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A Guide to Selecting Map Projections for World and Hemisphere Maps

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Selecting the most suitable projection can be challenging, but it is as essential a part of cartographic design as color and symbol selection and should be given the same degree of consideration. A poorly chosen projection can result in misinterpreted information and impact the effectiveness of a map. This chapter provides guidance in selecting projections for world and hemisphere maps .
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Chapter 9
A Guide to Selecting Map Projections
for World and Hemisphere Maps
Bernhard Jenny, Bojan Šavrič, Nicholas D. Arnold,
Brooke E. Marston and Charles A. Preppernau
Abstract Selecting the most suitable projection can be challenging, but it is as
essential a part of cartographic design as color and symbol selection and should be
given the same degree of consideration. A poorly chosen projection can result in
misinterpreted information and impact the effectiveness of a map. This chapter
provides guidance in selecting projections for world and hemisphere maps.
9.1 Introduction
Hundreds of different projections for world maps have been developed over the
centuries as cartographers sought a projection that best minimized distortion for
various applications. Each projection distorts space in a different way whether it is
the size of areas, directions, the distances between places, or a combination of these
properties. With so many projections to choose from, it can be challenging to select
one projection that is most appropriate for what is being mapped and the purpose of
the map.
B. Jenny
School of Science, Geospatial Science, RMIT University, Melbourne, Australia
B. Jenny (&)B. ŠavričN.D. Arnold B.E. Marston C.A. Preppernau
College of Earth, Ocean and Atmospheric Sciences, Oregon State University,
Corvallis, OR, USA
e-mail: bernhard.jenny@rmit.edu.au
B. Šavrič
Esri Inc., Redlands, CA, USA
N.D. Arnold
Arnold Geographics, Portland, OR, USA
B.E. Marston
U.S. Department of State, Washington, DC, USA
C.A. Preppernau
National Geographic, Washington, DC, USA
©Springer International Publishing AG 2017
M. Lapaine and E.L. Usery (eds.), Choosing a Map Projection,
Lecture Notes in Geoinformation and Cartography,
DOI 10.1007/978-3-319-51835-0_9
213
Guidelines exist to help the mapmaker select an appropriate projection. The most
commonly recommended and applied guide was published by John P. Snyder
(19261997), an American cartographer (Snyder 1987). Snyder created a hierar-
chical tree organized by the extent of the region that was to be mapped and the
desired property of the map (e.g., equal-area, conformal, or equidistant). The rst
selection in Snyders decision tree is among three different geographic extents:
(1) world maps; (2) maps showing a hemisphere; and (3) maps showing a continent
or smaller areas. This chapter focuses on projections for world and hemisphere
maps. Snyders selection guideline is not deterministic. Discretion must still be
exercised when selecting one of the suggested projections.
9.2 Criteria for the Selection of a Map Projection
Distortion is an inevitable consequence of transforming a sphere or an ellipsoid
onto a plane. It is impossible to cut and unfold the surface of the Earth onto a planar
surface, like a map, without distortion (Fig. 9.1). Distortion is easy to spot on
small-scale world maps where landmasses are considerably altered in geometric
appearance.
Because map projections cannot preserve all properties of the original sphere,
cartographers must consider which properties are the most important to retain. This
consideration is based on the purpose of the map and the cartographic technique
used to visualize information. Additional criteria are to be taken into account such
Fig. 9.1 The earth is impossible to unfold onto a planar surface without distortion
214 B. Jenny et al.
as aesthetic appearance of the map, aspect ratio, whether available software applies
the projection, and userspreferences.
9.2.1 Deciding What Property to Preserve
Because the primary objective for most maps is to minimize geometric distortion, it
is important to determine which geometric properties to preserve. This decision is
based on the purpose of the map, that is, what mapping technique is applied and for
what applications the reader will use the map.
Equal-area projections maintain the size of map elements relative to one
another. This is an essential property to preserve when comparing the size of objects
on a map. For example, a choropleth map should be equal-area because the size of
enumeration units is being compared.
Conformal projections preserve local angles about any point on a
map. Generally, this property is only required for large-scale maps when angles are
to be measured from maps, for example when reading an angle from a map using a
protractor for navigation or surveying. All conformal maps showing the entire
world or large portions of it grossly enlarge or reduce some areas.
Equidistant projections preserve distances between points along some directions.
This property is important for comparing distances between locations. For example,
a map showing concentric circles that denote the distance from a point requires the
distance relative to the center of the circles to be true. However, only some dis-
tances can be preserved; it is impossible to correctly display distances between all
points on a at map.
Compromise projections do not preserve area, local angles, or distance. As the
name suggests, a compromise projection is an attempt at balancing the distortion.
Compromise projections are generally only useful for maps showing the entire
world or large portions of it.
9.2.2 Aesthetics and Aspect Ratio
It is possible for the projection selection process to yield several potential projec-
tions for maps showing the entire world or a hemisphere. A cartographer should
consider making a selection based upon aesthetic preference. This is a subjective
decision made by the cartographer or the client. In this case, personal taste is a
major selection criterion (Šavričet al. 2015a).
There are often constraints on the size and format of the available space for a
map. Choosing a projection that ts the aspect ratio efciently can greatly improve
the page layout.
9 A Guide to Selecting Map Projections 215
9.2.3 Mapping Software
Another factor in the selection of a map projection is its availability in mapping
software. Many projections are supported across various packages, but some useful
projections are difcult to nd. A few of the projections recommended and dis-
cussed in this chapter are currently unavailable in some of the more commonly used
GIS software.
