Prof. Samirsinh P ParmarDharmasinh Desai University, Nadiad, Gujarat, India

Mail: samirddu@gmail.com

MAP PROJECTIONS IN GIS

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3 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

4 Developable Surfaces

5 Classification

A) Based on Extrinsic property Nature:

Plane, Cone, Cylinder

Coincidence: Tangent, Secant, Polysuperficial

Position: Normal, Transverse, Oblique

6 Azimuthal Projections

7 Cylindrical Projections

Tangent

Oblique

Transverse

Secant

8 Conic Projections

9 Classification contd.

B) Based on Intrinsic Property Property of Projection:

Equidistant

Conformal or Orthomorphic

Equivalent or Equal area

Generation: Geometric, Semi Geometric, Mathematical

10 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

11 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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14 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

16 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

18 Conic Projections

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

19 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

22 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.

23 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 PROJECTIONCENTRAL MERIDIAN: 100° W

26 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

27 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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29 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)

30 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 OriginCentral Parallel

Coordinate System Origin

False EastingFalseNorthing

32 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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35 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.

36 Projection Parameters contd.

The standard parallel(s) for conic projections. The false easting and false northing The units Reference ellipsoid

37 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

39 Some Related Terms Coordinate System Reference Ellipsoids Everest Ellipsoid GRS 80 WGS 84

40 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

41 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

Objects in Real World(Earth)

Geographic Coordinates( ø , λ )

Represented on Paperor Screen

(Map)

Planar Coordinates( x , y )

43 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.

44 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

46 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

47 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

49 Scale in Map Projections

50 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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