Distortions in Affine Mapping

Abstract

Affine mappings have a long tradition and are applied in various disciplines. Distortions of affine mappings between planes are discussed in this paper using the methodology taken from the theory of map projections. Formulae for the linear scale are derived, and it is shown that distances are generally not preserved. The length distortion depends on the direction. The distribution of the linear distortions around a point can be visualized by using the curve of local linear distortions or the distortion ellipse. Next, changes in angles and areas are explained. The paper concludes with an interpretation of the distortion ellipse as the image of a unit circle.

Keywords

• affine mapping, mapping distortions, length distortion, angle distortion, area distortion, curve of linear local distortion, distortion ellipse