical solutions and coeffi-cients, inspired by research on static cartographic anamorphoses (Markowska 2018), allowed to carry out an evaluation of its effectiveness of transfer of information and utility for didactic purposes.

RESULTS

In English, Japanese, Korean terminology cartographic anamorphoses are called ‘cartograms’, while in most of the European languages the similar terms are employed for method called in English ‘choropleth map’1. Till now there is no common terminology and consistent classification of anamorphoses. According to general definition in the case of these maps one feature – area or distance is distorted proportionately to the value of a given phenomenon (Faliszewska 2011). Many authors distinguish distance cartograms and area cartograms. In the sixth volume of The history of carto-graphy… (Monmonier 2015) other terms for area cartograms are mentionned: ‘anamorphosis’, ‘diagramic maps’, ‘map-like diagrams’, ‘varivalent projections’, ‘density equalized maps’, ‘isodensity maps’, ‘mass-distributing (pycnomirastic) map projections’. Terms of many area cartograms (anamorphoses) contain the name of the algorithm or method used in their preparation. When W. Tobler (2004) wrote about computer elaboration of area cartograms, he mentioned J. Dougenik, N. Chrisman and D. Niemeyer (Continuous Area Algorithm made with Rubber Sheet Distortion method, 1985) or Gastner-Newman (Diffusion-based Method, 2004) algorithms. It is possible to find other names related to algorithms used to generate these maps (A. Markowska, J. Korycka-Skorupa 2015), e.g.: W. Tobler algorithms (Rub-ber-map Method of 1973 and Pseudo-cartogram of 1986), D. Dorling (Cellular Automata Algorithm, 1990; Circular cartogram, 1996), D. House and C. Kocmoud algorithm (Continuous Area Cartogram Using the Constraint-based Method, 1988). It is to mention also solutions of J. Olson (Projector method, 1976), N. Kadmon, E. Shlomi (Polyfocal projection, 1978), S. Selvin, D.W. Merril and E.R. Close (DEMP - Radial Expansion method, 1984), C. Cauvin, F. Escobar, A. Serradj (Piezopleth maps, 1989), J. Torguson (Interactive polygon zipping method, 1990), V.S. Tikunov, S. Gusein-Zade (Line Integral method, 1993), M. Sarkar, M. Brown (Graphical fisheye views, 1997), H. Edelsbrunner, R. Waupotitsch (Combinatorial-based approach, 1997), D. Keim, S. North (Panse CartoDraw, 2001), G. Sluga (Lastna tehnika za izdelavo anamorfoz, 2004), M. Van Kreveld, B. Speckmann (Rectangular Cartogram, 2004), R. Heilmann, D. Keim, C. Panse, M. Sips (RecMap, 2004), D. Keim, C. Panse, S. North (Medial-axis-based cartograms, 2005), R. Henriques, F. Bação, V. Lobo (Carto-SOM, 2009), S. Sun (Opti-DCN and Carto3F, 2013), B. S. Daya Sagar (Mathe-matical Morphology-Based Cartograms, 2014), M.T. Gastner; V. Seguy; P. More (Fast Flow-Based Method, 2018). Some authors use new terms e.g. ‘gridded cartogram’ (B.D. Henning 2011), ‘circular-arc cartogram’, ‘rectilinear carto-gram’, ‘table cartogram or mosaic cartogram’ (S. Nusrat, S. Koborov 2016).

For the purposes of this research authors proposed classification of anamorphoses based on 7 criteria: mathematical bases, transformed object, methods of transformation, continuity, graphic presentation, grid transformation and location of the main distortion point. The criteria are divided depending on which map class they can be referenced:

• Cartographic anamorphoses: A) mathematical basis, B) transformed object, C) transformed method;

• Area cartograms: D) graphic continuity; E) graphic presentation;

• Anamorphical projections: F) grid transformation;

1 Probably the first usage of ‘continental’ term cartogram was these of C.J. Minard ‘cartogramme à foyer diagraphiques’ in 1851 (Friis 1974)


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• Distance cartograms: G) the main distortion point’s location.

Figure 1. Classification of anamorphoses

The criterion of mathematical basis (A) - mathematical accuracy of transformation was employed according to the proposition of Z. Mudrych (1976). The term ‘cartographic anamorphosis’ includes all presentations having certain ana-morphic features, though they may not be drawn up according to strict mathematical rules or may not maintain spatial relations. It is possible to distinguish:

− anamorphic maps (AM) – presentations which have been made according to mathematical and spatial rules; − anamorphic pseudomaps (APM) – graphically close to anamorphic maps, but elaborated in a One of the more arbi-trary way, often without clearly determined mathematical rules or rules connected to spatial relations.

