00 charlton map_projections

Spatial Data,
16th Century
Dutchmen,
GPS and GIS

Martin Charlton,
National Centre for Geocomputation
National University of Ireland Maynooth

Maps as truth
• Maps are cultural artifacts, comparable in history to
arms and amour, musical instruments, or ships.
• Almost all cultures have developed maps, but with
enormously varying degrees of sophistication and
intent.
• Their origin is instinctive, in that they are products
of both the intellect and the imagination in
confronting problems in reality.
Whitfield P, 2002, Outer Worlds and Inner Worlds:
An Introduction to World Maps London: The British Library

www.StratAG.ie

Maps
• MAPS ARE SOCIAL CONSTRUCTIONS
• They are not objective
• Maps have contexts: invasion, for example

• Maps are an abstraction from reality – a
production of intentions, assumptions and
compromises.

• MAPS ARE MODELS
www.StratAG.ie

GEP Box, Science and Statistics, JASA, 71, 791-799

www.StratAG.ie

Global Coordinate Systems
• Spherical
coordinates.
measured in
degrees
• Latitude: north or
south of the Equator
• Longitude: east or
west of the Prime
Meridian

www.StratAG.ie

Latitude
• Parallels of latitude
• Run from 0 (Equator) to
90N and 90S
• There are several named
latitudes:
– Tropic of Cancer: 23° 26′
21″ N
– Equator: 00° 00′ 00″
– Tropic of Capricorn: 23°
26′ 21″ S

www.StratAG.ie

Longitude
• Measured relative to the Prime Meridian (Greenwhich
Meridian)
• Meridian: arc which runs from N Pole to S Pole connecting
locations with the same longitude

www.StratAG.ie Source: USGS

Flat worlds
• Our atlases and PC screens
are flat
x
• Measurements of location are y axis
conventionally made in terms
y
of distance east and distance
north of an origin:
coordinates Origin
x axis
• The axes meet at a right angle
• Known as cartesian
coordinates

www.StratAG.ie

Map Projections
• A map projection is a mathematical
transformation between the location on a
sphere as latitude, longitude, and the
location on a flat map as cartesian
coordinates (x,y or easting,northing).

• As well as individual points, lines and areas
can also be mapped.
www.StratAG.ie

Projections
• There are thousands of different projections
• Some are designed to show the whole
globe, other are optimised for only part of
the globe.
• They are often categorised by the manner of
their creation
– Cylindrical
– Conic
– Planar

www.StratAG.ie

If we treat the longitude and latitude measurements as cartesian coordinates [1 degree
corresponds to 1 unit of distance on the ground] we obtain the plate carrée or equirectangular
projection: clearly areas and distances in the polar regions are badly distorted
www.StratAG.ie Source: Wikipedia

Cartographers use a device known as Tissot’s Indicatrix to visualise the amount of local
deformation. At the Equator there is little distortion – circles remain circles.

With increased distance from the Equator there’s greater horizontal stretching – circles become
ellipses

Gerhardus Mercator’s world projection of 1569 had the designed property that a sailing course of
constant bearing was represented by a straight line on the map [rhumb line or loxodrome].

Here is a projection which is directly related to maritime transport needs.


Although an advance in terms of maritime navigation, areas and distances in the polar regions
are badly distorted – nevertheless it was a favourite global representation for map publishers


Tissot’s Indicatrix gives some idea of the distortion of areas and distances – angles are
preserved so circles remain circles


Cylindrical: Mercator
• In a cylindrical
projection the lines
of latitude and
longitude are
projected onto the
inside of a cylinder
as if the earth were
a light bulb

• In the transverse
form the cylinder is
oriented east-west

Conic
• A conic projection
assumes that the earth
has been cut by a giant
cone
• The latitudes at which
it is cut are called
standard parallels
• The two examples are
Albers’ equal area and
Lambert’s conformal
conic

Projections Distort Shapes
• Thinking of the light bulb analogy, shapes
get distorted when shadows are cast.
• Properties of geographical features on the
globe can alter when projected onto a map.
• Angles, areas, distances cannot always be
reliably measured.
• It is possible to preserve some properties,
but not all.