9.2.4 User Preferences
When selecting a world map projection, cartographers can base their selection on
map-reader preferences for world maps. So far, three user studies (Gilmartin 1983;
Werner 1993;Šavričet al. 2015a) have assessed user preferences. Gilmartin (1983)
found a preference for elliptical maps over rectangular maps. Gilmartin also found
that projections with a distinctively longer width than height are preferred. A user
study by Werner (1993) showed that the most preferred projections are uninter-
rupted pseudocylindrical, followed by interrupted projections, and the least favored
were rectangular maps. Šavričet al. (2015a) conrmed that map-readers prefer
uninterrupted projections. They also found that map-readers dislike world map
projections with curved parallels, as well as pseudocylindrical projections with
bulging meridian curves.
9.3 Projections for World Maps
The main distinguishing characteristics of maps showing the entire world are the
distortion properties (equal-area, compromise, or equidistant), the curvature of
parallels and meridians, and the representation of poles as either points or lines. In
this section, recommendable equal-area and compromise projections are discussed
rst. Then, projections with other properties are discussed, as well as oblique
aspects and interruptions. This section concludes with a summarizing selection-tree
table for world map projections.
Conformal projections are not discussed here as they are not useful for world
maps. The major disadvantage of conformal projections when applied to world
maps is their gross distortion of areas.
1
1
Despite their gross area distortion, Snyder also includes conformal projections in his guideline.
He suggests the Mercator projection in the normal, transverse, or oblique aspect, for when scale
has to be preserved along the equator, a meridian, or an oblique great circle, respectively. Snyder
also recommends the conformal Lagrange, August, and Eisenlohr projections.
216 B. Jenny et al.
Most projections for world maps recommended here are pseudocylindrical
projections. When centered on the equator, these projections have straight parallels
and curved meridians.
9.3.1 Equal-Area World Map Projections
Equal-area world maps projections are required for area comparisons, such as with
choropleth and dasymetric maps, or when the number of features per area unit is
estimated, as is the case with dot maps.
The cartographer can select between world map projections representing poles as
either points or lines. The criteria for this selection are the cartographers aesthetic
preferences and the degree of acceptable deformation. When representing poles as
points, landmasses located close to both a pole and an edge of the map are greatly
deformed. When representing poles as lines, features located at these extreme
locations are also deformed, but to a lesser degree. Features are vertically com-
pressed when using an equal-area projection with a pole line (Fig. 9.2).
Commonly used projections representing the poles as points are the Mollweide,
Hammer, Boggs Eumorphic, and sinusoidal projections (Fig. 9.3). The Mollweide
projection is very popular for atlases (Canters and Decleir 1989) and is more
aesthetically pleasing to many cartographers than other projections due to its
elliptical shape (Snyder 1993, p. 112). The sinusoidal projection has signicant
angular distortion near the edges, especially in higher latitudes (Canters and Decleir
1989, p. 81). The Boggs Eumorphic projection is a blend between the sinusoidal
and Mollweide projections that better represents areas near the poles than the
sinusoidal projection (Snyder 1993, p. 200). The Hammer projection represents the
entire world in an ellipse with curved parallels and unequally distributed meridians.
Recommendable equal-area projections showing the poles as lines are the
Eckert IV, Eckert VI, Wagner IV, Wagner VII, and McBryde-Thomas Flat-Polar
Fig. 9.2 With a projection showing poles as points, the shape of Greenland tends to be more
deformed (left) than with a projection showing poles as lines (right). Mollweide (left) and
Eckert IV (right) projections centered on 90°E
9 A Guide to Selecting Map Projections 217
Quartic projections (Fig. 9.4).
2
Eckert IV is an equal-area projection with very low
mean angular distortion (Canters and Decleir 1989). Its rounded corners, where
meridians meet the pole line, suggest that the projection represents a spherical
Earth. However, Max Eckert preferred his sixth projection with sinusoidal merid-
ians, the Eckert VI projection (Canters and Decleir 1989). The Wagner IV pro-
jection is similar in appearance and distortion characteristics to the Eckert IV
projection, but the Wagner IV projection does not have the rounded corners of the
Eckert IV projection. The Wagner VII projection has curved parallels and pole
lines. Unfortunately, only a few software packages include this projection. Snyder
includes all projections by McBryde and Thomas in his selection tree, but out of
their nine projections, only the McBryde-Thomas at-polar quartic projection
(Fig. 9.4) is commonly used by cartographers (Snyder 1993).
9.3.2 Compromise World Map Projections
Compromise projections with low areal distortion are commonly used for a variety
of thematic world maps. These projections include the Robinson, Winkel Tripel,
Mollweide Hammer
Boggs Eumorphic Sinusoidal
Fig. 9.3 Equal-area world map projections with poles represented as points
2
Snyder states that any pseudocylindrical equal-area projection is suitable. He does not include the
Wagner VII projection, which is not a pseudocylindrical projection.
218 B. Jenny et al.
Natural Earth, and Wagner V projections (Fig. 9.5).
3
The Robinson projection is
perhaps the most used compromise projection for world maps. National Geographic
used the Robinson projection for their world maps for about a decade until the
Winkel Tripel projection replaced it in 1998 (Slocum et al. 2009). The Winkel
Tripel projection has curved parallels and a comparatively large height-to-width
ratio. It also has low area and scale distortion compared to other compromise
projections. The Natural Earth projection has characteristic rounded corners where
parallels meet the pole lines (Jenny et al. 2008;Šavričet al. 2011). The Natural
Earth II projection (not depicted here) is an alternative pseudocylindrical projection
with meridians steeply bending toward short pole lines resulting in a map with
highly rounded corners (Šavričet al. 2015b). The Wagner V projection is similar to
McBryde-Thomas Flat-Polar Quartic
Eckert IV Eckert VI
Wagner IV Wagner VII
Fig. 9.4 Equal-area world map projections with poles represented as lines
3
Snyders selection guideline contains only two compromise projections: the Robinson and the
Miller cylindrical projections. Snyders list of compromise projections is extended here with
projections with similar distortion characteristic as the two mentioned by Snyder.
