affine transformation
See Also: transformation
[Euclidean geometry] A geometric transformation that scales, rotates, skews, and/or translates images or coordinates between any two Euclidean spaces.
[edit] Affine transformation of the plane
To visualise the general affine transformation of the Euclidean plane, take labelled parallelograms ABCD and A′B′C′D′.
Affine transformation - A combination of linear transformations (rotation and scaling) followed by translation (shift of position). In geographic data processing, affine transformation is used to register maps of different scales and origins.
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2) Derive an affine transformation matrix by running a least-squares regression on the ground control points.
Linear affine transformation (1st order transformation)
x' = ax + by +c y' = Ax + Bt +C The a,b,c,A,B,C are determined by least squares regression based on the control points entered. This transformation applies scaling, translation and rotation.
In the case of an affine transformation the scale does not depend on location but it depends in general on direction.
B. a linear affine transformation can be used to apply a Shift (Tx, Ty), a Rotation (a) and/or a Scale change in X and Y direction (Sx, Sy ).
The simplest form, piecewise linear patches consisting of affine transformations, are constructed based on a triangulation of the control points in the output image. There exist many different triangulation criteria.
 See also: Transformation, Transform, Image, Object, Coordinate
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