Center for Modeling & Simulation. It is always necessary to unify objects recorded in different coordinate system, into one system using coordinate.

Center for Modeling & Simulation

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

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

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

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.

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

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

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

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