Fundamentals of Mapping
`
`11/21/2017
`
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`Fundamentals of Mapping
`Some Commonly Used Map Projections
`
`ICSM homepage
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`Introduction
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`GPS and Conclusion
`Projections
`About Projections
`Commonly used Map
`Projections
`
`This section outlines the features of a selection of more commonly used
`projects. It is by no means a full list projections which are commonly
`used today. Also, it describes each projection in its simplest form (e.g.
`only one Standard Parallel not two).
`
`Contents
`
` » Introduction
` » Stereographic
` » Lambert Conformal Conic
` » Mercator
` » Robinson
` » Transverse Mercator
` » A Special Case – Universal Transverse Mercator System (UTM)
` » UTM Zones
` » UTM Map grid and the Australian Map Grid
` » A Special Case – Geographic (or Plate Carree)
` » Further Reading
`
`Introduction
`
`Comparison of these projections:
`
`http://www.icsm.gov.au/mapping/map_projections.html
`
`ZTE Exhibit 1026
`
`

`

`Fundamentals of Mapping
`
`11/21/2017
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`Map as a Summary of
`the World
`
`Making Your Map
`
`Marginalia Information
`
`Cartographic
`Considerations
`
`Map Specifications
`
`Tactual Mapping
`
`Reference
`
`Projection
`
`Type
`
`Key virtues
`
`Stereographic
`
`azimuthal
`
`conformal
`
`Lambert
`Conformal Conic conic
`
`conformal
`
`Mercator
`
`cylindrical
`
`conformal and true direction
`
`Robinson
`
`Transverse
`Mercator
`
`pseudo-
`cylindrical
`
`all attributes are distorted to
`create a ‘more pleasant’
`appearance
`
`cylindrical
`
`conformal
`
`Created
`Best Use
`Poles or f
`continent
`Created
`Best Use
`e.g. USA
`Created
`Best Use
`Equator a
`navigatio
`Created
`Best Use
`Equator
`Created
`Best Use
`north-sou
`
`Azimuthal Projection – Stereographic
`
`The oldest known record of this projection is from Ptolemy in about 150 AD. However it is
`believed that this projection was well known long before that time – probably as far back as the
`2nd century BC.
`
`Today, this is probably one of the most widely used Azimuthal projections. It is most commonly
`used over Polar areas, but can be used for small scale maps of continents such as Australia. The
`great attraction of the projection is that the Earth appears as if viewed form space or a globe.
`
`This is a conformal projection in that shapes are well preserved over the map, although extreme
`distortions do occur towards the edge of the map. Directions are true from the centre of the map
`(the touch point of our imaginary ‘piece of paper’), but the map is not equal-area.
`
`One interesting feature of the Stereographic projection is that any straight line which runs through
`the centre point is a Great Circle. The advantage of this is that for a place of interest (e.g.
`Canberra, the capital city of Australia) a map which uses the Stereographic projection and is
`centred on that place of interest true distances can be calculated to other places of interest (e.g.
`Canberra to Sydney; or Canberra to Darwin; or Canberra to Wellington, New Zealand).
`
`http://www.icsm.gov.au/mapping/map_projections.html
`
`ZTE Exhibit 1026 - 2
`
`

`

`Fundamentals of Mapping
`
`11/21/2017
`
`These are two examples of maps using Stereographic projection over polar areas. In these
`the radiating lines are Great Circles. Projection information: Stereographic; centred on 140°
`East and 90° South (the South Pole) and 90° North (the North Pole), with a radius of 30° out
`from each Pole.
`
`http://www.icsm.gov.au/mapping/map_projections.html
`
`ZTE Exhibit 1026 - 3
`
`

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`Fundamentals of Mapping
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`11/21/2017
`
`Produced Using G.PROJECTOR – software
`developed by NASA and the Goddard Institute for
`Spatial Studies. Projection information:
`Stereographic; centred on 145° East and 30°
`South, with a radius of 30° out from the Pole. In
`this the Great Circles are not as obvious as with
`the two Polar maps above, but the same principle
`applies: any straight line which runs through the
`centre point is a Great Circle. This is an example
`of how a Great Circle does not have to be a set
`line of Longitude of Latitude.
`
`Conic Projection – Lambert Conformal Conic
`
`Johann Heinrich Lambert was a German ⁄ French mathematician and scientist. His mathematics
`was considered revolutionary for its time and is still considered important today. In 1772 he
`released both his Conformal Conic projection and the Transverse Mercator Projection.
`
`Today the Lambert Conformal Conic projection has become a standard projection for mapping
`large areas (small scale) in the mid-latitudes – such as USA, Europe and Australia. It has also
`become particularly popular with aeronautical charts such as the 1:100,000 scale World
`Aeronautical Charts map series.
`
`This projection commonly used two Standard Parallels (lines of latitudes which are unevenly
`spaced concentric circles).
`
`The projection is conformal in that shapes are well preserved for a considerable extent near to the
`Standard Parallels. For world maps the shapes are extremely distorted away from Standard
`Parallels. This is why it is very popular for regional maps in mid-latitude areas (approximately 20°
`to 60° North and South).
`
`Distances are only true along the Standard Parallels. Across the whole map directions are
`generally true.
`
`http://www.icsm.gov.au/mapping/map_projections.html
`
`ZTE Exhibit 1026 - 4
`
`

