Map projections

A map projection is a systematic transformation of the latitudes and longitudes of locations from the surface of a sphere or an ellipsoid into locations on a plane. Maps cannot be created without map projections.

1. Map ProjectionsEonhertin' tse Su Mofel to Cu Plane
Converting the 3D Model to 2D Plane

2. Map ProjectionMap Projection
Projecting Earth's Surface into a PlaneProjecting 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

3. Map ProjectionMap 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

4. Map Projection ClassificationMap Projection Classification
1.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
1.Based on Developable Surface: Considering the
Earth as a transparent sphere with a point source
of illumination at the centre.

5. DistortionDistortion
•The 4 basic characteristics of a map likely to be
distorted/preserved 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

6. Map ProjectionMap 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
•Where on map there is no distortion or least
distortion?

7. Map Projections Map Projections
1- Properties Based1- Properties Based
•Conformal projection preserves shape
•Equidistance projection preserves distance
•Equal-area map maintains accurate relative
sizes
•Azimuthal or True direction maps maintains
directions

8. Map Projection - ConformalMap Projection - Conformal
•Maintains shapes and angles in small areas of map
•Maintains angles. Latitude and Longitude intersects
at 90
o
•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

9. Lambert Conformal ConicLambert Conformal Conic
Conformal everywhere except at the poles.

10. •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
•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 - equal distance between all latitudes and longitudes
–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 - EquidistanceMap Projection - Equidistance

11. Polar Azimuthal Polar Azimuthal
EquidistantEquidistant

12. Equirectangular or Rectangular Equirectangular or Rectangular
ProjectionProjection

13. Map Projection – Equal AreaMap 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
Examples:
–Albers Conic Equal-Area
–Lambert Azimuthal Equal-Area

14. Albers Conic Equal-AreaAlbers Conic Equal-Area

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

16. Map Projection – True DirectionMap 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

17. Map ProjectionMap Projection
2- based on developable surface2- 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

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

19. Cylindrical ProjectionCylindrical Projection
Source: Longley et al. 2001

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

21. Examples of Cylindrical Examples of Cylindrical
ProjectionProjection
•Mercator
•Transverse Mercator
•Oblique Mercator
•Etc.

22. Conical ProjectionConical 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

23. Other Types of Conical Other Types of Conical
ProjectionProjection
Secant Conical

24. Examples of Conical ProjectionExamples of Conical Projection
•Albers Equal Area Conic
•Lambert Conformal Conic
•Equidistant Conic

25. Planar or Azimuthal ProjectionPlanar 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

26. Secant PlanarSecant Planar

27. Examples of Planar ProjectionExamples of Planar Projection
•Orthographic
•Stereographic
•Gnomonic
•Azimuthal Equidistance
•Lambert Azimuthal Equal Area

28. Map ProjectionMap Projection

29. Summary of Projection PropertiesSummary of Projection Properties

30. Map ProjectionMap Projection

31. Map ProjectionMap Projection

32. Map ProjectionMap Projection

33. Where at Map there is Least Where at Map there is Least
Distortion? Distortion?

34. Where at Map there is Least Where at Map there is Least
Distortion Distortion

35. Summary – Map ProjectionSummary – 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

36. Websites on Map ProjectionWebsites 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))