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Module II
Map Projections
Surveying II ajith sir class 1
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
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
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
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
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
Cadastral map
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
Topographic map
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”
Thematic map
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
Remotely sensed image
MAP PROJECTION
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
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
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
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
.
Surveying II ajith sir class 1
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
• 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
Geographic and Projected Coordinates
(φ, λ) (x, y)
Map Projection
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
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
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
Map scale (Contd…)
Representing the Scale of a Map
Representative fraction gives a number scale
represented by a fraction or a ratio
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
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.
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)
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.
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.

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Surveying II ajith sir class 1

  • 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
  • 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
  • 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”
  • 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
  • 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.