Reaching a Compromise between Contextual Constraints and Cartographic Rules: Application to Sustainable Maps
Hoarau, Charlotte, Cartography and Geographic Information Science
The ever-increasing demand for mapping, as well as the need for different kinds of maps and mapping products has accelerated the development of more diverse mapping applications. Cartographers and map designers have responded to these increasingly diverse needs by developing maps that are responsive to different visualization contexts and to individual user needs. In order to create these new visualizations, it is often useful to add some constraints to the traditional cartographic rules. For example, depending on the context, maps might sometimes be less complex, less luminous or maybe limit the use of color. Cartographers should consider these constraints in order to design the most suitable map for any given context keeping in mind that for a map to 'make sense', the chosen symbolization must be consistent with the semantic relationships it represents.
This article explores the extent to which a given topographic map can be modified according to a given constraint without loosing the meaning of the initial map. An evaluation of the semiotic quality of a modified map to an initial reference map is presented. This evaluation quantifies the semantic relationships of association, differentiation and order in the initial map, and measures how well the final map conveys these semantic relations.
The method employed in this study is based on map designs that have been created with decreasing adherence to cartographic guidelines so as to adapt a map for display on a mobile device. A practical constraint was to lower the energy required to display a map by redesigning the legend and modifying the colors. These energy savings are useful, for example to trekkers to increase the battery life of their GPS, or any other mobile user of GPS.
This article begins with a discussion of estimation of semiotic quality, and the energy required to display a map on a mobile device. The four map samples are compared to determine the relative compromises between traditional cartographic guidelines and the contextual constraint of reducing energy use for the display of maps on mobile devices.
Semiotic Quality of a Map
Cartographic theory provides a detailed formalization of graphical semiotics. Bertin (1967), as described in MacEachren (1995) presents different graphical variables and the correct ways to use them during cartographic conception. In this study the following two of Bertin's cartographic rules are considered: (1) conventional color uses, called conventional rules in this paper, and (2) semantic rules, that structure the organization of the legend by semantic relationships of association, differentiation and order.
Conventional rules limit the color space for some themes, as illustrated in Figure 1. In this example convention suggests that hydrography be represented by a color of the blue family, vegetation by a color of the green family and the background layer by a light color. Conventional rules facilitate the understanding of maps because people are often familiar with the conventions. Of course, it is possible to represent forest by red (which is sometimes relevant in fall) but this is not typical.
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As illustrated in Figure 2, semantic rules link two themes and their color. Two themes involved in an association relationship should be represented by similar colors, whereas two themes involved in a differential relationship should be represented by distant colors. Finally, themes involved in an ordered relationship should be represented by a color shading of the same hue.
In the legend, color choices play a major role because they are supposed to convey the existing semantic relationships between their corresponding themes. They ensure the semiotic quality of the map. For example, ColorBrewer (Brewer 2003) provides color schemas adapted to thematic cartography. Christophe (2009) proposes a cooperative method to design customized and original legends, by helping users to select suitable colors. These works show the importance of color choices. Thus, our work aims at preserving the quality of the map by recognizing and preserving the relationships between the layers, their semantics and their representation as shown on the initial map.
Preserving Cartographic Conventions
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In order to observe specific constraints, the colors of some or all themes in the legend might have to change with the goal of producing a final map that has sound cartographic quality. Our issues to preserve the quality of color choices include, 'which initial colors should be kept?,' 'which colors can be modified?' and finally, 'how will the final semiotic quality of the map be evaluated?' The quality of the initial map, the reference map is computed and compared to each newly designed map.
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In the global approach (see Figure 3), three guidelines are used when designing new legends to ensure map quality of the new maps. First, it is assumed that the initial map is cartographically correct, and that it can therefore be used to find the semantic relationships. This is not a classic semantic approach using ontologies, but instead relationships between legend symbologies are preserved in the legend of the new maps.
Second, the initial map employs conventional uses of color. Thus initial colors of hydrographic and vegetation themes, and the background were chosen as illustrated in Figure 1. Some or all of the colors of relevant themes are preserved in the new maps to retain the understanding of the map. Finally, color choices will be optimized regarding the low energy constraints described previously.