The second criterion of classification – transformed objects (B) concerns the solutions of application of the anamorphic transformation applied to the cartographical grid or to the thematic contents of the map. According to this criterion it is possible to distinguish:

− cartograms (CA) – anamorphic maps showing the value of the thematic phenomenon employing the area of individual units (area cartogram) or the distance between selected points (distance cartogram). − anamorphical projections (AP) – anamorphic maps resulting from a transformation of cartographical grid (Korycka-Skorupa, et al. 2015).

Anamorphical projections are a type of distortion projections in which cartographical grid is distorted (S. Grabarczyk-Walus 2007). In this case it is possible to distinguish:

− one-direction anamorphoses (distortion along one axis of the rectangular coordinate system) (AP1), − two-direction anamorphoses (distortion along two axes) (AP2), − radial anamorphoses (distortion in radial directions from a given central point) (APR).


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Taking into the consideration the criterion of transformed method (C) it is possible to distinguish anamorphoses in which the changes in the area of base units or distances between selected points can be introduced (Olson 1976). This way two classes of cartograms can be proposed:

− area cartograms (CAA) – maps on which the area of individual spatial units is changed depending on the value of a phnomenon; − distance cartograms (CAD) – maps on which the distance between selected points is changed depending on the value of a phenomenon.

In the case of distance cartograms, according to the location of the main points of distortion it is possible to distinguish:

− monocentric distance cartograms (CADm) – maps on which the thematic information is shown by the distance be-tween the central point and given points (point 4a, figure 2a); − polycentric distance cartograms (CADp) – maps on which the value of phenomenon is shown by distance between a subsequent pair of points in a given network (point 4b, figure 2a).

Using spatial continuity(D) as a criterion of classification of area cartograms two classes can be proposed:

− contiguous cartograms (CAAC) – area cartograms on which spatial continuity is preserved, which means that base units have not been separated (points 5a–7, figure 2a, 2b); − noncontiguous cartograms (CAAN) – area cartograms on which spatial continuity is broken, which means that base units have been separated (points 8 – 10, figure 2b).

The last criterion of classification refers to the shape of base units (E). This aspect can be considered in both contiguous and noncontiguous cartograms. Looking at the shape of base units contiguous cartograms could be divided into:

− contiguous diagram cartograms (CAACD) in which units of reference have been substituted by simple geometric figures, e.g. squares, rectangles, circles (e.g. Dorling cartogram, 5c, figure 2b); − contiguous regular (mosaic) cartograms (CAACR) (point 6, figure 2b) in which base units correspond in shape to spatial units, but their borders are geometrized, most often build of segments; − contiguous irregular cartograms (CAACIR) (point 7, figure 2b) in which base units correspond to the shape of statis-tical units, their borders are not geometrized, the shape of units depends on the distortion algorithm applied.

In the case of noncontiguous cartograms it is possible to distinguish:

- noncontiguous equiform cartograms (CAANE) (point 10, figure 2b) which preserve the shape of spatial units; - noncontiguous diagram cartograms (CAAND) (point 8, figure 2b) non preserving the shape of spatial units; - nocontiguous regular cartograms (CAANR) (point 9, figure 2b), in the case of which the shape of base units corre-sponds to spatial units, but their borders are geometrized, often built of segments.

The next stage was an analysis of possibilities of usage of static and dynamic visual variables during process of design-ing of distinguished main types of animated cartographic anamorphoses. Authors have employed the results of previous research on evaluation of the combined application of static and visual variables, sound variables and related methods of cartographic presentation for 8 age group of users2 (Dukaczewski 2019, 2016). The result was table of rules, includ-ing information on employed combination of static visual variables (and dynamized static visual variables), dynamic variables and sound variables, related methods of presentation as well as potential usefulness of these combinations for different groups of users. This table of rules is available as appendix 1 at http://www.igik.edu.pl/upload/File/dr-dariusz-dukaczewski/_20_Appendix1.pdf.

2 4-6, 7-9, 10-15, 16-19, 20-30, 31-60, 61-80, over 80 years


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No

Cartographic anamorphoses

Example

Information and source

1. Anamorphic maps (AM) 2. Anamorphic pseudomaps (APM) 3. Anamorphical

projections

Topographic map with two points of anamorphical projection (Grabarczyk-Walus 2007).

