This document discusses map projections and their characteristics. It defines map projections as systematic transformations of a spherical surface to a flat surface for mapping purposes. Several types of map projections are described, each with specific properties and distortions. An ideal map projection is defined as one that accurately represents distances, angles, great circles and coordinates without any distortions, but in practice no single projection can achieve this. Key factors like scale, scale factor and representing scale on maps are also covered.

1. Module II
Map Projections

3. MAPS
Definitions
"A representation, usually on a plane
surface, of all or part of the earth or
some other body showing a group of
features in terms of their relative size
and position."
»Norman Thrower

4. MAPS
Definitions
A map is a selective, symbolized,
generalized and planimetric picture
of spatial distribution of the earth’s
surface on a definite scale with
annotations

5. Map Types
It is not possible to represent all features of
earth on maps, since they are numerous.
Classification on the basis of
Scale
Usage

6. Map Types
1.Cadastral maps (Planimetric maps)1.Cadastral maps (Planimetric maps)1.Cadastral maps (Planimetric maps)1.Cadastral maps (Planimetric maps)
2.Topographic maps2.Topographic maps2.Topographic maps2.Topographic maps
3.Thematic maps3.Thematic maps3.Thematic maps3.Thematic maps
4.Remotely sensed images4.Remotely sensed images4.Remotely sensed images4.Remotely sensed images

7. Cadastral maps
A map which provides detailed information about real
property within a specific area
•Used to demarcate boundaries of fields and buildings
and for registering ownership of landed properties
•Prepared and compiled by government agencies and
used for revenue and tax purposes
Examples. Village maps or city plan maps

8. Cadastral map

9. Topographic maps
• A topographic map is a detailed and accurate
graphic representation of cultural and natural
features on the ground.
• Shows the shape and elevation of the terrain
• Used for designing gardens, parks, buildings, roads and
pipelines
• Examples. Flood control maps and engineering maps

10. Topographic map

11. Thematic maps
• A thematic map is a type of map or chart especially
designed to show a particular theme connected with a
specific geographic area.
• These maps "can portray physical, social, political,
cultural, economic, sociological, agricultural, or any
other aspects of a city, state, region, nation , or
continent”

12. Thematic map

13. Remotely sensed images
• These are geographic information
gathered by means of a sensor which
include aerial photographs, radar images
and satellite images
• These are important sources for producing
digital maps and are useful for monitoring
environmental changes and human activities

14. Remotely sensed image

15. MAP PROJECTION

16. Geodesy and Map Projections
• Geodesy - the shape of the earth and
definition of earth datums
• Map Projection - the transformation of a
curved earth to a flat map
• Coordinate systems - (x,y) coordinate
systems for map data

17. Coordinate System
(φo,λo)
(xo,yo)
X
Y
Origin
A planar coordinate system is defined by a pair
of orthogonal (x,y) axes drawn through an origin

18. Map Projections
Map projection: a system of parallels and meridians
representing the Earth’s curved surface drawn on a flat surface
• Curved surface cannot be projected onto a flat sheet without distortion
• Each map projection has a specific purpose
• Each projection has advantages and drawbacks

19. MAP PROJECTIONSMAP PROJECTIONS
• Map projection is a systematic transformation
of a spatial surface to a surface that is
convenient to work with.
• A spherical co-ordinate system (like latitude and
longitude) works well only if one is using a globe but
not if one has to display the data on a flat surface like
a map
.

21. Latitude and Longitude on a Sphere
Meridian of longitude
Parallel of latitude
ϕ
λ
X
Y
Z
N
EW
ϕ
ϕ=0-90°S
P
O
R
λ=0-180°E ϕ=0-90°N
•
Greenwich
meridian
λ=0°
•
Equator =0°
•
•
λ=0-180°W
λ - Geographic longitude
ϕ - Geographic latitude
R - Mean earth radius
O - Geocenter

22. • In practice map projections use mathematical
formulae to convert from one coordinate system to
the other.
• Where f and g are transformation functions for a
particular projection.
example relations for Mercator projection are:
( )
( )λφ
λϕ
,
,
gy
fx
=
=
,λ=x ( )4/2/tanln πφ +=y

23. Geographic and Projected Coordinates
(φ, λ) (x, y)
Map Projection

24. Transformation functionsTransformation functions
1.1. UniquenessUniqueness - The functions should be unique
so that a point on the surface of earth will
appear at only one position of the map.
2.2. FinitenessFiniteness – The function should be finite so
that a point will not appear at an infinite
distance and hence remain unplotted. There
are exceptions.
3.3. ContinuousContinuous – There should not be gaps on the
projected surface

25. Map Characteristics
Map Scale: Map distance to Real distance-
Expressed as a ratio or fraction
The unit on the left indicates distance on the map
and the number on the right indicates distance on
the ground. Eg 1:1000, 1/100,000
Small-Scale , Medium-Scale and Large-Scale
< 1 : 1,000,000 >1 : 75,000
Large scale maps have more details

26. Map scale
Representing the Scale of a Map
• Bar Scale A bar scale shows a graphic
representation, where the actual distance
on the map is measured and compared it
to the bar scale

27. Map scale (Contd…)
Representing the Scale of a Map
Representative fraction gives a number scale
represented by a fraction or a ratio

28. Map scale (Contd…)
Representing the Scale of a Map
Textual scale describes the scale in words
A representative fraction of 1:1,00,000
may be expressed as 1 cm on the map
equals to 1 kilometer on the ground

29. Scale factor
• It is the ratio of the map distance to the
globe distance
• Scale factor on a map is generally not
constant for various points, thus scale of a
map is not uniform for the entire map.
• This is in contrast to a plan which has a
uniform scale.

30. Earth to Globe to Map
Representative Fraction
Globe distance
Earth distance
=
Map Scale: Map Projection:
Scale Factor
Map distance
Globe distance
=
(e.g. 1:24,000) (e.g. 0.9996)

31. Ideal Map Projection
An ideal map projection is that in which there is no
distortion and all the lines and angles are
represented correctly. An ideal map projection
should satisfy the following conditions
1.All distances and areas on the map should have
correct relative magnitude as those on the surface
of the earth.
2. All angles and azimuths on the map should be the
same as those on the surface of the earth.

32. Ideal Map Projection (Contd…)
3. All great circles on the earth should appear as straight
lines on the map.
4. Longitudes and latitudes of all points should be shown
correctly on the map.
It is not possible to satisfy all these in the same map.
Only one or two conditions are satisfied in a
particular projection and selection for a particular
purpose and area made according to suitability.