4.4 Mercator projection
This direct cylindrical projection is in conformity, and transforms the curves into lines.
The projection of the meridian lines and the parallels thus gives a grid. This projection
deforms considerably the areas close to the poles, and is to be used with prudence for all
the areas which are not close to Ecuador. It should not be confused with the projection
UTM, which is a cylindrical transverse. The famous conformal cylindrical projection. It is
excellent for the limited purpose of marine navigation and very poor for thematic
presentation.
a) Selection of corresponding ellipsoid in the study zone
b) Selection of the ellipsoid for the study zone
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4.5 Cylindrical projection
In the case of a cylindrical projection, the surface of projection is a tangent or secant
cylinder with the model of the ground:
¾
¾
¾
¾
¾
¾
UTM
Mercator conformal
Gauss conformal
Equi rectangular (Not available)
Transverse Mercator (Not available)
Miller (Not available)
4.5.1 UTM projection
The UTM system applies the Transverse Mercator projection to mapping the world, using
60 pre-defined standard zones to supply parameters. The Universal Transverse Mercator
system of projections deals with this by defining 60 different standard projections, each
one of which is a different Transverse Mercator projection that is slightly rotated to use a
different meridian as the central line of tangency. UTM zones are six degrees wide. Each
zone exists in a North and South variant
4.5.2 Cylindrical Mercator conformal projection
The Mercator projection is a conformal projection. On a conformal projection, the scale is
constant in all directions about each point but scale varies from point to point on the map.
If we consider the parallels, on cylindrical projections, east-west scale increases as we
move towards the poles. Assuming tangent case, only the Equator is represented true to
scale. All other parallels are longer on the map than they are on the globe. In the extreme
case, the pole is subject to an infinite degree of distortion since it has been stretching into a
line having the same length as the Equator, although it is a point on the globe. Since eastwest scale is increasing as we move toward the poles, we must increase north-south scale
by an equal amount in order to obtain a conformal projection.
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4.5.3 Gauss conformal projection
The Gauss Conformal is useful for star maps of the kind that show how the sky appears at
a particular time on a particular day of the year, because the resulting map can be equally
useful for people who live at any latitude.
4.5.4 Equirectangular projection (Not available)
The Equirectangular map projection is a modification of the geographic projection, with
the longitude lines (meridians) spaced closer together, forming rectangles with the latitude
lines (parallels) instead of squares. In this projection, there are two standard parallels,
resulting in less distortion at mid latitudes, but causing distortion at the Equator.
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4.5.5 Transverse mercator projection (Not available)
This is the transverse aspect of the mercator projection. The Mercator projection has little
distortion near the Equator. By using the transverse aspect, that property of low distortion
runs north-south instead of east-west, so that some areas which would have high distortion
in the normal Mercator projection could be projected with less distortion
4.5.6 Miller projection (Not available)
A cylindrical projection that is neither conformal nor equal-area. A compromise between
the Mercator and other cylindrical projection that attempts to eliminate some of the scale
exaggeration of the Mercator. This is used for world maps and in several atlases, including
the National Atlas of the United States prepared by USGS in 1970
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4.6 Pseudo cylindrical projection (Not available)
Projection that, in the normal aspect, has straight parallel lines for parallels and on which
the meridians are (usually) equally spaced along parallels, as they are on a cylindrical
projection, but on which the meridians are curved.
4.7 Conical projection
A method of projecting maps of parts of the earth's spherical surface on a surrounding
cone, which is then flattened to a plane surface having concentric circles as parallels of
latitude and radiating lines from the apex as meridians.
It is carried out while placing a cone on the sphere, and by projecting the points of the
sphere on the surface of the cone. The surface of projection is a tangent or secant cone:
•
•
•
•
Lambert
Albers equivalent
Polyconic projection (Not available)
Equidistant projection(Not available)
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4.7.1 Lambert Conical projection
The Lambert conformal conic projection is analogous to the Mercator projection. Both are
conformal projections, meaning that at any point, scale is constant in all directions about
the point. As a result, shapes of small areas are represented with minimal distortion but
shapes of larger areas are distorted because of changes in scale from point to point. As with
the Mercator projection, the Lambert conformal projection is constructed by adjusting the
spacing of the parallels so that the stretching of the map in the east-west direction is
exactly matched by stretching in the north-south direction. The projection can be
constructed using either one or two standard parallels. Use of two standard parallels is
more common because it gives a better distribution of distortion over the entire map. The
Lambert conformal projection is extensively used for maps of Canada and Ontario.
The different types of Lambert projection is explained above in the menu Lambert
projection
4.7.2 Albers equivalent projection
Albers projection is constructed by modifying the spacing of parallels to obtain an
equivalent projection. The meridians are represented the same as on the simple conic, but
the spacing between parallels is adjusted to maintain constant area scale. Areas the size of
Canada or the United States can be mapped with little distortion of distances and shapes.