Cartographic anamorphoses / Cartograms (CA) Distance anamorphises / Distance cartograms (CAD)

4a

Monocentric distance anamorphoses / Monocentric distance cartograms (CADm)

London tube (time scale) http://www.tom-carden.co. uk/p5/tube_map_travel_times/applet

4b

Policentric distance anamorphoses / Policentric distance cartograms (CADp)

Distances between Warsaw metro stations expressed in travel time (fragment) (Korycka-Skorupa et al. 2015)

Area anamorphoses / Area cartograms (CAA) Contiguous anamorphoses / Contiguous cartograms (CAAC)

Anamorphic diagrams / Diagram cartograms (CAACD)

5a

Rectangular anamorphic cartodiagrams / Rectangular cartograms (CAACDr)

World population in 2006 (fragment) https://www.win.tue.nl/~speckman/Cartograms/ WorldCarto.html

5b

Square anamor-phic cartodi-agrams / Square carto-grams (CAACDs)

Population of the counties of the state of California http://www.ncgia.ucsb.edu/projects/Cartogram_ Central/types.html

Figure 2a. Examples of cartographic anamorphoses (part 1)


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No

Cartographic anamorphoses

Example

Information and source

5c

Dorling cartograms (CAACDd)

Population of counties of Britain (Dorling 1995) A new social atlas of Britain, Wiley, Chichester

6.

Regular ana-morphoses / Regular carto-grams (CAACR)

Infant mortality in North Carolina in 1991. The area of counties is the number of births (Meade, Earickson 2005) Medical Geogra-phy, New York: The Guilford Press

7.

Irregular anamor-phoses / Irregular cartodiagrams (CAACIR)

World population in 1500. Regions of the Word are distinguished by colors. www.worldmapper.org

Noncontiguous anamorphoses / Noncontiguous cartograms (CAAN) 8.

Noncontiguous anamorphic car-todiagrams / Noncontiguous diagram carto-grams (CAAND)

The area of hexagons is proportional to the population and area of voivodeships in Poland in 1969 (Ratajski 1989), Metodyka kartografii społeczno-gospodarczej, Wydanie II, PPWK, Warszawa – Wrocław

9. Noncontiguous regular anamorphoses / Noncontiguous regular carto-grams (CAANR)

Export of goods (fragments) Nowy atlas geograficzny. Gimnazjum, 2001, Demart, Warszawa

10. Noncontiguous equiform anamorphoses / Noncontiguous equiform carto-grams (CAANE)

Population over 65 in the United States (Olson 1976) Noncontinuous Area Cartogram, The Professional Geographer, Vol. 36, no 4

Figure 2b. Examples of cartographic anamorphoses (part 2)


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Figure 3. Possibilities and limitations of combined usage of main cartographic anamorphoses with other main carto-graphic methods of presentation


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The advent of complex cartographic animations employing anamorphoses together with other methods of cartographic presentation, noticeable more intensely from the beginning of 2010-ties3, convinced authors to carry out an analysis on possibilities and limitations of combined usage of main cartographic anamorphoses with other main cartographic meth-ods of presentation. The resulted table (figure 3) demonstrates the possible and conditional solutions of designing com-plex cartographic animations employing cartographic anamorphoses.

Using the results of previous research (A. Markowska 2018, 2019; Dukaczewski 2016, 2019) the authors have proposed the method facilitating the design of simple and complex animated cartographic anamorphoses (figure 4). The first stage is a definition of the goals of the cartographic animation, data compilation and analysis, as well as identification of the age of group of potential users (using the rules definied in five tables of the appendix 3, available at http://www.igik.edu.pl/upload/File/dr-dariusz-dukaczewski/_92_Appendix3.pdf). The next stage is a definition of the organization of type and organization of the animation. To do it it is necessary to define the organization of N sub-animation by identification of the entities, its measurement level and type, as well as to define the type of changes and to choose the type of animation, using typology of Dransch (1995), Block (1999) and Dukaczewski (2003). Then it is possible to select the combination of the method of cartographic presentation for animation or N-subanimation (and N-1 subanimation) employing typology of Korycka-Skorupa (2002), Dukaczewski (2003) and figures 2a, 2b. Verification of this choice can be done with table of rules of Dukaczewski (2009) and figure 3. The next stage is a choice and verifica-tion of static visual variables (including dynamized variables, employed for presentation of dynamic processes). This allow to choose the graphic form for the dynamized visual variable(s), definition of their relations with dynamic visuali-sation variables (& optional sound variables), as well as to select the method of cartographic presentation. These tasks can be carried out employing the appendix 1 available at http://www.igik.edu.pl/upload/File/dr-dariusz-dukaczewski/_20_Appendix1.pdf. The verification of the correctness of the choice of dynamized visual variable(s), other static visual variables and dynamic & sound variables, as well as verification of the correctness of selected meth-od(s) of cartographic presentation should be carried out using the tables of rules at http://www.igik.edu.pl/upload/File/dr-dariusz-dukaczewski/_92_Appendix2.pdf. These actions should allow to realiza-tion phase of the animation (or N –subanimation in the case of complex animation).

