Map Projections

1. Map Projections RG 620 April 20, 2016 Institute of Space Technology, Karachi

2. Converting the 3D Model to 2D Plane

3. Map Projection

4. Map Projection

5. Map ProjectionProjecting Earth's Surface into a Plane Earth is 3-D object The transformation of 3-D Earth’s surface coordinates into 2-D map coordinates is called Map Projection A map projection uses mathematical formulas to relate spherical coordinates on the globe to flat, planar coordinates

6. Map Projection Can not be accurately depicted on 2-D plane All flat maps are distorted to some degree There is always a distortion in 1 or 2 of its characteristics when projected to a 2-D map

7. Map Projection Classification Based on Distortion Characteristics Based on Developable Surface

8. Map Projection Classification Based on Distortion Characteristics: According to the property or properties that are maintained by the transformation. Some map projections attempt to maintain linear scale at a point or along a line, rather than area, shape or direction. Some preserve area but distortion in shape Some maintain shapes and angles and have area distortion

9. Distortion The 4 basic characteristics of a map likely to be preserved / distorted depending upon the map projection are: Conformity Distance Area Direction In any projection at least 1 of the 4 characteristics can be preserved (but not all) Only on globe all the above properties are preserved

11. Distortion • Transfer of points from the curved ellipsoidal surface to a flat map surface introduces Distortion

12. Distortion • In projected maps distortions are unavoidable • Different map projections distort the globe in different ways • In map projections features are either compressed or expanded • At few locations at map distortions may be zero • Where on map there is no distortion or least distortion?

13. Map Projection Each type of projection has its advantages and disadvantages Choice of a projection depends on Application – for what purposes it will be used Scale of the map Compromise projection?

14. Map Projections 1- Properties Based Conformal projection preserves shape Equidistance projection preserves distance Equal-area map maintains accurate relative sizes Azimuthal or True direction maps maintains directions

15. Map Projection - Conformal Maintains shapes and angles in small areas of map Maintains angles. Latitude and Longitude intersects at 90o Area enclosed may be greatly distorted (increases towards polar regions) No map projection can preserve shapes of larger regions Examples: Mercator Lambert conformal conic Mercator projection

16. Lambert Conformal Conic Conformal everywhere except at the poles.

17. Preserve distance from some standard point or line (or between certain points) 1 or more lines where length is same (at map scale) as on the globe No projection is equidistant to and from all points on a map (1 0r 2 points only) Distances and directions to all places are true only from the center point of projection Distortion of areas and shapes increases as distance from center increases Examples: Equirectangular – distances along meridians are preserved Azimuthal Equidistant - radial scale with respect to the central point is constant Sinusoidal projection - the equator and all parallels are of their true lengths Map Projection - Equidistance

18. Polar Azimuthal Equidistant

19. Equirectangular or Rectangular Projection

21. Map Projection – Equal Area Equal area projections preserve area of displayed feature All areas on a map have the same proportional relationship to their equivalent ground areas Distortion in shape, angle, and scale Meridians and parallels may not intersect at right angles No map projection can be both equivalent (equal area) and conformal Examples: Albers Conic Equal-Area Lambert Azimuthal Equal-Area

22. Albers Conic Equal-Area

23. Lambert Azimuthal Equal-Area Preserves the area of individual polygons while simultaneously maintaining a true sense of direction from the center

24. Map Projection – True Direction Gives directions or azimuths of all points on the map correctly with respect to the center by maintaining some of the great circle arcs Some True-direction projections are also conformal, equal area, or equidistant Example: Lambert Azimuthal Equal-Area projection

25. Map Projection2- based on developable surface A developable surface is a simple geometric form capable of being flattened without stretching Map projections use different models for converting the ellipsoid to a rectangular coordinate system Example: conic, cylindrical, plane and miscellaneous Each causes distortion in scale and shape

27. Cylindrical Projection Projecting spherical Earth surface onto a cylinder Cylinder is assumed to surround the transparent reference globe Cylinder touches the reference globe at equator

28. Cylindrical Projection Source: Longley et al. 2001

29. Other Types of Cylindrical Projections Transverse Cylindrical Oblique Cylindrical Secant Cylindrical

30. Examples of Cylindrical Projection Mercator Transverse Mercator Oblique Mercator Etc.

31. Conical Projection A conic is placed over the reference globe in such a way that the apex of the cone is exactly over the polar axis The cone touches the globe at standard parallel Along this standard parallel the scale is correct with least distortion

32. Other Types of Conical Projection Secant Conical

33. Examples of Conical Projection Albers Equal Area Conic Lambert Conformal Conic Equidistant Conic

34. Planar or Azimuthal Projection Projecting a spherical surface onto a plane that is tangent to a reference point on the globe If the plane touches north or south pole then the projection is called polar azimuthal Called normal if reference point is on the equator Oblique for all other reference points

35. Secant Planar

36. Examples of Planar Projection Orthographic Stereographic Gnomonic Azimuthal Equidistance Lambert Azimuthal Equal Area

37. Summary of Projection Properties

38. Where at Map there is Least Distortion?

39. Where at Map there is Least Distortion?

40. Where at Map there is Least Distortion

41. Great Circle Distance • Great Circle Distance is the shortest path between two points on the Globe • It’s the distance measured on the ellipsoid and in a plane through the Earth’s center. • This planar surface intersects the two points on the Earth’s surface and also splits the spheroid into two equal halves • How to calculate Great Circle Distance?

42. Great Circle Distance Example from Text Book

43. Summary – Map Projection • Portraying 3-D Earth surface on a 2-D surface (flat paper or computer screen) • Map projection can not be done without distortion • Some properties are distorted in order to preserve one property • In a map one or more properties but NEVER ALL FOUR may be preserved • Distortion is usually less at point/line of intersections of map surface and the ellipsoid • Distortion usually increases with increase in distance from points/line of intersections

44. Websites on Map Projection http://www.colorado.edu/geography/gcraft/notes/mapproj/mapproj.html http://erg.usgs.gov/isb/pubs/MapProjections/projections.html http://www.soe.ucsc.edu/research/slvg/map.html http://www.eoearth.org/article/Maps http://geography.about.com/library/weekly/aa031599.htm http://www.btinternet.com/~se16/js/mapproj.htm http://www.experiencefestival.com/a/Map_projection_-_Projections_by_preservation_of_a_metric_property/id/4822091 http://webhelp.esri.com/arcgisdesktop/9.2/index.cfm?TopicName=About_map_projections http://www.nationalatlas.gov/articles/mapping/a_projections.html http://en.wikipedia.org/wiki/ http://memory.loc.gov/cgi-bin/query/h?ammem/gmd:@field(NUMBER+@band(g5761b+ct001576))