The Alber's projection is extensively used in the United States as the basis for state plane
co-ordinate systems used for topographic maps.
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4.7.3 Polyconic projection (Not available)
The polyconic projection is neither conformal nor equivalent; it is a compromise projection
that attempts to minimize all distortions while not eliminating any particular type of
distortion. The Polyconic projection shows meridians curved, not straight. Mathematically,
it is projected onto cones tangent to each parallel of latitude (an infinite number of cones
tangent to an infinite number of parallels).
4.7.4 Equidistant projection (Not available)
The Equidistant Conic projection is commonly used in the spherical form in atlases for
maps of small countries. It can also cover large areas, and was used to map the Soviet
Union.
4.8 Azimuthal projection
Azimuthal projections are projections to a plane placed tangent to the globe at a point. In
normal (or polar) aspect, the point of tangency is either the north or south pole and
meridians of longitude are represented as radial straight lines through the pole while
parallels of latitude appear as concentric circles. Distortion in the map increases with
distance from the point of tangency. Since distortion is minimal near the point of tangency,
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azimuthal projections are useful for representing areas having approximately equal extents
in the north-south and east-west directions.
The azimuth projections which results from the perspective projection of a portion of the
terrestrial sphere on a tangent level with the sphere, starting from a point given (ex: polar
stereography with the sky charts or the charts of the polar areas.....).
4.8.1 Azimuthal Stereographic projection
The sterographic projection positions the light source at the antipode of the point of
tangency. Thus if the north pole is the point of tangency, the light source would be at the
south pole. The spacing of parallels increases with distance from the pole, but not as
rapidly as was the case with the gnomonic projection.
As a result, deformation of areas and angles is less severe and it is possible to show an area
of up to about 135 degrees from the pole on one map, although stereographic projections
are usually limited to showing one hemisphere. The stereographic projection is a
conformal projection and is commonly used for maps of the polar region. The
stereographic projection also has an important special property: with the exception of great
circles passing through the pole, circles on the globe appear as circles or circular arcs on
the map. This makes the stereographic projection useful for representing radial phenomena
such as shock waves from earthquakes.
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4.8.2 Azimuthal orthographic projection
The orthographic projection assumes that the light source is an infinite distance from the
point of tangency, resulting in the rays of light being parallel to each other and
perpendicular to the projection surface. The resulting projection can show only one
hemisphere. The spacing between parallels decreases towards the Equator. The
orthographic projection has no special properties but it does approximate a perspective
view of the Earth from outer space. It is therefore useful for visualizing spatial
relationships.
4.8.3 Universal polar stereographic projection (Not available)
This is a perspective projection on a plane tangent to either the North or South Pole. It is
conformal, being free from angular distortion. Additionally, all great and small circles are
either straight lines or circular arcs on this projection. Scale is true along latitudes 87
degrees, 7 minutes N or S, and is constant along any other parallel. This projection is not
equal area. This projection is a special case of the stereographic projection in the polar
aspect. It is used as part of the Universal Transverse Mercator (UTM) system to extend
coverage to the poles. This projection has two zones: `North' for latitudes 84º N to 90º N,
and `South' for latitudes 80º S to 90º S. The defaults for this projection are: scale factor is
0.994, false easting and northing are 2,000,000 meters.
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4.8.4 Azimuthal - Gnomonic projection (Not available)
Gnomonic the point of view is in the centre of the ground. It is especially used in
navigation and aviation. The surfaces are not to be preserved but the scale is preserved
only along one parallel and the long central meridian line.
The Gnomonic projection is one which has a greater expansion, away from the origin, than
a conformal projection. It gives quite distorted appearance; It is constructed by projecting
every point on the globe appearing in the map onto the plane of the map from an imagined
light source in the center of the globe. Great circles on the globe are all bands like the
Equator, which are defined by planes cutting the globe that intersect the center of the
globe. Hence, on the gnomonic projection, all great circles are represented by straight
lines, making it very useful in plotting great circle routes between arbitrary destinations.
As has doubtless often been said, it is the navigational chart for the air age much as the
Mercator was the navigational chart for the age of sail. It can also be employed fairly
simply for projecting the world onto the surface of various polyhedral.
4.8.5 Lambert azimuth projection (Not available)
Preserve surfaces, view of the whole ground, distances exact only to the center of the
ground. It is often used in the atlases to represent the polar areas, hemispheres Northern
and South. This map projection is one of the most popular projections used in atlases
today. it is well suited to mapping regions that do not have any large difference between
their north-south extent and their east-west extent.
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4.8.6 Hammer projection (Not available)
Hammer projection
Hammer, the point of tangency is located on Ecuador. This projection preserves surfaces.
