Map Projections
and Map
Coordinate
Systems
Jamie Wolfe
CITE
Marshall University
Huntington, WV - 25755
304-696-6042
[email protected]
IS 645 Introduction
to GIS
Lecture 03, May 23, 2000
Today’s class topics
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Map Projections
• Cylindrical
• Conical
• Azimuthal
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Map Distortions
Map Coordinate Systems
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Latitude, Longitude, height
Earth Centered, Earth Fixed XYZ
Universal Transverse Mercator (UTM)
Military Grid Reference System (MGRS)
World Geographic Reference System (GEOREF)
State Plane Coordinate Systems (SPCS)
IS 645: Geographic Information Systems, Summer 2000, J. Wolfe
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Map Projections
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Map projections are attempts to portray the
surface of the earth or a portion of the earth on a
flat surface
The map projection can be onto a flat surface or a
surface that can be made flat by cutting, such as a
cylinder or a cone
If the globe, after scaling, cuts the surface, the
projection is called secant. Lines where the cuts
take place or where the surface touches the globe
have no projection distortion
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Map Projections
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Some distortions of conformality (shape),
distance, direction, scale, and area always result
from this process. Some projections minimize
distortions in some of these properties at the
expense of maximizing errors in others. Some
projection are attempts to only moderately distort
all of these properties
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Map Projections
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Three common types of projections are:
• Cylindrical
• Conical
• Azimuthal (Planar)
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Map projections: Cylindrical
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A cylindrical projection can be imagined in its
simplest form as a cylinder that has been
wrapped around a globe at the equator. If the
graticule of latitude and longitude are projected
onto the cylinder and the cylinder unwrapped,
then a grid-like pattern of straight lines of latitude
and longitude would result. The meridians of
longitude would be equally spaced and the
parallels of latitude would remain parallel but may
not appear equally spaced anymore
Cylindricals are true at the equator and distortion
increases toward the poles
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Map projections: Cylindrical Regular
and Secant
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Map projections: Cylindrical Oblique
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Tangent or secant to
another point on the globe
is called oblique
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Map projections: Cylindrical
Transverse
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Tangent or secant to a
meridian is the transverse
aspect
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Map projections: Conical
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In the Conical Projection the
graticule is projected onto a cone
tangent, or secant, to the globe
along any small circle (usually a
mid-latitude parallel)
In the normal aspect (which is
oblique for conic projections),
parallels are projected as
concentric arcs of circles, and
meridians are projected as
straight lines radiating at uniform
angular intervals from the apex of
the flattened cone. Conic
projections are not widely used in
mapping because of their
relatively small zone of
reasonable accuracy
IS 645: Geographic Information Systems, Summer 2000, J. Wolfe
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Map projections: Conical
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The secant case, which produces
two standard parallels, is more
frequently used with conics. Even
then, the scale of the map rapidly
becomes distorted as distance
from the correctly represented
standard parallel increases.
Because of this problem, conic
projections are best suited for
maps of mid-latitude regions,
especially those elongated in an
east- west direction. The United
States meets these qualifications
and therefore is frequently
mapped on conic projections
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Map projections: Conical
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Conics are true along some
parallel somewhere between the
equator and a pole and distortion
increases away from this
standard
IS 645: Geographic Information Systems, Summer 2000, J. Wolfe
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Map projections: Planar or Azimuthal
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Imagine a plane being placed against (tangent to)
a globe. If a light source inside the globe projects
the graticule onto the plane the result would be a
planar, or azimuthal, map projection.
