Transcript Map Projections
Map Projections
RG 620 Week 5 May 08, 2013 Institute of Space Technology, Karachi
Converting the 3D Model to 2D Plane
Map Projection
Map Projection
Map Projection
Projecting 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
Map Projection
All flat maps are
distorted
to some degree
Can not be accurately
depicted on 2-D plane There is always a distortion in 1 or 2 of its characteristics when projected to a 2-D map
Map Projection Classification
1. Based on Distortion Characteristics 2. Based on Developable Surface
Map Projection Classification
1. Based on Distortion Characteristics: According to the property or properties that are maintained by the transformation. i.
Some map projections attempt to maintain linear scale at a point or along a line, rather than area, shape or direction. ii. Some preserve area but distortion in shape iii. Some maintain shapes and angles and have area distortion
Map Projection Classification
2. Based on Developable Surface: Considering the Earth as a transparent sphere with a point source of illumination at the centre.
Distortion
• The
4 basic characteristics preserved / distorted
of a map likely to be depending upon the map projection are: 1. Conformity 2. Distance 3. Area 4. Direction • In any projection
at least 1 of the 4
can be
preserved
(but not all) characteristics • Only on
globe preserved
all the
above properties
are
Distortion
• Transfer of points from the curved ellipsoidal surface to a flat map surface introduces
Distortion
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?
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?
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
Map 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
Lambert Conformal Conic
Conformal everywhere except at the poles.
Map Projection - Equidistance
• 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
Polar Azimuthal Equidistant
Equirectangular or Rectangular Projection
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 Examples: – Albers Conic Equal-Area – Lambert Azimuthal Equal-Area
Albers Conic Equal-Area
Lambert Azimuthal Equal-Area
Preserves the area of individual polygons while simultaneously maintaining a true sense of direction from the center
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
Map Projection
2- 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
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
Cylindrical Projection
Source: Longley et al. 2001
Other Types of Cylindrical Projections
Transverse Cylindrical Oblique Cylindrical Secant Cylindrical
Examples of Cylindrical Projection
• Mercator • Transverse Mercator • Oblique Mercator • Etc.
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
Other Types of Conical Projection
Secant Conical
Examples of Conical Projection
• Albers Equal Area Conic • Lambert Conformal Conic • Equidistant Conic
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
Secant Planar
Examples of Planar Projection
• Orthographic • Stereographic • Gnomonic • Azimuthal Equidistance • Lambert Azimuthal Equal Area
Summary of Projection Properties
Where at Map there is Least Distortion?
Where at Map there is Least Distortion
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?
Great Circle Distance Example from Text Book
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
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))