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Map projections
- 1. Map Projections Converting the 3D Model to 2D PlaneConverting 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 ProjectionsMap 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 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
- 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
- 12. Equirectangular or RectangularEquirectangular 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-AreaLambert 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 CylindricalOther Types of Cylindrical ProjectionsProjections Transverse Cylindrical Oblique Cylindrical Secant Cylindrical
- 21. Examples of CylindricalExamples 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 ConicalOther 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
- 27. Examples of Planar ProjectionExamples of Planar Projection • Orthographic • Stereographic • Gnomonic • Azimuthal Equidistance • Lambert Azimuthal Equal Area
- 29. Summary of Projection PropertiesSummary of Projection Properties
- 33. Where at Map there is LeastWhere at Map there is Least Distortion?Distortion?
- 34. Where at Map there is LeastWhere at Map there is Least DistortionDistortion
- 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))
Notas del editor
- In the graphic above data near the poles is stretched . Different projections have different spatial relationships between regions
- A developable surface is a simple geometric form capable of being flattened without stretching
- Projections may be classified on the basis of their distortion characteristics
- For example, a projection may have unacceptable distortions if used to map the entire country, but may be an excellent choice for a large-scale (detailed) map of a county. A compromise projection distorts all the properties of shape, area, distance, and direction, within some acceptable limit, example is Robison Projection used for World Maps
- Conformal map projections preserve angles locally. Mercator by Gerardus Mercator, in 1569
- superimposes a cone over the sphere of the Earth, with two reference parallels secant to the globe and intersecting it.
- Scale is not maintained correctly by any projection throughout an entire map. However, there are in most cases, one or more lines on a map along which scale is maintained correctly Azimuthal Equidistant map centered at Washington DC: shows the correct distance between Washington, DC, and any other point on the projection. It shows the correct distance between Washington, DC, and San Diego and between Washington, DC, and Seattle, but it does not show the correct distance between San Diego and Seattle.
- An equirectangular projection is a cylindrical equidistant projection.
- In some instances, especially maps of smaller regions, shapes are not obviously distorted, and distinguishing an Equal area projection from a Conformal projection is difficult unless documented or measured
- It is similar to the Lambert Conformal Conic projection except that Albers Conic Equal Area portrays area more accurately than shape.
- Azimuthal Accurate direction and therefore true angular relationship from a given center point
- miscellaneous =which include special cases not falling into the other three categories.
- Cylinder may be either tangent to the Earth along a selected line or secant (intersect the Earth) along 2 lines
- Notice how the continents look stretched or squashed depending on the projection
- The lines where the cylinder is tangent or secant are the places with the least distortion.