9 A Guide to Selecting Map Projections 219
the Robinson projection, but has a smaller height-to-width ratio and has slightly
more curved meridian lines.
Many cartographers do not recommend projections that transform the entire
Earth into a rectangle because they greatly distort space (Canters 2002, p. 263) and
because of the idea that rectangular world maps mislead the map readers inter-
pretation of the worlds shape. This selection guideline, therefore, does not rec-
ommend using rectangular projections for most world maps. However, there are
some rare phenomena based on longitude that are best represented by a map with
straight meridians, such as a map showing world time zones. Also, rectangular
projections may be preferred for aesthetic reasons. The Miller cylindrical projection
is a compromise projection that is recommended for these applications (Fig. 9.6).
When using the Miller cylindrical projection, one has to be aware of the fact that
this projection greatly exaggerates the size of Polar areas. The Plate Carrée (also
known as the equidistant cylindrical or geographic) is an alternative cylindrical
projection that takes up less space vertically than the Miller projection and has less
areal distortion in polar areas. The Plate Carrée is a common projection for
exchanging geospatial data, because its equations are trivial. The Patterson cylin-
drical projection is nearly identical in tropical and mid-latitude regions to the Miller
cylindrical projection, but polar regions are less exaggerated (Fig. 9.6, Patterson
et al. 2014).
Robinson Winkel Tripel
Natural Earth Wagner V
Fig. 9.5 Compromise world map projections
220 B. Jenny et al.
9.3.3 Equidistant World Map Projections
On some occasions, such as mapping airport connections where the cartographer
would like to preserve distances from the airport, an equidistant projection is
essential (Fig. 9.7). The azimuthal equidistant projection is the only projection that
preserves all distances relative to its center. Only distances along straight lines
passing through the center are portrayed correctly. When the cartographer selects
one of the poles as the center, parallels are equally spaced concentric circles
(Fig. 9.7).
The only projection that preserves distances relative to two points on a at map
is the two-point equidistant projection (Fig. 9.7 bottom). The cartographer can
dene the two points. Distances measured along lines passing through either point
are mapped without distortion. The two-point equidistant projection is appropriate,
for example, for determining the distance from a ship at a known location to the
start and end of its voyage (Snyder and Voxland 1989).
The Plate Carrée (Fig. 9.6 bottom) and the more general equirectangular pro-
jection preserve distances along all meridians and are useful when differences in
latitude are measured. The sinusoidal projection preserves distances along all par-
allels (Fig. 9.3).
Plate Carrée
Patterson
Miller Cylindrical
Fig. 9.6 Cylindrical world map projections show polar areas with considerable distortion
9 A Guide to Selecting Map Projections 221
Polar azimuthal equidistant Oblique azimuthal equidistant
(Washington)
Two-point equidistant
(Mexico City & London)
Fig. 9.7 Equidistant map projections
9.3.4 Interrupted World Map Projections
Small-scale world maps usually represent the world on a continuous space without
interruptions. An interrupted projection is an alternative (Fig. 9.8), however inter-
rupted projections are not frequently used, and they seem to be disliked by many
map readers (Šavričet al. 2015a). Interruption can be applied to most of the
equal-area and compromise world map projections suggested in the sections above.
Depending on the purpose of the map (i.e., whether showing land or ocean), the
locations of intersections and central meridians are adjusted.
The McBryde S3 projection is sometimes recommended as an interrupted
equal-area projection with a pole line (Fig. 9.8). The Goode homolosine is an
equal-area projection that is often used in interrupted form. A disadvantage of the
Goode homolosine is the discontinuities at approximately ±41°N and S latitudes,
222 B. Jenny et al.
which can be visually disruptive. The interrupted form of the Mollweide projection
is similar in appearance, but does not show the same discontinuities.
9.3.5 World Maps with Shifted Central Meridian
and Oblique Aspect
Many world maps are centered on the Greenwich meridian, but there are often good
reasons to center the map on a different meridian, mainly to better show spatial
relations of the centered area to neighboring areas (Fig. 9.9 left). Shifted meridians
can be applied to any projection.
World maps with an oblique aspect are centered on any point on Earths surface
(Fig. 9.9 right). While a shifted meridian only relocates the mapped features in an
Goode’s Homolosine
Mollweide
Boggs Eumorphic
McBryde S3
Fig. 9.8 Examples of interrupted projections for mapping continents (top) and oceans (bottom)
Robinson centered on 90° W Oblique Mollweide
Fig. 9.9 Examples of world maps with shifted central meridian and oblique aspect
9 A Guide to Selecting Map Projections 223
east-west direction, an oblique aspect better represents spatial relations of features
near one of the poles because the pole is moved toward the center of the
map. Oblique aspects can be applied to any world map projection.
9.3.6 Selection Tree for World Maps
Table 9.1 presents a selection tree for world map projections summarizing the
discussion above. The cartographer will reach a list of recommended projections
after considering a projections property (rst column) and its pole representation
(second column).