It is often used for the planispheres.This map projection is an equal-area map projection
which displays the world on an ellipse. However, it is completely unlike the Mollweide
projection. In the conventional case, the parallels are curved, and there is no stretching at
the center of the map. It’s possible to move all the important land masses out of the areas
with high shearing, producing quite a pleasing result. It consists of halving the vertical
coordinates of the equatorial aspect of one hemisphere and doubling the values of the
meridians from the center (Snyder 1987, p. 182). Like the Lambert azimuthal equal-area
projection, it is equal area, but it is no longer azimuthal.
4.8.7 Wagner IV projection (Not available)
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This projection was presented by Karlheinz Wagner in 1932. This is an equal-area
projection. Scale is true along the 42º59' parallels and is constant along any parallel and
between any pair of parallels equidistant from the Equator. Distortion is not as extreme
near the outer meridians at high latitudes as for pointed-polar pseudocylindrical
projections, but there is considerable distortion throughout the polar regions. It is free of
distortion only at the two points where the 42º59' parallels intersect the central meridian.
This projection is not conformal or equidistant.
4.8.8 Wagner VII projection (Not available)
This projection is developed by Karl Heinz Wagner of Germany in 1941.It is the
modification of the Hammer projection and the poles correspond to the 65 th parallel on
the hammer and meridians are repositioned. The scale decreases along the central meridian
and the equator with distance from the centre of the projection. The distortions in the map
are considerable shape distortion in polar areas. Meridians: Central meridian is straight and
half the length of the Equator. Equator is straight and other parallels are curves, unequally
spaced along the central meridian and concave toward the nearest pole.
4.9 Mosaic
This function allows to display the mosaic relation with the correct projection. If suppose
we opened some mosaic relation in the projection window and opening the new relation of
images is not possible due to some default projection. In this case we need to use this menu
to apply the proper projection to display the mosaic.
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The above mentioned warning dialogue box will appear if we try to open the mosaic in the
projection window.
For this error we have to define the relation projection with the help of mosaic function by
using the below steps.
After clicking the mosaic menu the below relation dialogue box will appear. In this we
need to select the relation which is to be opened with good projection in the frame.
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Then click ok to finish the process. Now we can open the relation in the projection window
by refresh the page or again click Draw all function.
4.10 Calculation
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This calculation helps to convert the geographic coordinates (degrees, minutes, seconds) in
to two dimensional parameters (X, Y) in meters or from (X,Y) coordinates into degrees
minutes and seconds.
Convert from (x , y) coordinates
into longitude and latitude
(deg,min,sec)
Convert from longitude and
latitude (deg,min,sec) into (x , y)
coordinates.
For example, if we assign the values as X=20000 and Y=20000 and click the arrow for
conversion it gives the answer in degrees, minutes and seconds
We can also perform in reverse manner like from degrees, minutes, seconds into (X,Y)
coordinate.
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Reference:
All the information’s are collected from the below mentioned reference for the users to
understand the map projection.
1.
2.
3.
4.
5.
http://www.echodelta.net/mbs/eng-overview.php
http://kartoweb.itc.nl/geometrics/Map%20Projections/body.htm
http://www.mathworks.com/access/helpdesk_r13/help/toolbox/map/hammer.gif
http://www.progonos.com/furuti/MapProj/Normal/ProjAz/projAz.html
http://www.mathworks.com/access/helpdesk/help/toolbox/map/wagnerivprojection.
html
6. http://www.3dsoftware.com/Cartography/USGS/MapProjections/ModifiedAzimuth
al/WagnerVII/
7. http://exchange.manifold.net/manifold/manuals/5_userman/index.htm
8. http://www.quadibloc.com/maps/mcy0101.htm
9. http://www.3dsoftware.com/Cartography/USGS/MapProjections/Cylindrical/Equir
ectangular/
10. http://www.warnercnr.colostate.edu/class_info/nr502/lg2/notes/pseudocylindrical.h
tml
Books:
1. An Album of Map Projections, USGS Professional Paper 1453, by John P. Snyder and Philip
M. Voxland ,1994, 249 pp.
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WINDOW
Description
Show info about projection window
This description dialogue box displays details of projection, resolution and also the latitude
longitude of the left lower point and right upper point which correspond to the extent of the
view in the projection window.
Right upper point
(lat, long)
Left lower point
(lat,long)
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On screen
Resize window directly on screen by dragging a rectangle.
This function allows the user to zoom a selection in the projection window.
Output zoom:
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Sheet
Set the projection window to fit the extent of a sheet integrated in a relation
A sheet encompasses a set of objects covering a specific geographical extent. In a relation,
objects are indexed by sheets. A relation contains one or more sheets. The indexation
allows the software to retrieve faster an object and its values. This menu allows us to
display the extent of selected sheet included in a relation in the projection window.
For example if central stream is selected then the extent of the central stream in the
projection window will be displayed.
Selection of sheet
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Once you selected and click finish you can see the extent of the sheet corresponding only
to the central stream.
If you select some other sheet in the relation for example “north stream” and click finish,
you will see the extent of the north stream.
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The below illustration shows the extent of the sheet corresponding to the north streams
displayed in the projection window.