What is a map projection?
 Because the earth is spherical and maps are flat, GIS
applications require that a mathematical formulation
be applied to the earth to represent it on a flat surface.
 This causes some distortions of distance, area, shape,
or direction.
Map Projections - Distortion
 preserve shape - conformal (orthomorphic)
 preserve scale – equidistant
 preserve direction – azimuthal
 preserve great circles - gnomic
 preserve circular shapes - stereographic
What are map projections?
 There are two types of coordinate systems
 Geographic – use latitude and longitude coordinates on
the surface of a sphere
 Projected – use mathematical conversion to transform
latitude and longitude coordinates to a flat surface.
ArcMap has over a hundred
projections
Albers – equal area conic projection
 Shape and linear scale
 Minimally distorted in the region between the standard
parallels
 Areas
 proportional to the same areas on the earth
 Direction
 Locally true
 Distance
 Most accurate in the middle latitudes
Robinson – world projection
Compromise projection used for world maps
 Shape
 Distortion is very low within 45° of the origin and along the
equator
 Areas
 Distortion is very low within 45° of the origin and along the
equator.
 Direction
 Generally distorted
 Distance
 Scale is constant along any given latitude and for latitude of
the opposite sign
 Limitations
 Useful only for world maps
State Plane
 Not a projection it is a coordinate system that divides
the fifty U.S. states, Puerto Rico, and the U.S. Virgin
Islands into more that 120 numbered sections, referred
to as zones.
 Designed for large-scale mapping in the U.S.
UTM – Universal Transverse Mercator
 Shape
 Accurate representation of small shapes
 Areas
 Minimal distortion within each UTM zone
 Direction
 Local angles are true
 Distance
 Scale is constant along the central meridian
 Limitations
 Error and distortion increase for regions that span more than
one UTM zone
Map Projections vs.
Datum Transformations
 A map projections is a systematic rendering
from 3-D to 2-D
 Datum transformations are from one datum to
another, 3-D to 3-D
 Changing from one projection to another may
require both
Datum
 To more accurately represent locations on the earth’s
surface
 A datum links a spheroid to a particular portion of the
earth’s surface.
Datum
Most commonly used datums in North America
 North American Datum (NAD) 1927 using the Clarke
1866 spheroid
 NAD 1983 using the Geodetic Reference system (GRS)
1980 spheroid
 World Geodetic System (WGS) 1984 using the WGS 1984
spheroid
Input geographic
coordinate system
NAD 1927
Output geographic
coordinate system
WGS 1984
Datum
 The coordinates for a location will change depending
on the datum and spheroid on which those
coordinates are based.
Georeferencing – what?
 Aligning geographic data to a known coordinate
system so it can be viewed, queried, and analyzed with
other geographic data
 Georeferencing may involve shifting, rotating, scaling,
skewing, and in some cases warping, rubbersheeting,
or orthorectifying the data
Georeferencing – why?
 Raster data is commonly obtained by scanning maps
or collecting aerial photographs and satellite images
 Scanned map datasets don't normally contain spatial
reference information
 aerial photography and satellite imagery, sometimes
the location information delivered with them is
inadequate and the data does not align properly with
other data you have. Thus, to use some raster datasets
in conjunction with your other spatial data, you may
need to align, or georeference, to a map coordinate
system.
Georeferencing - Transformation
 Coordinates
in the source
system
 Coordinates
in the target
system