Due to the specificity of perception of cartographic anamorphoses the vital problem is the utility of these maps for users from different age and education groups. Authors are preparing the research concerning perception of simple and com-plex animated cartographic anamorphoses. A. Markowska has carried out the research on utility of static area anamor-phoses / area cartograms for educational purposes in secondary schools in Poland (Markowska 2018, 2019a, 2019b). The tests made in different types of secondary schools, taking into the consideration the groups of pupils of different level and profile allowed to formulate hypotheses, verified employing the logistic regression of dichotomous data, one-way analyses of variance (one-way ANOVA) and chi-squared test (χ2 test). These research has proved that regular anamorphoses / regular cartograms were the most useful for presentation of socio-economical phenomena in school geography. The time of lecture of these maps is similar like in the case of traditional maps and the level of correctness of lecture is better in the case of pupils of better geographical knowledge. The tests have proved that regular anamor-phoses / regular cartograms and anamorphic diagrams / diagram cartograms were more comprehensible than irregular anamorphoses / irregular cartodiagrams, especially for less geographically skilled pupils.

CONCLUSION

The aim of this research was the following to contribute to the discussion about the possibilities for (and limitations on) the design of animated maps that are better adapted to the needs of users belonging to different age groups, through the application of solutions based on the choice of variables specifically tailored to a given user age group. Another objec-tive was to further advance the cartographic animation methodology itself, especially concerning the usage of animated anamorphoses. The analysis allowed to distinguish the main types of animated cartographic anamorphoses and to pro-pose its classification. The analysis of possibilities of usage of static and dynamic visual variables for building thedis-tinguished main types of animated cartographic anamorphoses allowed to formulate the tables of rules, which can be employed during the process of designing of animated cartographic anamorphoses. The analyses of properties of differ-ent types of anamorphoses and other methods of cartographic presentation allowed to propose the rules of its potential combined usage. Employing the proposed tables of rules and results of previous research it was possible to formulate the proposition of method facilitating the design of animated cartographic anamorphoses. The analysis on utility of static anamorphoses, carried out by A. Markowska (2018, 20191, 2019b) has proved that these maps (especially regular

3 One of the first such animations were: East Asia Internet Users 1993 – 2008, Han-Teng Liao, 2010; General Election 2005 – 2010, B. D. Hennig (SASI Group, University of Sheffield), 2010; The changing colors of America 1960 – 2000. Election results by county, M. Gastner, C. Stalizi, M. Newshaw (University of Michigan), 2010; Global Annual Precipi-tation [per month] 1950 – 2000, B. D. Hennig (University of Sheffield), 2011


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Figure 5. Entities – polystaimic method of design o complex animated maps employing cartographic anamorhoses


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anamorphoses / regular cartograms) are useful for educational processes in geography, as well as other methods of car-tographic presentation. It should be emphasized, that due to the specificity of animated cartographic anamorphoses it is necessary to carry out the research on perception of these maps by users of different age groups.

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Markowska A (2018) Użyteczność kartograficznych anamorfoz powierzchniowych. PhD Thesis, Uniwersytet Warszawski, Wydział Geografii i Studiów Regionalnych, Warszawa, 2018

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BIOGRAPHY

Ph. D. Dariusz R. Dukaczewski (born 28 May 1962) is a Chair of GIS and Cartography Department of the Institute of Geodesy and Cartography in Warsaw (Poland), cartographer (M.Sc. diploma in Geography with specialization in Cartog-raphy, University of Warsaw, Department of Geography, Institute of Cartography, Warsaw, Poland), remote sensing specialist (DESS diploma in Exact Sciences University of Paris VI, Department of Geotectonics, Paris, France) and specialist in Earth Sciences (Ph.D. diploma in Sciences of the Earth Polish Academy of Sciences, Institute of Geography, Warsaw, Poland). His major activities concentrate on research concerning: geoinformation and geoinformatics, SDI, geoportals, dynamic and interactive visualization, application of new media technologies to cartography, cartographic methodology, semiotics, web cartography, remote sensing and its application in thematic mapping, environmental mapping, decision – making management, Data Policy. Author and co-author of over 100 publications.

Ph.D. Anna Markowska is a lecturer in GIS and Cartography Department of the Institute of Geodesy and Cartography in Warsaw (Poland) and Expert in Central Examination Committee (Poland). She studied geography and cartography at Faculty of Geography and Regional Studies University of Warsaw. Her Ph.D. dissertation was “Usability of area carto-grams”. She is interesting in cartography, especially in the usability of maps, using geoportals in visualization data, geodatabases and school cartography. Previously she worked at Faculty of Geography and Regional Studies University of Warsaw, as well as Educational Research Institute, The T. Manteuffel Institute of History Polish Academy of Sci-ences, Children’s University Foundation, W.S. Atkins and Carta Blanka.


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application of entities methodology and rules for

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