Map Projections in GIS

Samirsinh P. Parmar
Dept. of Civil Engineering
Dharmsinh Desai University, Nadiad
Mail: spp.cl@ddu.ac.in, samirddu@gmail.com

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Map Projections in GIS, Samirsinh Parmar, DoCL, DDU, Nadiad.

Projection
Transformation of Three Dimensional Space onto a
two dimensional map
A systematic arrangement of intersecting lines on a
plane that represent and have a one to one
correspondence to the meridians and parallels on
the datum surface
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Developable Surfaces
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Classification
A) Based on Extrinsic property
 Nature:
 Plane, Cone, Cylinder
 Coincidence:
 Tangent, Secant, Polysuperficial
 Position:
 Normal, Transverse, Oblique
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Azimuthal Projections
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Cylindrical Projections
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Tangent
Oblique
Transverse
Secant

Conic Projections
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Classification contd.
B) Based on Intrinsic Property
 Property of Projection:
 Equidistant
 Conformal or Orthomorphic
 Equivalent or Equal area
 Generation:
 Geometric, Semi Geometric, Mathematical
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Cylindrical Map Projections
 Cylindrical map projections are made by projecting from the globe onto the
surface of an enclosing cylinder, and then unwrapping the cylinder to make a
flat surface
 Mercator
 Transverse Mercator
 Cassini-Soldner
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Mercator Projection
 Cylindrical, Conformal
 Meridians are equally spaced straight lines
 Parallels are unequally spaced straight lines
 Scale is true along the equator
 Great distortion of area in polar region
 Used for navigation
 Limitations
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REGULAR CYLINDRICAL PROJECTION:
THE MERCATOR

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Transverse Mercator Projection
 Cylindrical (Transverse)
 Conformal
 Central meridian and equator are straight lines
 Other meridians and parallels are complex curves
 For areas with larger north-south extent than east-west extent
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TRANSVERSE CYLINDRICAL PROJECTION:
THE TRANSVERSE MERCATOR

Cassini- Soldener Projection
Cylindrical, Tangent, Transverse
Equidistant
Cylinder is tangent along the meridian centrally located
Scale deteriorates away from central meridian
Normally used in 70 km belt from the central meridian,
as linear distortion factor at 70 km is 1.00006
Used for old cadastral surveys in India.
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CASSINI-SOLDENER PROJECTION

Conic Projections
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 For a conic projection, the
projection surface is cone shaped
 Locations are projected onto the
surface of the cone which is then
unwrapped and laid flat

Lambert Conformal Conic Projection
 Conical, Conformal
 Parallels are concentric arcs
 Meridians are straight lines cutting parallels at right angles.
 Scale is true along two standard parallels, normally, or along
just one.
 It projects a great circle as a straight line – much better than
Mercator
 Used for maps of countries and regions with predominant
east west expanse
 Used for plane coordinate system (SPCS) in USA
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LCC PROJECTION

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LCC PROJECTION

Polyconic Projection
In this projection all parallels are projected without
any distortion
Scale is exact along each parallel and central
meridian.
Parallels are arcs of circles but are not concentric.
It is neither conformal nor equal area.
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Polyconic Projection contd.
Central meridian and equator are straight lines;
all other meridians are curves.
Central Meridian cuts all parallels at 90 degrees
Free of distortion only along the central
meridian.
It has rolling fit with adjacent sheets in EW
direction.
Used in India for all topographical mapping on
1:250,000 and larger scales.
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Three partial equidistant conic maps, each based on a different standard
parallel, therefore wrapped on a different tangent cone (shown on the right
with a quarter removed plus tangency parallels). When the number of cones
increases to infinity, each strip infinitesimally narrow, the result is a
continuous polyconic projection

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POLYCONIC PROJECTION
CENTRAL MERIDIAN: 100° W

Azimuthal Projections
 For an azimuthal, or planar projection, projected forward onto
a flat plane.
 The normal aspect for these projections is the North or South
Pole. locations are
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Universal Polar Stereographic (UPS)
 Defined above 84 degrees north latitude and 80 degree south
 Conformal
 Meridians are straight lines
 Parallels are circles
 Scale increases from center point
 Used in conformal mapping of polar regions
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Grids
 Rectangular grids have been developed for the use of Surveyors.
 Each point can be designated merely by its ( x , y ) co-ordinates.
 Grid systems are normally divided into zones so that distortion and
variation of scale within any one zone are kept small.
 The UTM grid
 State Plane Coordinate System (SPCS)
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False Northing and False Easting
 Calculating coordinates is easier if negative number aren’t involved.
 Indian Grid and Universal transverse Mercator coordinates
 Expressed in coordinate units, not degrees.
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SPECIFYING AN ORIGIN SHIFT:
THE FALSE EASTING AND FALSE NORTHING
Central Meridian
Natural Origin
Central Parallel
Coordinate System
Origin
False Easting
False
Northing

