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Coordinate and Map
Projection Systems
Dr Muhammad Ateeq Qureshi
Assistant Professor
NCRG-IST
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From the early civilizations, the effort for determining shape and
size of earth was a major challenge to humans.
Earth Shape?
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Earth Shape?
A Greek geographer, gave the notion of spherical earth in
second century B.C.
Isaac Newton first proposed that Earth was not perfectly round
He suggested it was an oblate spheroid — a sphere that is
squashed at its poles and swollen at the equator.
Actually, the Earth is not perfectly spherical.
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Earth Shape?
What is the precise shape of the Earth?
Is it a sphere, spheroid, or something else?
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Spheres and Spheroids
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Spheres
• Sphere is based on a circle.
• The shape of Earth is represented as a sphere through
simplifies many mathematical calculations.
• Depending on the application, the Earth is modeled as a
sphere.
• Possible for small scale maps (1:5,000,000 or less)
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Spheroids
• The Earth shape can be mathematically modeled more
accurately as a spheroid.
• Spheroid approximates the shape of the Earth.
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The Earth is not a perfect spheroid.
Different spheroids are used in different parts of
the world to create the best possible model of
the Earth’s curvature in each location
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Earth Shape?
But now researchers have confirmed that earth’s surface is not
spherical or flat rather it is oblate ellipsoidal, which means all
points on the surface of the earth are not equidistant from the
geometric centre
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Latitude - Longitude
Latitude lines are parallel to the Equator and
Longitude lines are perpendicular to the Prime Meridian
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Latitude varies from 0o at the equator to 90o North and
South at the poles
Longitude varies from 0o at Greenwich to 180o East and
West
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Latitude
• Measured Northward or Southward from the Equator to poles
• Ranging 0 - 900 North or South
• The measuring units are degrees, minutes, and seconds, 10 =
60’ and 1’= 60”
• The length of one degree latitude is similar everywhere, ~69
miles / 111km. The range varies (due to the Earth's slightly
ellipsoid shape) from ~68.703 miles (110.567 km) at the
equator to ~69.407 (111.699 km) at the poles.
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• Measured Eastward or Westward from the Prime Meridian at
Greenwich, England to the International Date Line.
• Ranging 0 -1800 East or West, The measuring units are
degrees, minutes, and seconds, 10 = 60’ and 1’=60”
• Length of one degree longitude reduces toward poles.
• A degree of longitude is widest at the equator at ~69.172
miles / 111.321 km and gradually shrinks to zero at the poles.
• At 40° North or South the distance between a degree of
longitude is ~53 miles / 85 km
Longitude
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Datum
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Datum
• A datum is a mathematical model related to real-world
features.
• The datum consists of a series of numbers that define the
shape and size of the ellipsoid and it's orientation in space.
• A datum is chosen to give the best possible fit to the true
shape of the Earth.
• Most datums are created for use only in specific areas of the
Earth, but the World Geodetic Systems (WGS) can be used
globally.
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Major Types
• Geodetic: Aligns the spheroid to fit to a particular area.
• Geocentric: Uses the Earth’s centre of mass as the origin
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Coordinate Systems
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Coordinate System
• “Location” is the first step towards understanding the spatial
concept.
• The absolute or true location of any point in space can be
defined by its values knows as coordinates.
• A reference system used to measure horizontal and vertical
distance on a flat map.
• Actually, it is used to define a location on the Earth.
• It is created in association with a map projection, datum,
and reference ellipsoid and describes locations in terms of
distances or angles from a fixed reference point.
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Coordinate System
• The system may be either a Cartesian system, with
coordinates based on orthogonal or 90-degree angles, or it
may be polar, based on angles measured from a point such
as the center of the Earth.
• For example, in the latitude / longitude system, positions are
described based on angular measurements North or South of
the Equator and East or West of the Prime Meridian, which runs
through Greenwich, England. This is considered a polar
system.
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Coordinate System
X’ X
Y’
Y
0,0
Y1
X1
1, 1P (X Y )
180o 0o
270o
90o
P(r1,01)
r
0
Cartesian Polar
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Types of Coordinate Systems
The following are two common types of coordinate systems used in a
geographic information system (GIS):
• Geographic Coordinate System (GCS)
• Projected Coordinate System (PCS)
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Geographic Coordinate Systems (GCS):
• A coordinate system that enables every location on Earth to
be specified by a set of numbers, letters or symbols.
• The coordinates are often chosen such that one of the
numbers represents a vertical position and two or three of the
numbers represent a horizontal position; alternatively, a
geographic position may be expressed in a combined three-
dimensional Cartesian vector.
