00 charlton map_projections


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00 charlton map_projections

  1. 1. Spatial Data, 16th Century Dutchmen, GPS and GISMartin Charlton,National Centre for GeocomputationNational University of Ireland Maynooth
  2. 2. www.StratAG.ie
  3. 3. 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
  4. 4. 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
  5. 5. GEP Box, Science and Statistics, JASA, 71, 791-799 www.StratAG.ie
  6. 6. 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
  7. 7. 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
  8. 8. 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
  9. 9. 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
  10. 10. 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
  11. 11. 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
  12. 12. If we treat the longitude and latitude measurements as cartesian coordinates [1 degreecorresponds to 1 unit of distance on the ground] we obtain the plate carrée or equirectangularprojection: clearly areas and distances in the polar regions are badly distorted www.StratAG.ie Source: Wikipedia
  13. 13. Cartographers use a device known as Tissot’s Indicatrix to visualise the amount of localdeformation. At the Equator there is little distortion – circles remain circles.With increased distance from the Equator there’s greater horizontal stretching – circles becomeellipses www.StratAG.ie Source: Wikipedia
  14. 14. Gerhardus Mercator’s world projection of 1569 had the designed property that a sailing course ofconstant 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. www.StratAG.ie Source: Wikipedia
  15. 15. Although an advance in terms of maritime navigation, areas and distances in the polar regionsare badly distorted – nevertheless it was a favourite global representation for map publishers www.StratAG.ie Source: Wikipedia
  16. 16. Tissot’s Indicatrix gives some idea of the distortion of areas and distances – angles arepreserved so circles remain circles www.StratAG.ie Source: Wikipedia
  17. 17. 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 www.StratAG.ie Source: USGS
  18. 18. 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 www.StratAG.ie Source: USGS
  19. 19. 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
  20. 20. Angle Preservation• Lamberts Conformal Conic Projection• Angles on the map correspond to equivalent angles on the sphere www.StratAG.ie
  21. 21. Area Preservation• Albers Projection• Areas on the map are in proportion with their areas on the sphere www.StratAG.ie
  22. 22. 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
  23. 23. 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
  24. 24. UTM zones www.StratAG.ie Source: Wikipedia
  25. 25. 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. www.StratAG.ie Source: USGS
  26. 26. 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
  27. 27. 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
  28. 28. 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
  29. 29. 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, ) www.StratAG.ie Source: Wikipedia
  30. 30. 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
  31. 31. James Craig’s retroazimuthal projection of 1909 – it was designed to help Muslims find thecorrect direction to face Mecca for the purposes of prayer. www.StratAG.ie Source: Wikipedia
  32. 32. There are any number of textbooks on the mechanics of cartography, but until recently ratherfewer on theoretical aspects. www.StratAG.ie
  33. 33. More recent texts have taken a critical stance – taking a map at face value and regarding it asthe truth is no longer a satisfactory position. www.StratAG.ie
  34. 34. It’s been known since the early 1930s that data for spatialunits presents some rather awkward problems. Confirmedin 1979 in a famous paper… in Wrigley N, 1979, ed, Statistical Applications in the Spatial Sciences, London: Pion 127-144 www.StratAG.ie
  35. 35. 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