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Define Projection :
Transferring three-dimensional space into a two-dimensional map is called 'projection'.
Define Datum :
Set of parameters defining a coordinate system, and a set of control points where geometric relationships are known. It is defined by a spheroid, approximating the shape of the Earth, and its relativity to the center of the Earth
Polyconic Projection
Since Survey of India Topographical Maps use Polyconic projection. I think it will be useful to explain this projection.
This Projection is modified version of the simple conic projection. The very name of the projection implies the concept of using several cones at the same time. It was developed by Prof. Ferdinand Hassler, the first superintendent of the Coast and Geodetic Survey of the U.S.A.
In the simple conic projection, the radius of the standard parallel is equal to the radius of the corresponding parallel on the globe of the same scale. Meridians intersect the parallels at right angles. It is, therefore possible to fit the maps of adjacent areas lying east and west of each other. But in the absence of bounding parallels of constant length (the length of parallel will depend upon the selected parallel) maps of areas north or south of one another cannot be fitted together. The polyconic projection is a device to minimise this drawback.
In the construction of this projection it is presumed that there are as many cones covering a globe as parallels to be drawn. Each of these cones is tangent to its corresponding latitude, there by making each parallel a standard parallel. The representation along all the parallel is, therefore, correct. This projection divides the map surface into east-west running belts. These belts fit each other only along the central meridian and hence an element of error enters as one moves away from the central meridian. Only along the central meridian the areas as well as the shapes are correct.
Cylindrical projection
The cylindrical projection projects the earth from the center of the earth to a cylinder which envelops or intersects the earth. The Mercator projection is a typical cylindrical projection with the equator tangent to the cylinder. The Universal Transverse Mercator (UTM) is also an internationally popular map projection. UTM is a type of Gauss-Kruger projection, with the meridian tangent to the cylinder. The UTM has an origin point at every six degrees of longitude with a scale factor of 0.9996 at the origin and 1.0000 at a distance of 90 kilometres from the central meridian.
Coordinate System Origin
The origin is the point specified in longitude and latitude from which all coordinates are referenced. It is chosen to optimize the accuracy of a particular coordinate system. As we move north from the origin, Y increases. X increases as we move east. These coordinate values are generally called northings and eastings.
Standard Parallels
In conic projections a cone is passed through the earth intersecting it along two parallels of latitude. These are the standard parallels. One is the north and one is to the south of the projection zone. To use a single standard parallel specify that latitude twice. Both are expressed in degrees of latitude.
Scale Factor
A scale factor is applied to cylindrical coordinates to average scale error over the central area of the map while reducing the error along the east and west boundaries. The scale factor has the effect of recessing the cylinder into the earth so that it has two lines of intersection. Scale is true along these lines of intersection
False Northing and False Eastings
Calculating coordinates is easier if negative number aren't involved. To eliminate this problem in calculating State Plane and Universal transverse Mercator coordinates, it is common to add measurement offsets to the northings and eastings. These offsets are called False Northings and False Eastings. They are expressed in coordinate units, not degrees.