If the imaginary light is inside the globe it is
called Gnomonic
If the light is antipodal (diametrically opposite) it
is called Sterographic
If light source is at infinity, it is called
Orthographic
Azimuthals are true only at their center point, but
generally distortion is worst at the edge of the
map
IS 645: Geographic Information Systems, Summer 2000, J. Wolfe
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Map projections: Azimuthal or Planar
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Map Projections: Distortions
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Projections can be based on axes parallel to the
earth's rotation axis (equatorial), at 90 degrees to
it (transverse), or at any other angle (oblique)
A projection that preserves the shape of features
across the map is called conformal
A projection that preserves the area of a feature
across the map is called equal area or equivalent
No flat map can be both equivalent and
conformal. Most fall between the two as
compromises
To compare or edge-match maps in a GIS, both
maps MUST be in the same projection
IS 645: Geographic Information Systems, Summer 2000, J. Wolfe
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Map Projections Distortions
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Conformality
• When the scale of a map at any point on the map is the
same in any direction, the projection is conformal.
Meridians (lines of longitude) and parallels (lines of
latitude) intersect at right angles. Shape is preserved
locally on conformal maps
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Area
• When a map portrays areas over the entire map so that
all mapped areas have the same proportional
relationship to the areas on the Earth that they
represent, the map is an equal-area or equivalent map
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Distance
• A map is equidistant when it portrays distances from the
center of the projection to any other place on the map
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Map Projections Distortions
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Direction
• A map preserves direction when azimuths (angles from
a point on a line to another point) are portrayed
correctly in all directions
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Scale
• Scale is the relationship between a distance portrayed
on a map and the same distance on the Earth
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Different map projections result in different
spatial relationships between regions
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Map projections: Cylindrical (Normal)
Characteristics
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Lines of latitude and longitude are parallel
intersecting at 90 degrees
Meridians are equidistant
Forms a rectangular map
Scale along the equator or standard parallels is
true
Simple construction
Can have the properites of equidistance,
conformality or equal area
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Map Projections: Cylindrical Equal
Area: Behrmann
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Uses 30 degree North as parallel of no distortion
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Map Projections: Cylindrical
Conformal: Mercator
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Straight lines are lines of constant azimuth
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Map Projections: Cylindrical
Stereographic: Gall’s
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Secant intersection at 45 N and 45 S
Moderately distorts area, direction, distance, shape
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Map projections: Conical
Characteristics
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In the normal aspect (which is oblique for conic
projections), parallels are projected as concentric
arcs of circles, and meridians are projected as
straight lines radiating at uniform angular
intervals from the apex of the flattened cone.
Conic projections are not widely used in mapping
because of their relatively small zone of
reasonable accuracy.
IS 645: Geographic Information Systems, Summer 2000, J. Wolfe
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Map projections: Conical
Characteristics
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The secant case, which produces two standard
parallels, is more frequently used with conics.
Even then, the scale of the map rapidly becomes
distorted as distance from the correctly
represented standard parallel increases.
Because of this problem, conic projections are
best suited for maps of mid-latitude regions,
especially those elongated in an east- west
direction. The United States meets these
qualifications and therefore is frequently mapped
on conic projections.
IS 645: Geographic Information Systems, Summer 2000, J. Wolfe
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Map projections: Conical Equal Area
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Distorts scale and distance except along standard
parallels
Areas are proportional and directions are true in
limited areas
Used in the United States and other large countries
with a larger east-west than north-south extent
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Map projections: Conical Equal Area
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Map projections: Conical Equidistant
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Equally Spaced Parallels. Equidistant Meridians
converging at a common point
Direction, area, and shape are distorted away
from standard parallels. Used for portrayals of
areas near to, but on one side of, the equator
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Map projections: Conical Equidistant
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Map projections: Conical Conformal
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Area, and shape are distorted away from
standard parallels. Directions are true in limited
areas. Used for maps of North America
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Map projections: Conical Conformal.
USA
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Map projections: Azimuthal (Planar)
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Imagine a plane being placed against (tangent to)
a globe. If a light source inside the globe projects
the graticule onto the plane the result would be a
planar, or azimuthal, map projection
If the imaginary light is inside the globe it is
called Gnomonic
If the light is antipodal (diametrically opposite) it
is called Sterographic
If light source is at infinity, it is called
Orthographic
Azimuthals are true only at their center point, but
generally distortion is worst at the edge of the
map
IS 645: Geographic Information Systems, Summer 2000, J. Wolfe
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Map projections: Azimuthal Lambert
Equal Area
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Used to map large ocean areas. The central
meridian is a straight line, others are curved. A
straight line drawn through the center point is on
a great circle.
