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Prof. Samirsinh P ParmarDharmasinh Desai University, Nadiad, Gujarat, India
Mail: [email protected]
MAP PROJECTIONS IN GIS
2
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
12
REGULAR CYLINDRICAL PROJECTION:THE MERCATOR
13
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
15
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.
17
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
20
LCC PROJECTION
21
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.
24
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
25
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
28
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.
31
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
33
Figure
34
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
38
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
45
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.
48
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
51