surveying ii ajith sir class 1

Module II

Map Projections

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 ofScaleUsage

Map Types

1.Cadastral maps (Planimetric maps)1.Cadastral maps (Planimetric maps)

2.Topographic maps2.Topographic maps

3.Thematic maps3.Thematic maps

4.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

(o,o)(xo,yo)

X

Y

Origin

A planar coordinate system is defined by a pairof orthogonal (x,y) axes drawn through an origin

Map ProjectionsMap 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

.

Latitude and Longitude on a Sphere

Meridian of longitude

Parallel of latitude

X

Y

ZN

EW

=0-90°

S

P

OR

=0-180°E

=0-90°N

•

Greenwichmeridian

=0°

•

Equator =0°

•

•=0-180°W

- Geographic longitude - 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:

,,

gyfx

,x 4/2/tanln y

Geographic and Projected Coordinates

() (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 distanceEarth distance

=

Map Scale: Map Projection:

Scale Factor

Map distanceGlobe 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.