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Map projections: Azimuthal
Equidistant
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Used to show air-route distances. Distances
measured from the center are true. Distortion of
other properties increases away from the center
point.
IS 645: Geographic Information Systems, Summer 2000, J. Wolfe
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Map projections: Azimuthal Conformal
(Stereographic)
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Used for navigation in polar regions. Directions
are true from the center point and scale increases
away from the center point as does distortion in
area and shape.
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Map projections: Azimuthal
Orthographic
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Used for perspective views of hemispheres. Area
and shape are distorted. Distances are true along
the equator and other parallels.
IS 645: Geographic Information Systems, Summer 2000, J. Wolfe
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Map projections: Azimuthal Gnomonic
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Neither conformal nor equal area.
Is used by navigators and aviators because greatcircle paths (shortest distances) are shown as
straight lines.
Less than one hemisphere can be viewed from a
given origin.
Scale is true only where the central parallel and
meridian cross.
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Map projections: Azimuthal Gnomonic
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Coordinates basics
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Polar to cartesian coordinates
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Coordinate Systems
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A coordinate system is a standardized method for
assigning codes to locations so that locations
can be found using the codes alone
Standardized coordinate systems use absolute
locations
A map captured in the units of the paper sheet on
which it is printed is based on relative locations
or map millimeters
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Coordinate Systems
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Some standard coordinate systems used are:
• geographic coordinates
• Lat-long, geodetic lat long, Earth Centered Earth Fixed XYZ
• Universal Transverse Mercator (UTM) system
• military grid
• state plane coordinate system
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To compare or edge-match maps in a GIS, both
maps MUST be in the same coordinate system.
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Latitude, Longitude, Height
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The most commonly used coordinate system
today is the latitude, longitude, and height system
The Prime Meridian and the Equator are the
reference planes used to define latitude and
longitude
Geographic coordinates are the earth's latitude
and longitude system, ranging from 90 degrees
south to 90 degrees north in latitude and 180
degrees west to 180 degrees east in longitude
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Latitude, Longitude, Height
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A line with a constant latitude running east to
west is called a parallel
A line with constant longitude running from the
north pole to the south pole is called a meridian
The zero-longitude meridian is called the prime
meridian and passes through Greenwich,
England
A grid of parallels and meridians shown as lines
on a map is called a graticule
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Latitude, Longitude, Height
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Distances on the great circle
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Geodetic Latitude, Longitude, Height
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The geodetic latitude of a point is the angle from
the equatorial plane to the vertical direction of a
line normal to the reference ellipsoid.
The geodetic longitude of a point is the angle
between a reference plane and a plane passing
through the point, both planes being
perpendicular to the equatorial plane.
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Geodetic Latitude, Longitude, Height
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The geodetic height at a point is the distance
from the reference ellipsoid to the point in a
direction normal to the ellipsoid.
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Earth Centered Earth Fixed XYZ
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Cartesian coordinates (XYZ) define three
dimensional positions with respect to the center of
mass of the reference ellipsoid.
The Z-axis points toward the North Pole
The X-axis is defined by the intersection of the
plane defined by the prime meridian and the
equatorial plane
The Y-axis completes a right handed orthogonal
system by a plane 90 degrees east of the X-axis
and its intersection with the equator
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Earth Centered Earth Fixed XYZ,
Example
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Eastings and Northings
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Traditionally, rectangular coordinates are used
when reading maps, with the X value first and the
Y value second
When map is oriented with north on top, X value
is called easting because it measures distances
east of the origin and the Y value is called
northing because it measures distances north of
the origin
Origin is placed so that all references are positive
False origins may have to be placed at several
places to ensure more accurate measurements.