`

`Fundamentals of Mapping
`
`11/21/2017
`
`These two maps highlight the importance of selecting your Standard Parallel(s) carefully.
`For the first one the Standard Parallels are in the North and for the second they are in the
`South. Projection information: Lambert Conformal Conic; centred on 140° East and the
`Equator.
`
`First map has standard Parallels at 30° and 60° North and the second has standard
`Parallels at 30° and 60° South.
`
`The Lambert Conformal Conic is the preferred
`projection for regional maps in mid-latitudes. In
`Australia the national mapping agency prefers to use
`this projection using 18° and 36° South as the two
`Standard Parallels. Projection information: Lambert
`Conformal Conic; centred on 140° East and 25°
`South, and two Standard Parallels 18° and 36° South.
`
`http://www.icsm.gov.au/mapping/map_projections.html
`
`ZTE Exhibit 1026 - 5
`
`

`

`Fundamentals of Mapping
`
`11/21/2017
`
`Cylindrical Projection – Mercator
`
`Notice the huge distortions in the Arctic and Antarctic regions,
`but the reasonable representation of landmasses out to about
`50° north and south. Projection information: Mercator; centred
`on 140° East and the Standard Parallel is the Equator
`
`One of the most famous map projections is the Mercator, created by a Flemish cartographer and
`geographer, Geradus Mercator in 1569.
`
`It became the standard map projection for nautical purposes because of its ability to represent
`lines of constant true direction. (Constant true direction means that the straight line connecting
`any two points on the map is the same direction that a compass would show.) In an era of sailing
`ships and navigation based on direction only, this was a vitally important feature of this projection.
`
`The Mercator Projection always has the Equator as its Standard Parallel. Its construction is such
`that the lines of longitude and latitude are at right angles to each other – this means that a world
`map is always a rectangle.
`
`Also, the lines of longitude are evenly spaced apart. But the distance between the lines of latitude
`increase away from the Equator. This relationship is what allows the direction between any two
`points on the map to be constant true direction.
`
`While this relationship between lines of lines of latitude and longitude correctly maintains
`direction, it allows for distortion to occur to areas, shapes and distances. Nearest the Equator
`there is little distortion. Distances along the Equator are always correct, but nowhere else on the
`map. Between about 15° north and south the areas and shapes are well preserved. Further out
`(to about 50° north and south) the areas and shapes are reasonably well preserved. This is why,
`for uses other than marine navigation, the Mercator projection is recommended for use in the
`Equatorial region only.
`
`Despite these distortions the Mercator projection is generally regarded as being a conformal
`projection. This is because within small areas shapes are essentially true.
`
`http://www.icsm.gov.au/mapping/map_projections.html
`
`ZTE Exhibit 1026 - 6
`
`

`

`Fundamentals of Mapping
`
`11/21/2017
`
`See also Transverse Mercator and Universal Transverse Mercator below.
`
`Cylindrical Projection – Robinson
`
`In the 1960s Arthur H. Robinson, a Wisconsin geography professor, developed a projection
`which has become much more popular than the Mercator projection for world maps. It was
`developed because modern map makers had become dissatisfied with the distortions inherent in
`the Mercator projection and they wanted a world projection which ‘looked’ more like reality.
`
`In its time, the Robinson projection replaced the Mercator projection as the preferred projection
`for world maps. Major publishing houses which have used the Robinson projection include Rand
`McNally and National Geographic.
`
`Compare this to the Mercator projection map above.
`Projection information: Robinson; centred on 140°
`East and the Standard Parallel is the Equator.
`
`As it is a pseudo-cylindrical projection, the Equator is its Standard Parallel and it still has similar
`distortion problems to the Mercator projection.
`
`Between about 0° and 15° the areas and shapes are well preserved. However, the range of
`acceptable distortion has been expanded from approximately 15° north and south to
`approximately 45° north to south. Also, there is less distortion in the Polar regions.
`
`Unlike the Mercator projection, the Robinson projection has both the lines of altitude and
`longitude evenly spaced across the map. The other significant difference to the Mercator is that
`only the line of longitude in the centre of the map is straight (Central Meridian), all others are
`curved, with the amount of curve increasing away from the Central Meridian.
`
`In opting for a more pleasing appearance, the Robinson projection ‘traded’ off distortions – this
`projection is neither conformal, equal-area, equidistant nor true direction.
`
`Cylindrical Projection – Transverse Mercator
`
`Johann Heinrich Lambert was a German ⁄ French mathematician and scientist. His mathematics
`was considered revolutionary for its time and is still considered important today. In 1772 he
`released both his Conformal Conic projection and the Transverse Mercator projection.
`
`http://www.icsm.gov.au/mapping/map_projections.html
`
`ZTE Exhibit 1026 - 7
`
`