Universal Transverse Mercator (UTM)
 Particular case of Transverse Mercator Projection.
The earth between latitudes 84 N and 80 S, is divided
into 60, 6 wide strips;
Latitude origin – the Equator
Assumed (false) northing (y) at Equator
0 m for northern hemisphere
10,000,000 m for southern hemisphere
Assumed (false) easting (x) at Central Meridian
500,000 m
Scale factor at the central meridian : 0.9996
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Figure

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Projection Parameters
To define the coordinate system completely, it is not
sufficient simply to name the kind of projection used,
it is also necessary to specify the projection
parameters.
The set of parameters required depends on the kind of
projection.
The central meridian of the projection for cylindrical,
where it touches the ellipsoid surface.
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Projection Parameterscontd.
 The standard parallel(s) for conic projections.
 The false easting and false northing
 The units
 Reference ellipsoid
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Choosing a map Projection
The choice of map projection is made to give the most
accurate possible representation of the geographic
information, given that some distortion is inevitable.
The choice depends on:
The location
Shape
Size of the region to be mapped
The theme or purpose of the map
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SHAPE OF AREA

Some Related Terms
 Coordinate System
 Reference Ellipsoids
 Everest Ellipsoid
 GRS 80
 WGS 84
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Implications for GIS
Knowing the datum and reference ellipsoid
information is very important.
For converting the maps of one system to another
system.
When incorporating maps or GPS field data into a
GIS
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Coordinate System
Need to describe the location, i.e. referencing
network by which positions are measured and
computed.
Relative location (with respect to some other place).
E.g. Street address.
• Absolute location (with respect to the Earth as a
whole).
E.g. Geographic coordinates
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Objects in Real World
(Earth)
Geographic Coordinates
( ø , λ )
Represented on Paper
or Screen
(Map)
Planar Coordinates
( x , y )
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REFERENCE ELLIPSOID
 All the measurements are done on the surface of the Earth.
Various computations are required to determine the
coordinates, distances, area etc.
 The surface of the earth is irregular and therefore unsuitable
for such computations. We need a smooth mathematical
surface for these computations.
 The best mathematical figure that can represent the earth is
an ellipsoid. Ellipsoid is used as reference surface.
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TYPES OF ELLIPSOIDS
1. Best-Fit Ellipsoid/Local Ellipsoid: based on the measurements
within a region, so it best fits that region only. The centre of
such reference ellipsoid does not coincide with the centre of
gravity of the Earth.
Example : Everest Ellipsoid
2. Geocentric Ellipsoid: The centre of geocentric ellipsoid
coincides with the centre of the Earth. This type of the
ellipsoid can be used worldwide.
Example : WGS 84 ellipsoid
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Best Fit and Geocentric Ellipsoids
Centre of Best Fit
Ellipsoid
Centre of Geocentric Ellipsoid
Best Fit
Ellipsoid
Geocentric Ellipsoid
Earth Surface
Best Fit
Ellipsoid

DATUM
Datum is a model that describes the position,
direction, and scale relationships of a reference
surface to positions on the surface of Earth
Indian Datum
WGS 84
ITRF
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Scale
Only on a globe is a scale constant. It is impossible
to have a constant scale in different areas of a map
(but we can get close)
Map has fixed scale but GIS is scale-less, i.e. data
may be enlarged or reduced to any size.
However, if we go too far from the scale at which
map was made before it was captured into the GIS,
problems of scale appear.
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Map Distance
Scale = -----------------------------
Ground Distance
 Representative fraction (RF) is the ratio of distances on the map to the
same distance on the ground. E.g., 1 : 1,000,000 or 1/1,000,000
 Statement (verbal) scale expresses the ratio in words. for 1 : 1,000,000 :
“One millimeter to one kilometer”
 Bar scale is a linear graphical scale drawn on the map
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Scale in Map Projections
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Conclusions
 We need to project geospatial data for any analysis
 Makes it possible to use data from different sources
 Several Projections to choose from
 Projections inevitably distorts at least one property
 Can choose suitable Map Projection
 Can control scale error
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Map Projections in GIS

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