Easting and Northings from the false origin are
called false eastings and false northings
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Universal Transverse Mercator (UTM)
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Universal Transverse Mercator (UTM) is the most
prevalent system used for mapping and other
work
UTM zone numbers designate 6 degree
longitudinal strips (60 vertical zones) extending
from 80 degrees South latitude to 84 degrees
North latitude. Zone numbers start from the 180th
meridian in an eastward direction
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Universal Transverse Mercator Grid
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Universal Transverse Mercator (UTM)
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For eastings, a false origin (easting value 500,000
meters) is established at the center of each zone
UTM zone characters designate 8 degree zones
extending north and south from the equator
For northings, it has two primary ordinate points,
one at the equator and the other at 80 degrees
south
For small scale maps, the last digit may be
dropped to decrease resolution to 10 meters.
Decimal may be used for more accuracy on large
scale maps
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UTM zones in the lower 48
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UTM Zone 14
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Each zone has a central
meridian. Zone 14, for
example, has a central
meridian of 99 degrees
west longitude. The zone
extends from 96 to 102
degrees west longitude.
Eastings are measured
from the central meridian
(with a 500km false easting
to insure positive
coordinates).
Northings are measured
from the equator (with a
10,000km false northing
for positions south of the
equator).
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Reading a UTM measurement
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Military Grid Reference System (MGRS)
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MGRS is an extension of the UTM system. UTM
zone number and zone character are used to
identify an area 6 degrees in east-west extent and 8
degrees in north-south extent.
UTM zone number and designator are followed by
100 km square easting and northing identifiers.
The system uses a set of alphabetic characters for
the 100 km grid squares.
Starting at the 180 degree meridian the characters
A to Z (omitting I and O) are used for 18 degrees
before starting over.
From the equator north the characters A to V
(omitting I and O) are used for 100 km squares,
repeating every 2,000 km. The reverse sequence
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(fromIS 645:
V to
A) is used for southern hemisphere
Military Grid Reference System (MGRS)
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Military Grid Reference System (MGRS)
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Military Grid Reference System
(MGRS)
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UTM zone number, UTM zone, and the two 100 km
square characters are followed by an even
number of numeric characters representing
easting and northing values.
If 10 numeric characters are used, a precision of
1 meter is assumed.
2 characters imply a precision of 10 km.
From 2 to 10 numeric characters the precision
changes from 10 km, 1 km, 100 m 10 m, to 1 m.
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Military Grid
Reference
System (MGRS)
Example
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World Geographic Reference System
(GEOREF)
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The World Geographic Reference System is used
for aircraft navigation.
GEOREF is based on latitude and longitude.
The globe is divided into twelve bands of latitude
and twenty-four zones of longitude, each 15
degrees in extent.
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World Geographic Reference System
(GEOREF)
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World Geographic Reference System
(GEOREF)
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These 15 degree areas are further divided into
one degree units identified by 15 characters.
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State Plane Coordinate System (SPCS)
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In the United States, the State Plane System was
developed in the 1930s and was based on the
North American Datum 1927 (NAD27).
NAD 27 coordinates are based on the foot
While the NAD-27 State Plane System has been
superseded by the NAD-83 System, maps in NAD27 coordinates (in feet) are still in use. The State
Plane System 1983 is based on the North
American Datum 1983 (NAD83)
NAD 83 coordinates are based on the meter.
State plane systems were developed in order to
provide local reference systems that were tied to
a national datum
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State Plane Coordinate System (SPCS)
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Some smaller states use a single state plane
zone.
Larger states are divided into several zones.
State plane zone boundaries often follow county
boundaries.
Lambert Conformal Conic projections are used
for rectangular zones with a larger east-west than
north- south extent.
Transverse Mercator projections are used to
define zones with a larger north-south extent.
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State Plane Coordinate System (SPCS)
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State Plane Coordinate System (SPCS)
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State Plane Coordinate System (SPCS)
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WV SPCS
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Has two zones: North and South
Uses the Lambert Conformal Conic projection
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