www.StratAG.ie

Angle Preservation
• Lambert's
Conformal Conic
Projection
• Angles on the
map correspond
to equivalent
angles on the
sphere

www.StratAG.ie

Area Preservation
• Albers Projection
• Areas on the map
are in proportion
with their areas
on the sphere

www.StratAG.ie

True Distance Preservation
• Azimuthal
Projection
• This preserves
distances along
meridians. It is not
possible to define a
projection to
preserve distance
everywhere
• This can be shown
mathematically.
www.StratAG.ie

Universal Transverse Mercator
• You will sometimes see UTM or Universal
Transverse Mercator used as a projection
• UTM divides the world into 60 6 degree wide
segments between 80S and 84N, numbered 1 … 60
– The meridian between zones 30 and 31 is the Prime Meridian
• A UTM zone is usually specified by a code pair:
– Zone 29N covers Ireland
– Zone 55S covers Tasmania
– Larger countries are covered by several zones.

www.StratAG.ie

UTM zones


USGS advice
• A map projection is used to portray all or part of
the round Earth on a flat surface. This cannot be
done without some distortion.
• Every projection has its own set of advantages and
disadvantages. There is no "best" projection.
• Mapmakers and mathematicians have devised
almost limitless ways to project the image of the
globe onto paper.


Specifying projections
• Some map datasets come with projection
information (.prj in ArcGIS shapefiles)
• Some software will provide on-the-fly
transformation which allows you to mix
datasets with different projections
• If you haven’t got projection data, then you
made need add this – ArcGIS and QGIS have
details of hundreds of projections built in;
R hasn’t

www.StratAG.ie

No projection details?
• Data in decimal degrees: WGS84
– Longitude: -180 to 180 and latitude: -90 to 90
– Unlikely to be metres
• Irish National Grid: metres
– No easting on the mainland in greater than 400000
– No northing on the mainland is greater than 500000
• Irish Transverse Mercator: metres
– No easting on the mainland is less than 400000
– No northing on the mainland is less than 500000
• UTM Zone 29N: metres
– Northings will be between 5679000 and 6079000
– Eastings will be between 366570 and 766570
www.StratAG.ie

Spatialreference.org
• Projections require parameters:
– Datum: spheroid name/dimensions
– Latitude of the origin
– Longitude of the central meridian
– Scale factor at the central meridian
– Latitudes of the standard parallels (if any)
– False easting/northing (ensures coordinates are
positive)
• More details at http://spatialreference.org
for thousands of different projections
www.StratAG.ie

Politicised cartography: Peters 1973

• The cartographic profession is, by its retention of old precepts based on the Eurocentric global concept,
incapable of developing this egalitarian world map which alone can demonstrate the parity of all peoples of
the earth.
(Peters, Arno (1983). Die Neue Kartographie/The New Cartography (in German and English). Klagenfurt, )


Post-cold war cartography: 1995

• A remarkable volume was
published in 1995 by
Taylor and Francis

• It details hundreds of
different projections from
boths sides of what used
to be the Iron Curtain.

www.StratAG.ie

James Craig’s retroazimuthal projection of 1909 – it was designed to help Muslims find the
correct direction to face Mecca for the purposes of prayer.


There are any number of textbooks on the mechanics of cartography, but until recently rather
fewer on theoretical aspects.

www.StratAG.ie

More recent texts have taken a critical stance – taking a map at face value and regarding it as
the truth is no longer a satisfactory position.

www.StratAG.ie

It’s been known since the early 1930s that data for spatial
units presents some rather awkward problems. Confirmed
in 1979 in a famous paper…

in Wrigley N, 1979, ed, Statistical Applications in the Spatial Sciences, London: Pion 127-144

www.StratAG.ie

Further info:
• Peter Dana’s excellent pages at:
http://www.colorado.edu/geography/gcraft/notes
/mapproj/mapproj_f.html

• http://spatialreference.org

• http://www.worldmapper.org/
(Soon to be hosted at the NCG)

www.StratAG.ie

00 charlton map_projections

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