Table 9.1 Selection tree for projections for mapping the entire sphere (adapted from Snyder
1987)
Property/characteristic Poles as Named projection
Equal-area Points
Mollweide
Hammer (or Hammer-Aitoff)
*Boggs Eumorphic
Sinusoidal
Lines
Eckert IV
Wagner IV (or Putnins P2)
Wagner VII (or Hammer-Wagner)
McBryde-Thomas at-polar quartic
Eckert VI
Compromise distortion Lines
Natural Earth
Natural Earth II
Winkel Tripel
Robinson
Wagner V
Plate Carrée (or geographic)
Miller (or Miller Cylindrical I)
Interrupted (equal-area) Points *Mollweide
*Boggs Eumorphic
Goode homolosine
Lines *McBryde S3
*Any of the equal-area projections with a pole
line listed above
Equidistant Centered on a pole Points Polar azimuthal equidistant
Centered on
arbitrary point
Oblique azimuthal equidistant
Relative to two
points
Two-point equidistant
Along meridians Lines Plate Carrée (or geographic)
An asterisk (*) marks projections that are often not available in GIS and mapping software.
Synonyms are given in parentheses.Anobelisk () marks a group of projections ordered by mean
scale distortion, from least to greatest weighted mean error in the overall scale distortion index
(after Canters 2002)
224 B. Jenny et al.
9.4 Projections for Hemisphere Maps
Three recommendable projections exist for creating maps depicting a hemisphere
with a circular boundary. The three projections, which all belong to the azimuthal
class of projections, are the Lambert azimuthal equal-area projection, the azimuthal
equidistant projection, and the orthographic projection (Fig. 9.10).
4
Adjusting the central longitude and latitude of the three recommendable pro-
jections can shift the area of interest to the center of the map. Polar aspect, that is,
maps showing one of the poles in the center of the map, can be created with the
three projections (for an example, see Fig. 9.7 top left).
Of the three recommendable projections, the Lambert azimuthal projection is the
only projection that preserves areas. It is, therefore, a useful projection for hemi-
sphere maps where the size of countries or other features are compared. The
Lambert azimuthal projection is not limited to a single hemisphere, but can show
the entire globe in a circle. However, the projection is rarely used to show the entire
sphere because of the considerable distortion of angles and distances close to the
edge of the circle.
The orthographic projection shows the globe as seen from space at an innite
distance. The orthographic projection is particularly useful for locator maps in
combination with large- and medium-scale maps to show the location and extent of
a mapped area because it creates pictorial views of the Earth, accentuating its round
shape.
The azimuthal equidistant projection preserves distances relative to the central
point of the map. Consequently, it is a useful projection for reading distances to a
point of interest placed in the center of a map. For example, a map showing the
Lambert Equal-area Equidistant Orthographic
Fig. 9.10 Azimuthal projections for hemisphere maps (centered on 45°N and 45°E)
4
Snyder also includes the conformal azimuthal stereographic projection for hemisphere maps in his
selection schema. The azimuthal stereographic projection is not generally useful for mapping a
hemisphere as it grossly distorts shape and area along the border of the projected hemisphere.
Preserving angles is rarely needed for hemisphere maps and certainly not for locator inset maps, a
typical use case for these projections. The azimuthal stereographic projection is therefore not
recommended for maps showing an entire hemisphere in a circle.
9 A Guide to Selecting Map Projections 225
relative distance of a country to immediate and distant neighboring countries, or the
location of a tsunami wave over time, should use the azimuthal equidistant pro-
jection. Because distances are only correct along straight lines when they pass
through the projection center, it is crucial to dene the central point accordingly.
The visual difference between the Lambert azimuthal equal-area projection and
the equidistant projection are small when used for a hemisphere (Fig. 9.10). For
locator inset maps, the selection of a projection is a matter of personal taste. The
authors recommend using the orthographic projection when the spherical shape of
the globe is to be accentuated in inset maps.
9.5 Selecting a Projection with Projection Wizard
Projection Wizard is an online map projection selection tool available at projec-
tionwizard.org that assists cartographers in selecting projections (Fig. 9.11)(Šavrič
et al. 2016). Projection Wizard integrates Snyders selection guideline with the
extensions suggested in this book chapter. It includes the projections for world
Fig. 9.11 Selecting a projection with Projection Wizard at projectionwizard.org
226 B. Jenny et al.
maps listed in Table 9.1 and the projections for hemisphere maps discussed above.
The user selects the desired distortion property, and a projection is then suggested
and a preview map generated. Projection Wizard is simple to use and can also
suggest projections for maps at larger scales, showing continents or smaller areas.
For these maps, the user denes the area to be mapped on an interactive web map.
9.6 Conclusion
Although the selection of map projections is one of the most important aspects of
mapping, it is often given little consideration. The map projection is the basis for
the rest of the map and is therefore, an important component of cartographic design.
Map projections must be selected carefully according to criteria such as the maps
extent, purpose, and cartographic visualization technique. An appropriate projection
can minimize distortion when measuring distances, angles, or areas. Most impor-
tantly, a poorly chosen projection can result in misinterpreted information and
impact the effectiveness of a map.
This chapter only includes a selection of projections for world and hemisphere
maps. Many alternative projections exist with similar distortion properties and
visual appearance that may also be appropriate for small-scale maps.
Snyders selection guideline relies on the answers to two main questions: what is
the geographic extent mapped, and, which distortion properties need to be pre-
served? The selection guideline then leads the cartographer to a set of appropriate
projections for world and hemisphere maps.
Snyder published his selection guideline in 1987 at a time when cartographers
were using computer algorithms for creating maps with a variety of projections, but
before Web mapping services, such as Google Maps, existed. Google introduced
their Web mapping service in 2005 and the underlying Mercator projection quickly
became the de facto standard for Web maps (Battersby et al. 2014). While the
Mercator projection is included in Snyders selection tree for some maps, it is a
poor choice for world maps because it shows polar areas with enormous areal
distortion. Web mapping services will hopefully include more alternative projec-
tions for world maps in the future. A viable option could be adaptive composite
map projections (Jenny 2012) that automatically adjust the maps geometry in
accordance with Snyders selection guideline.