• A common choice of coordinates is latitude, longitude and
elevation.
• To specify a location on a plane requires a map projection.
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Projected Coordinate System (PCS)
• A PCS is defined on a flat, two-dimensional surface.
• Unlike a GCS, a PCS has constant lengths, angles, and areas
across the two dimensions.
• A PCS is always based on a GCS that is based on a sphere or
spheroid.
• In addition to the GCS, a PCS includes a map projection, a set
of projection parameters that customize the map projection
for a particular location, and a linear unit of measure.
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What is Map Projection?
Systematic arrangement of lines of latitudes and longitudes
on a plane is called map projection
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Map Projection
• A map projection is a mathematical model for conversion of
locations from a three-dimensional Earth surface to a two-
dimensional map.
• This conversion necessarily distorts some aspect of the Earth's
surface, such as Area, Shape, Distance, or Direction.
• Projection types are based on the geometric form used in the
transfer from the spherical Earth to a flat surface.
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Steps in Map Projection
Reduction &
Projection
Reduction Generating
Globe
Projection
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Classification of Map Projection
Basis Classes
Method of Construction 1. Perspective
2. Non-perspective
Preservation of qualities 1. Homolographic/equal area
2. Orthomographic/conformal
Developable surface area 1. Cylindrical
2. Conical
3. Azimuthal/zenithal
4. Conventional
Position of tangent surface 1. Polar
2. Equidistant/Normal
3. oblique
Position of viewpoint or light 1. Gnomonic
2. Stereographic
3. Orthographic
4. Others
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Construction of Map Projection
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Gnomonic
The light source at the centre of the globe
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The light source at the antipode of the point of tangency
Stereographic
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The light source an infinite distance from the point of tangency,
resulting in parallel light rays.
Orthographic
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Types of Map Projections
Cylindrical
• (Transverse Mercator) - good for North-South land areas.
Conical
• (Albers Equal Area, Lambert Conformal Conic) - good
for East-West land areas.
Azimuthal
• (Lambert Azimuthal Equal Area) - good for global views.
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Types of Map Projections
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Basic of Map Projections
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Also called azimuthal or zenithal
Can be any aspect
Planar Projections
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Planar Projections - Perspective
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Planar Projections - Orthographic
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Planar Projections - Sterographic
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Planar Projections - Gnomonic
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Cylindrical projections
Best for equatorial or low latitudes
Rotate cylinder to reduce distortion along a line
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Normal - equatorial / East-West
Transverse - North-South regions
Oblique - other angles
Cylindrical Projections
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Cylindrical Projections - Mercator
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Cylindrical Projections - Miller
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Cylindrical Equal-Area Projection
Mollweide Projection
(equal-area, psuedo-cylindrical)
Cylindrical Projections
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Conical Projections
Best for mid-latitudes with an
East-West orientation.
Tangent or secant along 1 or 2 lines of latitude known as
‘standard parallels’.
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Conical Projections
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Conical Projections
Albers Equal AreaLambert Conformal
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Map projection
Projection always introduces distortion of entities
Conformity: when the scale of a map at any point on the map is the same in
any direction, the projection is caller conformal. Meridians (lines of longitude)
intersect at right angles. Shape is preserved locally on conformal maps.
Distance : A map is equidistant when it portrays distance from the
center of the projection to any other place on the map.
Direction: A map preserve direction when azimuths (angles from a point
on a line to another point) are portrayed correctly in all directions.
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Map projection
Scale: Scale is the relationship between a distance portrayed on a map
and the same distance on the Earth.
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 map
Source: Dana,1999
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Robinson Projection -- 16,930 Miles
Length of the Arctic Coastline of Russia
Oblique Mercator Projection
-- 10,473 Miles
Mercator Projection
-- 31,216 Miles
Length distortion on World Maps
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Montana State Plane Coordinates
-- 13,138.6 Meters
Oblique Mercator Projection --
13,143.5 Meters
Difference = 4.88 Meters One part in 2692 0.0371 Percent
Length distortion on local Maps
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Mercator Projection
Lower 48 States --
52,362,000 Sq Miles
Columbia --
4,471,000 SqMiles
Mollweide Projection (equal-area)
Lower 48 States --
30,730,000 Sq Miles
Columbia --
4,456,000 SqMiles
Area distortion on World Maps
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Montana State Plane Coordinates
-- 122,314.3 Acres
Albers Equal Area Projection --
122,425.2 Acres
Difference = 110.9 Acres One part in 1104 0.091 Percent
Area distortion on local Maps
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ThanksQuestions?