Download - Projections 2011
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Map Projections andCoordinate Systems
Jan-Van Sickle
Khang-tsung Chang
ESRI Using ArcMap
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Basic Map projection Types Conformal: preserves local shapes and angles
Equivalent/equal area: represents areas in correctrelative size (shapes not preserved)
Equidistant: preserves consistency of scale along
certain lines Azimuthal: preserves accurate directions (e.g.,
angles preserved, but length of lines is not)
Property is often included in name (e.g., Lambertconformal conic projection)
Map can have more than one property, but conformaland equivalent are mutually exclusive
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Conformal projections
Conformal projections preserve local shape.
To preserve individual angles describingthe spatial relationships, a conformal
projection must show the perpendicular
graticule lines intersecting at 90-degree
angles on the map.
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Equal area projections
Equal area projections preserve the area
of displayed features. To do this, the otherpropertiesshape, angle, and scalearedistorted. In equal area projections, the
meridians and parallels may not intersectat right angles.
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Equidistant projections
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. Most equidistant
projections have one or more lines for
which the length of the line on a map is thesame length (at map scale) as the same
line on the globe.
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True-direction or Azimuthal
projections
True-direction,orazimuthal, projections give the
directions or azimuths of all points on the mapcorrectly with respect to the center. Some true-direction projections are also conformal, equalarea, or equidistant.
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Examples
Planer Projections
Polar Map Projections
Secant Map Projections
Simple Conic Projections Lambert Conic Projection
Cylindrical Projections
Universe Transverse Mercator
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Planar Projections
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Plane Polar Map Projections
One tangent plane
A plane touching the globe at a single
point
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Question
Is the Polar Projection an Azimuthal
Projection?
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Answer
YES:
Direction of any line from the central tangent
point on the map to any other point
represents the actual direction of the line.Preserves accurate directions (e.g., angles
preserved, but length of lines is not)
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1 - Stereographic
Imaginary light source
on the opposite pointof tangency
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Question
Is the stereographic projection a Conformal
projection (i.e., preserves shapes)?
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AnswerConformal: preserves
local shapes andangles
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Question
Where is the no distortion (of scale) zone
on the map?
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Answer
Center of map
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Question
Where on the map does distortion increase?
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Answer
Away from the Center
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Rule
The point (standard point) or the line
(standard line) where a map & a globetouch are the only locations on the map
where there are no distortions
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2 - Gnomonic Imaginary light source
at the center of theglobe
Conformal: preserveslocal shapes and
angles
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Modifications to Decrease
Distortions
Basis: Decrease the distance between the
map projection surface and the ellipsoidal
surface
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Surface cuts theellipsoid
The area where
distortion is inacceptable range is
increased
Secant Projection
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Simple Conic Projections
The most simple conic projection is tangent to the
globe along a line of latitude. This line is called the
standard parallel.Straight converging lines (meridians) and concentric
circular arcs (parallels). Central meridian center of
map.
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QuestionFor Simple Conic Projections
Distortion increases as you move
away (E or W) from the Central Meridian
away from the standard parallel (approach pole)
Conic projections are used for mid-latitude
zones that have an EW orientation (True or False)
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Answer Distortion increases as you approach the
poles
Conic projections are used for midlatitudezones that have an EW orientation
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Secant Conic Projections
More complex conic projections that contact the
global surface at two locations.
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Cylindrical Projections
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Universe Transverse Mercator
Projection
Cartesian coordinates
For each zone, the enclosing cylinder is
rotated so that a particular centralmeridian (longitude) is touched.
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Universal Transverse Mercator
(UTM)
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Special Case: State Plane Really a meta-projection
Each state has one or more projections,with one or more zones.
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Data from maps of varying
projections can not be integrated
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Solution: Projection and
Reprojection
Projection: Converts from a geographic
coordinate system to projectedcoordinate system
Re-projection: Projects from one type of
projected coordinates to another type