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... Cartographers and mathematicians have devised hundreds of projection techniques [Sny97], including rectangular projections such as Mercator projection, commonly used in Google Maps, Quincuncial, Miller, Patterson projections, and non-rectangular projections, such as Hammer, Mollweide, and unusual projections such as Lee's conformal projection (i.e., map projections that preserve every angle between two curves that cross each other on the surface of a globe [Jen+17]) in a tetrahedron, with different mappings between data points across the map's boundaries. The reason for this diversity is that the surface of a sphere is "non-flat" and thus when geographic data is presented on a 2D flat screen, none of existing cartographic projection techniques can be considered optimal in depicting the original geographic information on the surface of a sphere [Sch+21]. ...
... Chapter 2 Background and Related Work Jen+17]. They have also invented compromise projections that do not preserve any of these criteria exactly but instead trade them off, creating a map that does not distort area, shape, distance or direction "too much." ...
... Maps such as these in which the projection region is split are said to be interrupted. The ORTHOGRAPHIC HEMISPHERE , in particular, has a naturalistic appearance as it shows the Earth viewed from infinity [Jen+17]. and found that people may find it difficult to understand path continuity across the edges of the map. Hruby et al. [HAA16] found that viewers find it difficult to understand the distance or direction between two points if this requires reasoning about the discontinuity in the projection and mentally wrapping the projection around a globe to understand their relative position. ...
Thesis
Full-text available
Visualisation has become increasingly important in helping people understand and gain insights from data; and, ultimately, to make better decisions. Traditional visualisations are designed to be shown on a flat surface (screen or page) but most data is not “flat”. For example, the surface of the earth exists on a sphere, however, when that surface is presented on a flat map, key information is hidden, such as geographic paths on the spherical surface being wrapped across the boundaries of the flat map. Similarly, cyclical time-series data has no beginning or end. When such cyclical data is presented on a traditional linear chart, the viewer needs to perceive continuity of the visualisation across the chart’s boundaries. Mentally reconnecting the chart across such a boundary may induce additional cognitive load. More complex data such as a network diagram with hundreds or thousands of links between data points leads to a densely connected structure that is even less “flat” and needs to wrap around in multiple dimensions. To improve the usability of these visualisations, this thesis explores a novel class of interactive wrapped data visualisations, i.e., visualisations that wrap around continuously when interactively panned on a two-dimensional (2D) projection of surfaces of 3D shapes, specifically, cylinder, torus, or sphere. We start with a systematic exploration of the design space of interactive wrapped visualisations, characterising the visualisations that help people understand the relationship within the data and benefit from being understood as ‘cylindrical’, ‘toroidal’, or ‘spherical’. Subsequently, we investigate the design, development and implementation of a series of wrappable visualisations for cyclical time series, network, and geographic data. We show that these interactive visualisations better preserve the spatial relations in the case of geospatial data, and better reveal the data’s underlying structure in the case of abstract data such as networks and cyclical time series. Furthermore, to assist future research and development, we contribute layout algorithms and toolkits to help create pannable wrapped visualisations.
... Cartographers and mathematicians have devised hundreds of projection techniques [Sny97], including rectangular projections such as Mercator projection, commonly used in Google Maps, Quincuncial, Miller, Patterson projections, and non-rectangular projections, such as Hammer, Mollweide, and unusual projections such as Lee's conformal projection (i.e., map projections that preserve every angle between two curves that cross each other on the surface of a globe [Jen+17]) in a tetrahedron, with different mappings between data points across the map's boundaries. The reason for this diversity is that the surface of a sphere is "non-flat" and thus when geographic data is presented on a 2D flat screen, none of existing cartographic projection techniques can be considered optimal in depicting the original geographic information on the surface of a sphere [Sch+21]. ...
... Chapter 2 Background and Related Work Jen+17]. They have also invented compromise projections that do not preserve any of these criteria exactly but instead trade them off, creating a map that does not distort area, shape, distance or direction "too much." ...
... Maps such as these in which the projection region is split are said to be interrupted. The ORTHOGRAPHIC HEMISPHERE , in particular, has a naturalistic appearance as it shows the Earth viewed from infinity [Jen+17]. and found that people may find it difficult to understand path continuity across the edges of the map. Hruby et al. [HAA16] found that viewers find it difficult to understand the distance or direction between two points if this requires reasoning about the discontinuity in the projection and mentally wrapping the projection around a globe to understand their relative position. ...
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Traditional visualisations are designed to be shown on a flat surface (screen or page) but most data is not "flat". For example, the surface of the earth exists on a sphere, however, when that surface is presented on a flat map, key information is hidden, such as geographic paths on the spherical surface being wrapped across the boundaries of the flat map. Similarly, cyclical time-series data has no beginning or end. When such cyclical data is presented on a traditional linear chart, the viewer needs to perceive continuity of the visualisation across the chart's boundaries. Mentally reconnecting the chart across such a boundary may induce additional cognitive load. More complex data such as a network diagram with hundreds or thousands of links between data points leads to a densely connected structure that is even less "flat" and needs to wrap around in multiple dimensions. To improve the usability of these visualisations, this thesis explores a novel class of interactive wrapped data visualisations, i.e., visualisations that wrap around continuously when interactively panned on a two-dimensional projection of surfaces of 3D shapes, specifically, cylinder, torus, or sphere. We start with a systematic exploration of the design space of interactive wrapped visualisations, characterising the visualisations that help people understand the relationship within the data. Subsequently, we investigate a series of wrappable visualisations for cyclical time series, network, and geographic data. We show that these interactive visualisations better preserve the spatial relations in the case of geospatial data, and better reveal the data's underlying structure in the case of abstract data such as networks and cyclical time series. Furthermore, to assist future research and development, we contribute layout algorithms and toolkits to help create pannable wrapped visualisations.
