A geographical transformation is a mathematical operation that converts the coordinates of a point in one geographic coordinate system to the coordinates of the same point in another geographic coordinate system.
Since geographic coordinate systems contain datums that are based on spheroids, a geographic transformation also changes the underlying spheroid. There are several methods, which have different levels of accuracy and ranges, for transforming between datums.
A geographic transformation always converts geographic (latitude–longitude) coordinates. Some methods convert the geographic coordinates to geocentric (X,Y,Z) coordinates, transform the X,Y,Z coordinates, and convert the new values back to geographic coordinates
Affine transformation is a geographic transformation that scales, rotates, skews, and/or translates images or coordinates between any two Euclidean spaces. It is commonly used in GIS to transform maps between coordinate systems.
In an affine transformation, parallel lines remain parallel, the mid-point of a line segment remains a mid-point and all points on a straight line remain on a straight line.
Geometric transformation is the process of using a set of control points and transformation equations to register a digitised map, satellite image, or an air photo to a projected coordination system.
Geometric transformation converts a newly digitised map into projected coordinates by a process called map-to-map transformation. A remotely sensed image is converted to projected coordinates using image-to-map transformation. This is also called georeferencing.
Different methods have been proposed for transformation from one coordinate system to another. Each method is differentiated based on the geometric property it preserves and the changes it allows. Transformation results in either:
- Changes in position and direction
- Uniform change of scale or
- Changes in size and shape
Below are listed the various transformations and their effect on a rectangular object:
- Equiarea transformation permits rotation of rectangle and preserves its shape and size.
- Similarity transformation permits rotation of rectangle and preserves its shape but not the size.
- Affine transformation allows angular distortion but preserves parallelism of lines
- Projective transformation allows both angular and length distortions and thus allows the rectangle to be transformed into an irregular quadrilateral.
Generally, Affine transformations are used for map-to-map or image-to-map transformations and projective transformation is used for aerial photographs with relief displacement.