`

`Fundamentals of Mapping
`
`11/21/2017
`
`The Transverse Mercator projection is based on the highly successful Mercator projection. The
`main strength of the Mercator projection is that it is highly accurate near the Equator (the ‘touch
`point’ of our imaginary piece of paper – otherwise called the Standard Parallel) and the main
`problem with the projection is that distortions increase away from the Equator. This set of virtues
`and vices meant that the Mercator projection is highly suitable for mapping places which have an
`east-west orientation near to the Equator but not suitable for mapping places which have are
`north-south orientation (eg South America or Chile).
`
`Lambert’s stroke of genius was to change the way the imaginary piece of paper touched the
`Earth… instead of touching the Equator he had it touching a line of Longitude (any line of
`longitude). This touch point is called the Central Meridian of a map. This meant that accurate
`maps of places with north-south orientated places could now be produced. The map maker only
`needed to select a Central Meridian which ran through the middle of the map.
`
`A Special Case – Universal Transverse Mercator System (UTM)
`
`It took another 200 years for the next development in take place for the Mercator projection.
`
`Again, like Lambert’s revolutionary change to the way that the Mercator projection was calculated;
`this development was a change in how the Transverse Mercator projection was used. In 1947 the
`North Atlantic Treaty Organisation (NATO) developed the Universal Transverse Mercator
`coordinate system (generally simply called UTM).
`
`NATO recognised that the Mercator/Transverse Mercator projection was highly accurate along its
`Standard Parallel/Central Meridian. Indeed as far as 5° away from the Standard Parallel ⁄ Central
`Meridian there was minimal distortion.
`
`Like the World Aeronautical Charts, the UTM system was able to build on the achievements of the
`International Map of the World. As well as developing an agreed, international specification the
`IMW had developed a regular grid system which covered the entire Surface of the Earth. For low
`to mid-latitudes (0° to 60° North and South) the IMW established a grid system that was 6° of
`longitude wide and 4° of latitude high.
`
`Using this NATO designed a similar regular system for the Earth whereby it was divided into a
`series of 6° of longitudinal wide zones. There are a total of 60 longitudinal zones and these are
`numbered 1 to 60 – east from longitude 180° . These extend from the North Pole to the South
`Pole. A central meridian is placed in middle of each longitudinal zone. As a result, within a zone
`nothing is more than 3° from the central meridian and therefore locations, shapes and sizes and
`directions between all features are very accurate.
`
`Please note that this is not a new ⁄ revised projection, but a series of maps using the same
`projection (Transverse Mercator). This is not commonly appreciated and UTM is often wrongly
`described as a projection in its own right – it is not – it is a projection system.
`
`This is why UTM is regarded as a Special Case.
`
`The shortcoming in the UTM system is that between these longitude zones directions are not true
`– this problem is overcome by ensuring that maps using the UTM system do not cover more than
`one zone.
`
`http://www.icsm.gov.au/mapping/map_projections.html
`
`ZTE Exhibit 1026 - 8
`
`

`

`Fundamentals of Mapping
`
`11/21/2017
`
`World wide, including Australia, this UTM system is used by mapping agencies for local and
`national, topographic maps.
`
`UTM Zones
`
`Compare this to the Mercator projection map above. Projection
`information: Robinson; centred on 140° East and the Standard
`Parallel is the Equator.
`
`As already noted, the UTM system involves a series of longitudinal zones which are 6° wide and
`numbered 1 to 60 – east from longitude 180°.
`
`However, unlike the International Map of the World (IMW) the UTM system opted to use latitudinal
`zones which were twice as wide – i.e. 8° of latitude wide. There are 20 of these and they are
`numbered A to Z (with O and I not being used) – north from Antarctica. Like the IMW system
`each feature on the Earth is now able to be described based on the UTM grid it is located in. One
`confusing item is that these grid cells are variably called a UTM zone.
`
`For example, in the case of Sydney, Australia, its UTM grid cell (zone) would be identified as:
`
`• H – for the latitudinal zone it belongs to
`• 56 – for the longitudinal zone it belongs to
`
`Add the two together – the UTM grid zone (grid cell) which contains Sydney is 56H
`
`UTM Map grid and the Australian Map Grid
`
`As is explained in the section tiled Explaining Some Jargon – Graticules and Grids there is a
`significant difference between the two. This is
`
`http://www.icsm.gov.au/mapping/map_projections.html
`
`ZTE Exhibit 1026 - 9
`
`

