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Home , Gnomonic projection, Hammer projection, Map projection, Mercator projection, Scale (map), Stereographic projection

4.4 Mercator

This direct cylindrical projection is in conformity, and transforms the curves into lines. The projection of the lines and the parallels thus gives a grid. This projection deforms considerably the 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 and very poor for thematic presentation.

a) Selection of corresponding 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 of projection is a or secant with the model of the ground:

¾ UTM ¾ Mercator conformal ¾ Gauss conformal ¾ Equi rectangular (Not available) ¾ Transverse Mercator (Not available) ¾ Miller (Not available)

4.5.1 UTM projection

The UTM system applies the Transverse 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 and South variant

4.5.2 Cylindrical Mercator conformal projection

The Mercator projection is a conformal projection. On a conformal projection, the is constant in all directions about each point but scale varies from point to point on the . If we consider the parallels, on cylindrical projections, east-west scale increases as we move towards the poles. Assuming tangent case, only the is represented true to scale. All other parallels are longer on the map than they are on the . In the extreme case, the pole is subject to an infinite degree of since it has been stretching into a line having the same length as the Equator, although it is a point on the globe. Since east- west 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 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 .

4.5.4 Equirectangular projection (Not available)

The Equirectangular is a modification of the geographic projection, with the 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 , 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-. 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 , including the National of the 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 's spherical surface on a surrounding , which is then flattened to a surface having concentric as parallels of latitude and radiating lines from the apex as meridians.

It is carried out while placing a cone on the , 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, 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 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 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 while not eliminating any particular type of distortion. The Polyconic projection shows meridians curved, not straight. Mathematically, it is projected onto 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 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 projections which results from the 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

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 .

As a result, deformation of areas and 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

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 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 (Not available)

Hammer projection

Hammer, the point of tangency is located on Ecuador. This projection preserves surfaces. It is often used for the .This map projection is an equal-area map projection which displays the world on an ellipse. However, it is completely unlike the . 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 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 allows to display the mosaic relation with the correct projection. If suppose we opened some mosaic relation in the projection 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. http://www.echodelta.net/mbs/eng-overview.php 2. http://kartoweb.itc.nl/geometrics/Map%20Projections/body.htm 3. http://www.mathworks.com/access/helpdesk_r13/help/toolbox/map/hammer.gif 4. http://www.progonos.com/furuti/MapProj/Normal/ProjAz/projAz.html 5. 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

SAVAMER122 9.02 Menu - 5

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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.

Savamer 9.02 User manual - 5 The below illustration shows the extent of the sheet corresponding to the north streams displayed in the projection window.