Estimation of Semantic Relationships
Let us assume that an initial map is cartographically correct. Figure 4 illstrates a reference of quality and sign-meaning relationships. The aim of this article is to adapt this map to be displayed on a mobile device while limiting energy comsumption and preserving the map's initial quality.
The estimation of the semantic relationships among the themes of the initial map is made by two successive steps. First, the relationships among themes are computed in the reference legend through color distances. Then a metric compares these relationships to those relationships presented in another legend.
Determining Semantic Relationships Color Distances
As described in the global approach, the initial map introduced in Figure 4 is considered as a reference. It provides for semantic relationships to be preserved. Here colors in the legend are compared to see how well the colors link the themes. The distances between the colors of each legend are first computed by the Euclidean distance in the CIELab Color Space (see Table 1). This color space gives an independent device color definition and has been designed by the International Commission on Illumination to be perceptually uniform as detailed in Fairchild (2005). This distance has been chosen because it gives global information about the similarity or the difference between two colors. This is useful for grouping colors together in order to find the semantic relationships conveyed by these colors.
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Then a threshold is introduced. Colors are considered close if the color distance is less than 50 and distant if it is greater. As shown in Table 2, binary distance matrices are then filled by 0 if the two colors are close enough and by 1 otherwise. It is obvious that this threshold is arbitrary and does not convey the real complexity of color representation. But it is a first approximation to group similar colors. This process illustrates the association and differentiation relationships in the legend. Order relationships are not studied here, but will be include in future research using hue or lightness contrasts between colors.
Using a threshold of 50, table 2 shows the existing relationships in the legend of Figure 4. Some association relationships are highlighted between blue hues for hydrographic themes and brown hues for themes concerning railways. Moreover, the background layer contrasts well with other themes.
Quantification of Semantic Relationships
In this step the legend from the initial map is compared to the legend of a new map to see how well the new- legend preserves the semantic meaning of the initial map. The sample legend in Figure 5 displays the initial legend. The matrix shown in Table 3 is the corresponding color relationship matrix. It conveys the sign-meaning relationships to be preserved. The sample legend in Figure 6 is the legend compared to the legend in Figure 5, with the corresponding color relationships matrix show in Table 4.
An indicator (Equation 1) is processed to quantify the distance between the two legends. It ranges from 0 for colors that are not easily distinguishable to 1 colors that are easily distinguishable. It will quantify the semantic relationships of the initial legend (Figure 5) by the second legend (Figure 6) using both relationships matrices (Table 3 and Table 4):
Dist = [p.summation over (i,j=0)]|[M.sub.ij]-[N.sub.ij]|/p (1)
M = binary distance matrix of reference legend,
N = the binary distance matrix for the new legend,
p = the number of colors in each legend.
Taking into Account Area Covered
It is necessary to consider the area covered on the map by each theme. Area covered will provide the relative importance of particular themes. It is important to take into account both the areal dimension and geometry of a feature. The width of linear object symbols, as well as the contour of polygonal objects, is considered. For point symbols, the area covered is estimated using the area of the pixel that contains the symbol. The background layer is under all the other layers. Thus, for the background layer, only the visible area need be considered. For the other themes, overlays are disregarded. A refined equation 2 below shows covered areas used as a weighting in the calculation of the distance between legends. Values still range from 0 to 1 for color similarity:
Dist = [p.summation over (i,j=0)]|[M.sub.ij]-[N.sub.ij]| x [area.sub.i]/[p.sup.2] (2)
M = binary distance matrix of the reference legend,
N = binary distance matrix of the second legend,
p = number of colors in each legend,
[area.sub.i] = visible area on the map of each layer
In the example shown in Table 5, the "reference" legend is on the left, and this legend is compared to the other four legends. The color relationships matrices have been calculated by the method described previously, and the distance from them to the reference legend has been calculated using equation 2.
Legends 1 and 3 have a similarity equal to 0; this means that they are cartographically similar to the reference legend regarding the semantic and color relationships. Indeed, the three legends contain three close colors with the same hue (respectively red, green and violet), two close colors with a same hue (respectively blue, red and green) and an isolated color (respectively yellow, purple and blue).