... The NEP and the SCR from Shanghai to Rotterdam cover almost the entire coastal region between Asia and Europe. Due to its suitability for large-area projections, the equidistant cylindrical projection (Jenny et al. 2017) is used to calculate the distances between the two routes in this study. As shown in Figure 1, the distance of the SCR (L total ) with pure blue water is 11,057.23 nm (black line). ...
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The Northeast Passage (NEP) holds immense potential as a link for maritime transport activities between Europe and Asia, primarily due to the extended sailing season resulting from global warming. However, the economic viability of the Arctic shipping route remains disputed. This study aims to comprehensively evaluate the feasibility of container transportation along the NEP compared to that along the Suez Canal Route (SCR) by using current (2021–2023) and future (2025–2065) scenarios. The results reveal that larger vessels have lower CO2 emissions and costs than small vessels in the NEP, but the costs for larger vessels in the NEP are still higher than those in the SCR throughout both summer and winter seasons under the current scenario. The outcomes also show that a progressive carbon tax scheme will increase the unit shipping costs for all routes in the future scenario, with the NEP being most economically viable during summer. Furthermore, the extended navigable period (NP) bolsters the NEP’s economic cost advantage during a seasonal period. Nevertheless, from a year-round operations standpoint, the NEP remains less competitive than the SCR before 2065. The conclusions drawn from this research serve as a significant resource for decision-makers when formulating operational plans.
... For mapping regions that are predominantly east-west or northsouth in orientation, conic projections are being applied inlcuding Albers, Lambert and Polyconic ones [21]. In cases where polar regions are being mapped or for global maps centred on a specific location, azimuthal projections such as Lambert Azimuthal Equal-Area, Stereographic and Orthographic are utilized [22]. All projections, however, distort the size, shape, distance or direction of features on the Earth's surface, so it is essential to choose the one that minimizes distortion for the specific purpose of the map [19]. ...
Conference Paper
Prior high definition maps are currently required in the perception stack of autonomous vehicles since they encode road-level features in centimetre accuracy. This rapid map establishment has led to a vast range of different map vendors, formats, structures and standards. In this study, the landscape of high-definition maps is being analyzed, evaluated and compared. Unlike other similar works, the maps in this study are categorized by their formats and structures since map vendors have started to provide single structure maps in multiple formats. Although this wide availability helps to expand the map usage, many aspects have to be considered and evaluated for choosing the most appropriate one. Apart from the detailed review, key issues and a discussion concerning the use of prior maps is provided to facilitate better map usage and adoption in the intelligent vehicles era. Keywords—High definition maps, Localization, Autonomous vehicles, Map conversion, Standardization
... These resulted in a total of 40,380 PAs. The layer was projected to WGS_1984_Eckert_IV, which is an equal-area projection which are used when comparing areas or estimating the number of features per area unit and that has very low mean angular distortion [27,28]. Based on this layer, we produced several rasters of 700 × 700 m resolution used for all subsequent analyses. ...
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Human activities can degrade landscape connectivity and disrupt ecological flows, jeopardising the functional integrity of processes. This study presents a quantitative assessment of Asia’s protected areas’ (PAs) structural connectivity using landscape metrics, as well as analyses of the Cost-Effective Zones’ (CEZs). Using nine landscape metrics, we assessed connectivity at zonal (country borders and interior), national, regional, and geographical (islands and continent) levels. The results showed that the structural connectivity of Asia’s PAs network measured by a Connectance index was very low (0.08% without country borders and 9.06% for the average country analysis). In general, connectivity was higher within borders (0.36%) than within the countries (0.22%). Islands exhibited significantly higher Area-weighted mean patch area, Proximity index and Largest patch index, suggesting more integrity and connectiveness. When comparing Asian regions, Western Asia presented the lowest values for Percentage of landscape and Proximity index. We found that only 15% of the CEZs in Asia were under PAs designation, and more CEZs are located in the interior, but the majority with the highest priority was in the borders (9%). We advocate that expanding PAs coverage, specifically targeting areas that increase connectivity (e.g., through transboundary PAs), should be a priority to maintain their ecological function.
... Sustainable development goals (SDGs) as a blueprint to build a better world for humanity must balance social, economic, and environmental dimensions (GA, 2015). Government policies, human capital accumulation, and technology diffusion are substantial for delivering these targets (Benhabib & Spiegel, 2005;Jenny et al., 2017). Spatial data infrastructure plays a pivotal role in e-government, and thus the investment in it will boost SDG achievement (Barbero et al., 2019). ...
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Over the last nine years, the ongoing armed conflict in Syria has had a devastating impact on properties and infrastructure, making it necessary to rebuild everything from scratch. As spatial data are a pillar to enhance sustainable socio-economic development, it should be georeferenced and reformed to keep up with the tremendous growth in information and communication technology. On the other hand, the low-distortion conformal mapping contributes significantly to changing the position of any feature on the earth's surface onto a plane to create accurate large-scale spatial data. The current research conducts an analytical study using spatial statistics tools to investigate an optimal conformal projection for representing the Syrian area in a single zone that preserves angles locally, reduces linear distortions, and fulfills modern geospatial technologies' requirements. The findings have shown the applicability of the proposed model as an alternative solution to minimize the scale error over the interest area. In addition, the isograms pattern is close to the shape of the area, and better fits the quality criteria of the chosen projection.
