1. Center for Modeling & Simulation

3.  It is always necessary to unify objects recorded in different coordinate system, into one system using coordinate transformations  Transformation is the derivation of one set of coordinates for a point whose coordinates in another system are known  It changes the positions of points in the plane. A set of points, when transformed, may as a result acquire a different shape  In map projections positions of points on the curved surface of earth are transformed to their corresponding positions on a flat paper  Two types of linear transformations are used

4.  Also known as linear conformal or Helmert transformation  A subsidiary coordinate system is brought into coincidence with the principal coordinate system by means of a translation (horizontal shift), a rotation through an angle and a change of scale by a factor (Richardus, 1966)  There are four unkonwn points (x,y in subsidary system and x,y in principal system)  So minimum of two points should be given for same object in two systems

5.  They are called as control points  At least two control points are required  They should be well spread  The shape of the original feature doesn't change  But the size and orientation towards the axes may change  As the shape remain intact also known as orthogonal transformation

6.  The transformations that move lines into lines, while preserving their intersection properties, and move all polylines into polylines and all polygons into polygons are called as the affine transformations.  However there is a slight change in the original figure due to a change of angle (circle to ellipse)  At least three control points are required  This is generally used in GIS since transformation of geographic space generally involves changes in shape.

7.  The shape of the earth is assumed to be a perfect sphere, however it is highly irregular  That makes it impossible to transform systematically the geometric relations from three dimensional surface to a paper without assumption  Earth regarded as a simple, solid shape of ellipsoid-geoid  In the georeferencing they represent two distinct surfaces for different purposes  Ellipsoid is the reference surface for horizontal position and geoid is for elevation

8.  Earth is slightly flattened at the poles which mathematically approximated by the rotational ellipsoid  It is used as a reference surface for horizontal coordinates  Numerous ellipsoids have been calculated for different regions, which best fit that part of the earth  There are around 30 ellipoids in use today  However, the ellipsoids calculated using the satellite data (geocentric ellipsoids) are able to represent the earth more precisely  As they are defined using the centre of mass of the earth unlike the physical origin of the earth surface in the previous ones

9.  Means earthlike  It is the shape of the earth which would be formed if the ocenas flow freely under the continents to create a single undistrubed global sea level covering the entire earth  Geophysically it is a an equipotential surface (gravity potential is constant everywhere)  Generally the geoid coincides very well with the Mean Sea Level (MSL)  Since open oceans make up most of the earth’s surface all elevations computed are represented by the MSL  Thus it is a reference surface for the vertical coordinates  Ellipsoid is defined entirely by mathematical method, where as geoid is obtained by gravity measurements  Thus these two surfaces are different, though they both talk about the shape of the earth

10.  The geoid and ellipsoid in the contex of vertical and horizontal positions in georeferencing are called as datums  It is a model that describes the position, direction and scale relationships of a reference surface to positions on the surface of the earth  There are two datums in georeferening  Geodeic  Vertical  Geodetic datum provide positional control for large geographic areas  Vertical datum is zero surface from which all elevations are measured  Generally MSL is used for this purpose