Energy Required for Map Display
In physics, energy is defined as the ability of a system to produce changes on another system. Light is an example of these changes when energy is transferred to convert electricity to colors on a screen. For some emerging display technologies, the energy required to display an image is directly linked to its colors. Therefore, a map can be more sustainable using dark colors rather than light ones. Our first issue, then is to evaluate the energy consumption of a mobile device. This estimation is considered as a quantification of the suitability of our map according to its display technology.
Estimation of Energy for Color Display
Colors displayed on a screen are usually described in an RGB color space. Therefore, RGB coordinates are used to evaluate the energy required to display each color. Chuang (2006) describes the energy required to display pixels on a mobile device according to their color. Two different equations estimate the energy depending on the type of screen of the mobile device. The sum of the maximum of the R, G, and B color components of each pixel is an appropriate estimation for HDR (High Dynamic Range) displays:
[Energy.sub.color] = max(r, g, b) (3)
Where r, g, b = RGB color components of the color layer i.
The sum of the sum of the R, G, and B color components of each pixel is an appropriate estimation for OLED (Organic Light Emitting Diode) displays:
[Energy.sub.color] = r + g + b (4)
Where r, g, b = RGB color components of the color layer i.
Figures 8 and 9 present the application of these energy estimations on three chromatic wheels (E. Chesneau 2006; Buard and Ruas 2007) used at the COGIT laboratory for map improvement and conception purposes (see Figure 7). This reference color system provides a discrete and structured space of colors. Figures 8 and 9 illustrate the value of both energy estimations for those colors. The left images show gradients of energy estimations, and images on the right display the same information in a 3D view. Figure 8 is computed with equation 3, the result ranging from 0 to 1. Figure 9 is computed with equation 4, the result ranging from 0 to 3.
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These two figures also show that globally bright colors use less energy for display than do dark colors. Moreover, grey tints use less energy. Concerning our reference map shown in Figure 4, it is now possible to estimate the energy required to display the different colors of the legends shown in Figures 8 and 9. Figure 10 illustrates the energy required to display the colors shown on the reference map on a mobile display
Energy Estimations for Area Covered
Next is an estimate of the energy required to display covered area on a map. In this estimation, the covered area is used as a weighting of the energy required to display each color. Equations (5) and (6) are used to estimate the energy for an entire map:
[Energy.sub.map] = [n.summation over (i=0)] max(r, g, b) x [area.sub.i] (5)
[Energy.sub.map] = [n.summation over (i=0)] (r + g + b) x [area.sub.i] (6)
[area.sub.i] = visible area of layer i on the map
r, g, b = color components of the color of layer i
n = number of layers on a map
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The geographic area considered for calculating the energy is the user's area of interest, not only the visible area on the screen. Indeed, the legend cannot change while the user is moving. So, the energy is calculated initially, and then users are able to pan or zoom in a mapping application as needed.
The geographic area used for our study when computing energy and semiotic quality estimations is the whole French administrative area of Isere. It is important to note that this global area is rural, presenting significant areas of vegetation cover and of undeveloped land represented by the background layer. Therefore, these two themes are relevant in our study because of their important role in the weighting matrix shown in Table 6, and their use for both estimations of the cartographic quality and the energy required to display the map.
The reference map shown in Figure 4 requires a weighted energy of 0.77 to be displayed on a mobile device (using Table 6 as weighting matrix and equation 5 to compute the energy consumption). The illustrations in Figures 11 and 12 show a focused zone symbolized with different European legends coming from Jolivet (2009). Which country proposes the more sustainable map?
The map with a Dutch legend requires a weighted energy of 0.77 whereas the map with a Norwegian legend requires a weighted energy of 0.80. Therefore, The Netherlands presents the most sustainable map. This was expected because of the very light colors of the background and the vegetation theme on the legend. For the same themes, the Dutch legend uses darker colors without using a light color for the background layer.
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Compromise Between Cartographic Quality and Energy Saving
Here are proposed new legends that observe the low energy constraint. Of course, changing the colors might either alter the use of conventional rules, or the change the semantic relationships. By relaxing these constraints, other maps are considered with the aim of exploring how much change in color changes the semantic relationships shown on the reference map. To accomplish this, four maps were designed while keeping in mind, more or less, the cartographic rules that produced the initial map and optimizing for energy consumption on mobile mapping devices. The goal is to propose cartographically correct, sustainable maps.
