Review article

Geometrical Interpretations of Affine Mapping

Miljenko Lapaine orcid.org/0000-0002-9463-2329 ; Faculty of Geodesy, University of Zagreb, Zagreb, Croatia

Abstract

Affine mapping is applied in different fields of geodesy and surveying. The paper describes two possible interpretations of affine mapping of a plane onto another plane. The first interpretation explains affine mapping as a composition of a rotation, non-uniform scaling and shear mapping including a translation. It is shown that such an approach is not unique and that considering it two translations, two modifications of scale or two rotations does not make any sense. The second interpretation of affine mapping is parallel projection of a plane into a plane in space. Common expressions for affine mapping by using coordinates of related points are derived from the vector approach to mapping. Such an approach enables clear geometric interpretation of mapping parameters.

Keywords

affine mapping; affine transformation; translation; rotation; non-uniform scaling; shear mapping

Hrčak ID:

137559

URI

https://hrcak.srce.hr/137559

Publication date:

20.3.2015.

Article data in other languages: croatian

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