Perspective Affinity
Affine transformation or affinity is a special case of plane perspective collineation where the center is a point at infinity.
Line at infinity is also an affine ray. A line parallel to the affine axis is mapped onto a line also parallel to the axis. The affine ray is determined with the corresponding pair of points, hence the center of affinity is also determined. This way of setting an affinity will be denoted by (o, A_{1}, A_{2}). For the defining pair we can choose any pair of corresponding points with respect to the given affinity. Affine image of a pointAn affinity (o, A_{1}, A_{2}) and point B_{1} are given in Figure 25. Construct the point B_{2} i.e. the affine image of the point B_{1}.(Although the ray z_{A} determines the center of affinity in this figure the center is pointed out with an arrow. In the following this will not be specially pointed out.)
Created by Sonja Gorjanc, translated by Helena Halas and Iva Kodrnja - 3DGeomTeh - Developing project of the University of Zagreb, made with GeoGebra |