The reference map and its corresponding legend used in our example are presented in Figure 4 and the associated surface weights matrix in Table 6. Colors of the initial map's legend will be modified to be adapted to a mobile device. This map initially requires a weighted energy of 0.77. Energetic estimations are then computed with equation 5 and the cartographic quality of the different proposals are computed regarding the reference legend by equation 2. In the map presented in Figure 13 the original colors of the background layer have been retained, whereas other colors have been modified.
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This map requires a weighted energy of 0.67, saving approximately 13% with regard to energy use due to the dark colors used to represent the vegetation theme and the light background. Quantitatively this map does not seem to differ greatly from the initial reference map, but upon visual inspection it is not so easy to understand. The background layer has a powerful visual impact, but this does not appear to be enough to design an easily readable map.
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The cartographic distance between legend of Figure 13 and the reference legend is equal to 0.003. Semantic relationships between roads, building, railways and hydrography have been preserved. Colors have not been kept, nor their tint, but the map still presents association relations between layers in the same theme, differentiation relation between layers in different themes and order relationships for the hierarchical representation of the road for example. The resulting map is not conventional, but its legend still presents a hierarchical structure. In the next map shown in Figure 14, original colors of the hydrographic and vegetation themes have been kept whereas other colors have been modified.
This map requires a weighted energy of 0.65, a savings of 16%. The economy has increased because of uses of dark colors for both the background layer and the vegetation theme. But the map has lost efficiency and readability. Indeed, the cartographic distance between legend of Figure 14 and the reference legend is equal to 0.016. This map possess higher cartographic quality than the map in figure 13 map even though association relationships among roads, buildings or railway themes have been kept.
Keeping the colors of the hydrographic and vegetation themes may be difficult because it takes away a lot of the colors. It is also difficult to find colors that are both well-contrasted with the background layer and that preserve the semantic relationships between themes.
The conventional rule concerning the background layer is widely used to improve the color contrast (Chesneau 2006). If the background color is light enough, the darker geographic objects contrast well. Nevertheless, this conventional rule is not inevitable nor can it be used in all cases. For example, some GPS navigation systems offer visualization modes adapted to nighttime. These visualization modes are darker than the daytime mode so as to not disturb the driver. The background layer is definitely a powerful way to lower the energy required to display the map. This strategy to save energy has been used in Blackle (HeapMedia 2010), a version of the famous Google search engine with a black background. However, this strategy can turn against the first aim of this map design, which is the energy efficiency of the map.
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Modifying AU Colors on the Reference Map
In Figures 15 and 16, all of the colors on the maps have been modified. The design has been guided by the low energy constraint. Indeed, conventional rules are powerful when they are used all together. They are even more flexible if all the colors are modified. In this case, only the relevant geographic objects will help users to find traditional markers in the map. It opens a question for future work: which is more relevant to recognize a map, its legend or its geographic objects?
The map in Figure 15 requires a weighted energy of 0.22 i.e. it saves 70%. This important energy savings is due to the darkness of almost every color and especially the colors of the background layer and of the vegetation theme. However, the resulting map is not readable. The initial meaning of the map is completely lost. The legend is not well structured; all of the relationships of association are missing and the background layer is not contrasted with the other themes. In this map, the optimization of the colors has been too strong. The objective of adaptation to display on a mobile device is not attained because the map is no longer energy efficient. It is obvious that a compromise is necessary to preserve the meaning of the reference map. For example, for the map in Figure 16 all of the colors have been modified keeping in mind the goals of low energy consumption and preservation of semantic relationships illustrated on the initial map.
This map requires a weighted energy of 0.46 i.e. it saves 40%. The freedom for the modification of all the colors gives priority to dark colors for the background layer and the vegetation theme, which are the layers with the most area covered, and light colors for others themes. Color contrasts are good and facilitate comprehension by highlighting important geographic objects. The resultant map appears as a "reverse" image from the initial map, but achieves the goal of energy efficiency. The cartographic distance between the legend in Figure 16 and the reference legend is equal to 0.0078. The semantic relationships between themes have been preserved using less energy-consuming colors. Thus, this last map is a reasonable compromise between cartographic quality and energy efficiency. The different aspects of this compromise are discussed below.