Chapter
Es gibt schätzungsweise 400 unterschiedliche Kartenabbildungen – was ist der Grund für diese hohe Anzahl? Auf den ersten Blick sind Globen ein gutes Modell für die Abbildung der Erde, da sie aufgrund ihrer gekrümmten Oberfläche Distanzen, Flächen und Winkel (kaum) verfälschen. Aus praktischen Gesichtspunkten sind aber ebene Karten geeigneter: Sie sind leichter transportabel, kostengünstiger, erlauben großmaßstäbige Darstellungen für kleine Ausschnitte der Erde und ermöglichen einfache Messungen. Mit der Nutzung von ebenen Karten ergibt sich die Aufgabe, Punkte von der gekrümmten Oberfläche einer Bezugsfläche in die Ebene zu übertragen. Die Verfahren hierzu werden als Kartenabbildungen bezeichnet und in diesem Kap. 11 im Detail behandelt. In der Literatur findet man eine eher unübersichtliche Darstellung verwandter und anderer Begriffe zum Thema Kartenabbildungen – in Abschn. 11.1 wird darauf näher eingegangen. Es gibt eine sehr große Anzahl möglicher Kartenabbildungen – es wird geschätzt, dass es mehr als 400 Varianten gibt. Diese unterscheiden sich in erster Linie in ihren Verzerrungseigenschaften. Eine Abbildung kann maximal eine der drei Eigenschaften Längen-, Flächen- oder Winkeltreue aufweisen. Kartenabbildungen werden danach ausgewählt, welche dieser Eigenschaften für eine gegebene Anwendung notwendig sind. Weitere Details zu den Verzerrungen, inklusive ihrer Größenordnungen, behandelt Abschn. 11.2. In Abschn. 11.3 wird das generelle Vorgehen der Kartenabbildungen dargestellt: Es wird eine Hilfsfläche (Ebene, Zylinder oder Kegel) ausgewählt und an die Bezugsfläche (Kugel oder Ellipsoid) angelegt. Mittels einer Abbildungsvorschrift werden dann Punkte, Linien oder Flächen auf die Hilfsfläche übertragen. In den Abschn. 11.4, 11.5 und 11.6 werden die Prinzipien und ausgewählte Vertreter der drei genannten Hilfsflächen-Typen näher betrachtet. Eine weitere Gruppe mit speziellen Verzerrungseigenschaften, die sog. vermittelnden Abbildungen, wird in Abschn. 11.7 behandelt. Schließlich ist es aus praktischer Sicht notwendig, aus der sehr großen Anzahl möglicher Varianten eine für die konkrete Anwendung geeignete Kartenabbildung auszuwählen. Entsprechende Kriterien und deren Anwendung werden in Abschn. 11.8 behandelt.
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Biodiversity usually needs time to respond to changes in external forces such as climate and landscape, making the assessment of biodiversity crises more complex and challenging. The phenomena of delay in species tracking suitable climate under changing environments can be described as climate debt. Amphibians are the most dispersal-limited vertebrate group with extreme sensitivity to climatic changes; thus, they are more vulnerable to accumulating climatic debts. Furthermore, different amphibians usually have different habitat requirements and preferences; thus, their exposure to climatic changes can vary. Here, we conducted one of the most comprehensive assessments on the features of current and future climatic debts for amphibians, for different orders and families, and over different geographic regions of the world. Our study showed that global amphibians tended to accumulate higher climatic debts in different regions when the climate was further warmed up from the present to the future periods. At the taxonomic level, it was found that families like Pelodryadidae, Mantellidae, Limnodynastidae, Dicroglossidae, Bufonidae, and Ptychadenidae were major contributors to climatic debts. For IUCN red list categories, the least-concern species nevertheless contributed the largest proportion of climatic debts. As a comparison, at the spatial scale, biomes such as temperate broadleaf and mixed forests, boreal forests/Taiga, temperate conifer forests and tundra experienced dramatic increases in debt from the present to the future. Tropical and subtropical forests constantly contribute major climatic debts. For zoogeographic regions, debt increased in Palearctic and Sino-Japanese regions over time. Landscape heterogeneity was the principal predictor of spatial climatic debt patterns for amphibians but not life-history traits and phylogenetic relationships of the taxa. Conclusively, this study can provide insights into the global priority area and species needed for conserving amphibians under different climate change scenarios.
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Using the symbolic calculation program Mathematica and based on the power series expansions of the common latitude with geodetic latitude as a variable, power series expansions of the common latitude with geocentric latitude as the variable are derived. The coefficients of the two groups of formulas are based on the ellipsoid eccentricity e and the ellipsoid third flattening n, which make the expansions more uniform. Taking the CGCS2000 as an example, numerical analysis is applied to verify the accuracy and reliability of the derived power series expansions. By analyzing and calculating the truncation error of the common latitude based on ellipsoidal eccentricity e and the third flattening n expansion to different orders, we obtain simplified, practical formulas for the common latitude that satisfy the requirement of geodesic accuracy. Moreover, we show that the practical formula derived has higher calculation efficiency and easier dissemination, enriches the theory of map projection, and provides a basis for better display of remote sensing images.
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The selection of map projections is difficult and confusing for many. This article introduces Projection Wizard, an online map projection selection tool available at projectionwizard.org that helps mapmakers select projections. The user selects the desired distortion property, and the area to be mapped on an interactive web map. Projection Wizard then proposes a projection, along with projection parameters (such as standard parallels). The tool also creates a preview map with the proposed projection, and provides the corresponding projection code in PROJ.4 format, if applicable. The automated selection process is based on John P. Snyder’s selection guideline with a few adjustments. This article discusses the automated selection process, and the map projections suggested. Projection Wizard solves the problem of map projection selection for many applications and helps cartographers and GIS users choose appropriate map projections.