`

`Fundamentals of Mapping
`
`11/21/2017
`
`• Graticules are lines of Longitude and Latitude. These never form a square or rectangular
`shape and their shape changes dramatically from the Equator to the Pole – from being close
`to square shaped to being close to triangle shaped.
`• Grids are a regularly shaped overlay to a map. They are usually square, but they may be
`rectangular.
`
`Grids rarely run parallel to lines of Longitude and Latitude.
`
`Besides ease of use, there is another advantage to a grid – on any given map it always covers
`the same amount of the Earth’s surface. This is not true of a graticule system! A 1° x1° block of
`latitude and longitude near the Equator will always cover vastly more of the Earth’s surface and a
`1° x1° block closer to a Pole. Therefore it is easy to measure distances using a grid – it removes
`the foibles of distortions inherent in each map projection.
`
`When NATO created the UTM system it recognised this fact and built a grid system into it. This
`involves a regular and complex system of letters to identify grid cells. To identify individual
`features or locations distances are first measured from the west to the feature and then measured
`from the south to the feature. The three are combined to give a precise location – based on the
`map grid.
`
`Explaining some jargon:
`
`• The Australian Map Grid (AMG) is the map grid which had been developed as part of the
`UTM system to best suit Australian needs.
`• Northings – these are the vertical parallel lines of the grid – i.e. they are series of lines which
`run from the south to the north (similar to lines of latitude – but not the same)
`• Eastings – these are the horizontal parallel lines of the grid – i.e. they are series of lines
`which run from the east to the west (similar to lines of longitude – but not the same)
`
`A Special Case – Geographic (or Plate Carrée)
`
`This is a mathematically simple projection. It is also an ancient projection (possibly developed by
`Marinus of Tyre in 100).
`
`Because of its simplicity it was commonly used in the past (before computers allowed for very
`complex calculations) and it has been adopted as the projection of choice for use in computer
`mapping applications – notably Geographic Information Systems (GIS) and on web pages. Also,
`again because of its simplicity, it is equally able to be used with world and regional maps.
`
`Plate Carrée is the French term for flat square. In GIS operations this projection is commonly
`referred to as Geographicals.
`
`This is a cylindrical projection, with the Equator as its Standard Parallel. The difference with this
`projection is that the latitude and longitude lines intersect to form regularly sized squares. By
`way of comparison, in the Mercator and Robinson projections they form irregularly sized
`rectangles.
`
`http://www.icsm.gov.au/mapping/map_projections.html
`
`ZTE Exhibit 1026 - 10
`
`

`

`Fundamentals of Mapping
`
`11/21/2017
`
`While we have described the Geographic or Plate Carrée as a projection, there is some debate as
`to whether it should be considered to be a projection. This is because it makes no attempt to
`compensate for distortions due to the transfer of information from the surface of the Earth onto a
`‘flat piece of paper’ (our map).
`
`This is why we are describing the Geographical projection as a Special Case.
`
`Refer to the section on Projections for more information about distortions generated by
`projections.
`
`Projection information: Equirectangular; centred on 140° East and the Standard Parallel is the Equator. Produced Using G.PROJECTOR — software
`developed by NASA and the Goddard Institute for Spatial Studies. Projection information: Equirectangular; centred on 140° East and the Standard Parall
`is the Equator
`
`Further Reading
`
`Paul B. Anderson FCCS (USN, Retired) Old Dominion University Geography Department, GIS
`Teaching Assistant Kingsport – Map Projections
`http://www.csiss.org/map-projections/index.html/
`http://www.galleryofmapprojections.com/images/Aust_Centered_2009.jpg
`http://www.galleryofmapprojections.com/gedymin/gedymin_prof_11x17.pdf
`
`Carlos A Furuti – Map Projections
`http://www.progonos.com/furuti/MapProj/
`
`(US) National Atlas Map Projections
`From Spherical Earth to Flat Map
`
`If you have any suggestions for additional hyperlinks or improvements to the content please contact the ICSM Executive
`Officer:
`
`phone: +61 2 6249 9677 (international) or (02) 6249 9677 (within Australia); email: icsm@ga.gov.au
`
`Unless otherwise noted, all ICSM material on this website is licensed under the Creative
`Commons Attribution 3.0 Australia Licence
`© Commonwealth of Australia 2016 on behalf of ICSM view the Creative
`Commons Licence terms
`
`http://www.icsm.gov.au/mapping/map_projections.html
`
`ZTE Exhibit 1026 - 11
`
`

`

`Fundamentals of Mapping
`
`11/21/2017
`
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`Last Updated: 18 Jan 2017
`
`http://www.icsm.gov.au/mapping/map_projections.html
`
`ZTE Exhibit 1026 - 12
`
`