The weighting of both estimations of energy use and cartographic quality highlights the importance of the background layer. Conventional rules would suggest that the background layer is generally represented by a light color. Therefore, darkening the background layer is a good way to lower the energy required to display a map. Nevertheless, it is a relevant semiotic component to give sense to the map. Thus, it is important to keep the contrast between geographic objects and the background layer, even if this figure/ground contrast is reversed.
Moreover, when lowering the energy required to display a map, dark colors are favored relatively to lighter ones or yellowish ones. Result maps cannot be entirely dark or grey. It is important to keep distinct tints when choosing new colors. Chuang (2006) sets a minimal distance between the different colors and a range of lightness. In this article, the colors of the legend are guided by the semantics of the initial map. Our metric allows us to check that the semantic relationships that exist on the reference map are preserved in the new legends. This is essential to ensure the readability of the new maps. Figure 17 shows the evolution of the compromise through the different legends design in this part.
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Conclusions and Perspectives
The first conclusion of this study is the highlighting of the importance of the background layer. It should be well-contrasted to all the other themes, and it does not necessarily have to be light. It can be represented by a dark color as long as other colors can be easily differentiated. The background layer is definitely a significant method for lowering the energy needed to display a map on a mobile device.
Moreover, it is not necessary to preserve all conventional uses of color, as long as the colors that are selected enhance comprehension of the map at first glance. In addition, it is possible to relax color use conventions if all colors are modified. Indeed, if the user does not recognize any conventional color, attention will focus on geographic objects in order to make sense of the graphic. It is therefore advantageous to modify all the colors in order to adapt the map to a specific constraint.
A second result is the importance of semantic relationships, and how they are represented by color. The structures of the map are conveyed by the symobology in the legend. Original colors of the legend can be modified as long as the initial relationships among them are preserved. This article puts forth a metric that quantifies the sign-meaning relationships of a reference map. This metric allows an analysis of the semantic quality of new legends in comparison to a reference legend.
The approach used here to get the best compromise between cartographic rules with contextual constraints has been applied in a specific application that is designed to minimize the energy required to display a map on a mobile device. The required energy estimation by Chuang (2009) to display a color has been extended to the display of an entire map.
Some map samples have been created that offer a best compromise between cartographic quality and the energy-savings constraint. It is obvious that finding the best compromise is not easy because it involves the symbolization on the entire map. A good strategy to save energy involves the employment of dark colors for the background layer, and in contrast to the foreground colors thereby preserving the readability of a map.
An application for automatic improvement of colors is under development in the GIS platform GeOxygene (Bucher and al. 2009). It will allow for the design of more sustainable maps. It will also be useful to test different automatic optimizations in order to study user feelings about those original maps, and to conduct experiments in real life conditions on mobile devices. Furthermore, other constraints could be studied. For example, if we limited the use of some tints, maps could be adapted for partially sighted persons, especially color blind users. Finally, it will be interesting to study the sensitivity of color choices regarding the type of geographical zone. Urban zones present more built-up areas whereas rural zones like those used in this study present more vegetation areas as a prominent background layer.