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The Natural Earth II projection is a new compromise pseudocylindrical projection for world maps. The Natural Earth II projection has a unique shape compared to most other pseudocylindrical projections. At high latitudes, meridians bend steeply toward short pole lines resulting in a map with highly rounded corners that resembles an elongated globe. Its distortion properties are similar to most other established world map projections. Equations consist of simple polynomials. A user study evaluated whether map-readers prefer Natural Earth II to similar compromise projections. The 355 participating general map-readers rated the Natural Earth II projection lower than the Robinson and Natural Earth projections, but higher than the Wagner VI, Kavrayskiy VII and Wagner II projections.
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The Patterson cylindrical, a new projection designed for general-purpose mapmaking, is an alternative to other cylindrical projections. It is positioned between the Plate Carrée projection, which has a 1:2 aspect ratio, and the Miller 1 projection, which excessively exaggerates the size of polar areas. The Patterson cylindrical balances polar exaggeration against maintaining the familiar shape of continents and has a compact height-to-width aspect ratio. Creating the projection started with a graphical template made in Flex Projector that served as a guide for developing the polynomial equations, which are introduced in this article. The reference source code is available in the Java Map Projection Library.
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Many small-scale map projections exist, and they have different shapes and distortion characteristics. World map projections are mainly chosen based on their distortion properties and the personal preferences of cartographers. Very little is known about the map projection preferences of map-readers; only two studies have addressed this question so far. This article presents a user study among map-readers and trained cartographers that tests their preferences for world map projections. The paired comparison test of nine commonly used map projections reveals that the map-readers in our study prefer the Robinson and Plate Carrée projections, followed by the Winkel Tripel, Eckert IV, and Mollweide projections. The Mercator and Wagner VII projections come in sixth and seventh place, and the least preferred are two interrupted projections, the interrupted Mollweide and the interrupted Goode Homolosine. Separate binominal tests indicate that map-readers involved in our study seem to like projections with straight rather than curved parallels and meridians with elliptical rather than sinusoidal shapes. Our results indicate that map-readers prefer projections that represent poles as lines to projections that show poles as protruding edges, but there is no clear preference for pole lines in general. The trained cartographers involved in this study have similar preferences, but they prefer pole lines to represent the poles, and they select the Plate Carrée and Mercator projections less frequently than the other participants.
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Flex Projector is a free, open-source, and cross-platform software application that allows cartographers to interactively design custom projections for small-scale world maps. It specializes in cylindrical, and pseudocylindrical projections, as well as polyconical projections with curved parallels. Giving meridians non-uniform spacing is an option for all classes of projections. The interface of Flex Projector enables cartographers to shape the projection graticule, and provides visual and numerical feedback to judge its distortion properties. The intended users of Flex Projector are those without specialized mathematical expertise, including practicing mapmakers and cartography students. The pages that follow discuss why the authors developed Flex Projector, give an overview of its features, and introduce two new map projections created by the authors with this new software: the A4 and the Natural Earth projection.
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Online interactive maps have become a popular means of communicating with spatial data. In most online mapping systems, Web Mercator has become the dominant projection. While the Mercator projection has a long history of discussion about its inappropriateness for general-purpose mapping, particularly at the global scale, and seems to have been virtually phased out for general-purpose global-scale print maps, it has seen a resurgence in popularity in Web Mercator form. This article theorizes on how Web Mercator came to be widely used for online maps and what this might mean in terms of data display, technical aspects of map generation and distribution, design, and cognition of spatial patterns. The authors emphasize details of where the projection excels and where it does not, as well as some of its advantages and disadvantages for cartographic communication, and conclude with some research directions that may help to develop better solutions to the problem of projections for general-purpose, multi-scale Web mapping.
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The Natural Earth projection is a new projection for representing the entire Earth on small-scale maps. It was designed in Flex Projector, a specialized software application that offers a graphical approach for the creation of new projections. The original Natural Earth projection defines the length and spacing of parallels in tabular form for every five degrees of increasing latitude. It is a pseudocylindrical projection, and is neither conformal nor equal-area. In the original definition, piece-wise cubic spline interpolation is used to project intermediate values that do not align with the five-degree grid. This paper introduces alternative polynomial equations that closely approximate the original projection. The polynomial equations are considerably simpler to compute and program, and require fewer parameters, which should facilitate the implementation of the Natural Earth projection in geospatial software. The polynomial expression also improves the smoothness of the rounded corners where the meridians meet the horizontal pole lines, a distinguishing trait of the Natural Earth projection that suggests to readers that the Earth is spherical in shape. Details on the least squares adjustment for obtaining the polynomial formulas are provided, including constraints for preserving the geometry of the graticule. This technique is applicable to similar projections that are defined by tabular parameters. For inverting the polynomial projection the Newton-Raphson root finding algorithm is suggested.
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This study surveyed 60 people and asked them to rank nine common equator-centered map projections, in order to ascertain user preference for projections. Results show that those who view world maps preferred pseudocylindric projections (and a polyconic), followed by interrupted projections, least favored were rectangular projections. The greatest preference was for the Voxland hyperelliptic, followed by Robinson’s. Map readers gave a low ranking to two frequently used projections: Goode’s and Mercator’s. By a considerable margin, map users least preferred the Peters (Gall orthographic). Map users’familiarity with various projections was not an important factor in their preferences. Cartographers should be able to introduce well-designed map projections without concern about how often map readers have seen them. The analysis accounted for differences in preference by age, cartographic experience, education, and whether or not subjects considered themselves to be geographers; however, few significant differences emerged. Survey subjects could rank the map projections by whatever criteria of preference they wished to use, and the survey included an open-ended question to determine how they ranked the projections.