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Charlotte Hoarau, Institut Geographique National, Paris, France, E-mail:
Table 1. CIELab matrix distances (a) (b) (c) (d) (e) (f) (g) (h) (i) (j) (a) 0 39 58 82 110 74 53 51 64 89 (b) 39 0 58 83 119 83 67 61 65 107 (c) 58 58 0 29 77 40 30 62 59 107 (d) 82 83 29 0 52 24 34 67 58 106 (e) 110 119 77 52 0 39 60 73 64 86 (f) 74 83 40 24 39 0 22 49 43 82 (g) 53 67 30 34 60 22 0 43 43 82 (h) 51 61 62 67 73 49 43 0 17 49 (i) 64 65 59 58 64 43 43 17 0 57 (j) 89 107 108 106 86 82 82 49 57 0 (k) 60 73 100 111 115 94 83 45 59 50 (l) 58 63 109 129 147 118 102 73 86 92 (m) 23 51 43 66 96 59 37 54 63 93 (k) (l) (m) (a) 60 58 23 (b) 73 63 51 (c) 100 109 43 (d) 111 129 66 (e) 115 17 96 (f) 94 118 559 (g) 83 102 37 (h) 45 73 54 (i) 59 86 63 (j) 50 92 93 (k) 0 41 76 (l) 41 0 81 (m) 76 81 0 Table 2. Identification of association or differentiation relationships between themes (a) (b) (c) (d) (e) (f) (g) (h) (i) (j) (a) 0 0 1 1 1 1 1 1 1 1 (b) 0 0 1 1 1 1 1 1 1 1 (c) 1 1 0 0 1 0 0 1 1 1 (d) 1 1 0 0 1 0 0 1 1 1 (e) 1 1 1 0 0 1 1 1 1 (f) 1 1 0 0 0 0 0 0 0 1 (g) 1 1 0 0 1 0 0 0 0 1 (h) 1 1 1 1 1 1 1 0 0 0 (i) 1 1 1 1 1 0 0 0 0 1 (j) 1 1 1 1 1 1 1 1 1 0 (k) 1 1 1 7 1 1 1 0 1 1 (l) 1 1 1 1 1 1 1 1 1 1 (m) 0 1 0 1 1 1 0 1 1 1 (k) (l) (m) (a) 1 1 0 (b) 1 1 1 (c) 1 1 0 (d) 1 1 1 (e) 1 1 1 (f) 1 1 1 (g) 1 1 0 (h) 0 1 1 (i) 1 1 1 (j) 0 1 1 (k) 0 0 1 (l) 0 0 1 (m) 1 1 0 Table 3. Semantic relation ships of the inital legend (see Figure 5) (a) (b) (c) (d) (e) (f) [L.sub.1] (a) 0 0 0 1 1 1 [L.sub.2] (b) 0 0 0 1 1 1 [L.sub.3] (c) 0 0 0 1 1 1 [L.sub.4] (d) 1 1 1 0 1 1 [L.sub.5] (e) 1 1 1 1 0 0 [L.sub.6] (f) 1 1 1 1 0 0 Table 4. Semantic relationships of the new legend (see Figure 6) (a) (b) (c) (d) (e) (f) [I.sub.1] (a) 0 0 1 1 1 1 [I.sub.2] (b) 0 0 1 1 1 1 [I.sub.3] (c) 1 1 0 0 0 1 [I.sub.4] (d) 1 1 0 0 0 1 [I.sub.5] (e) 1 1 0 0 0 1 [I.sub.6] (f) 1 1 1 1 1 0 Table 6. Corresponding color legend and surface weights in percentage of the initial map. Color Theme Surface weight white Background Layer 28 green Vegetation 40 sky blue Lake, Sea 0,6 blue River 0,5 pink Sports-ground 0,02 purple Cemetery 0,01 violet Buildings 0,5 orange Marshalling yard 0,001 blown Railway 0,02 red Highway 4 yellow orange Main road 4 yellow Secondary road 4 white Otherroad 4 Figure 5. Initial legend. (a) [L.sub.1] Landslide high hazards (b) [L.sub.1] Landslide medium hazards (c) [L.sub.1] Landslide low hazards (d) [L.sub.1] Background layer (e) [L.sub.1] Sea, Lakes (f) [L.sub.1] Rvers Figure 6. New Legend. (a) [I.sub.1] Landslide high hazards (b) [I.sub.1] Landslide medium hazards (c) [I.sub.1] Landslide low hazards (d) [I.sub.1] Background layer (e) [I.sub.1] Sea, Lakes (f) [I.sub.1] Revers…
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Publication information: Article title: Reaching a Compromise between Contextual Constraints and Cartographic Rules: Application to Sustainable Maps. Contributors: Hoarau, Charlotte - Author. Journal title: Cartography and Geographic Information Science. Volume: 38. Issue: 2 Publication date: April 2011. Page number: 79+. © 2008 American Congress on Surveying & Mapping. COPYRIGHT 2011 Gale Group.
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