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- Affine_transformation abstract "In geometry, an affine transformation or affine map or an affinity (from the Latin, affinis, "connected with") is a function between affine spaces which preserves points, straight lines and planes. Also, sets of parallel lines remain parallel after an affine transformation. An affine transformation does not necessarily preserve angles between lines or distances between points, though it does preserve ratios of distances between points lying on a straight line. Examples of affine transformations include translation, scaling, homothety, similarity transformation, reflection, rotation, shear mapping, and compositions of them in any combination and sequence. Every linear transformation is affine, but not every affine transformation is linear.If and are affine spaces, then every affine transformation is of the form , where is a linear transformation on and is a vector in . Unlike a purely linear transformation, an affine map need not preserve the zero point in a linear space. For many purposes an affine space can be thought of as Euclidean space, though the concept of affine space is far more general (i.e., all Euclidean spaces are affine, but there are affine spaces that are non-Euclidean). In affine coordinates, which include Cartesian coordinates in Euclidean spaces, each output coordinate of an affine map is a linear function (in the sense of calculus) of all input coordinates. Another way to deal with affine transformations systematically is to select a point as the origin; then, any affine transformation is equivalent to a linear transformation (of position vectors) followed by a translation.".
- Affine_transformation thumbnail Fractal_fern_explained.png?width=300.
- Affine_transformation wikiPageExternalLink AffineTransform.
- Affine_transformation wikiPageExternalLink affine.htm.
- Affine_transformation wikiPageExternalLink AffineTransformation.html.
- Affine_transformation wikiPageExternalLink index.php?p=1_6_PC-AffineTrans.
- Affine_transformation wikiPageID "38449".
- Affine_transformation wikiPageRevisionID "606778292".
- Affine_transformation hasPhotoCollection Affine_transformation.
- Affine_transformation id "p/a011140".
- Affine_transformation title "Affine Transformation".
- Affine_transformation title "Affine transformation".
- Affine_transformation urlname "AffineTransformation".
- Affine_transformation subject Category:Affine_geometry.
- Affine_transformation subject Category:Transformation_(function).
- Affine_transformation comment "In geometry, an affine transformation or affine map or an affinity (from the Latin, affinis, "connected with") is a function between affine spaces which preserves points, straight lines and planes. Also, sets of parallel lines remain parallel after an affine transformation. An affine transformation does not necessarily preserve angles between lines or distances between points, though it does preserve ratios of distances between points lying on a straight line.".
- Affine_transformation label "Affiene transformatie".
- Affine_transformation label "Affine Abbildung".
- Affine_transformation label "Affine transformation".
- Affine_transformation label "Application affine".
- Affine_transformation label "Przekształcenie afiniczne".
- Affine_transformation label "Transformación afín".
- Affine_transformation label "Transformação afim".
- Affine_transformation label "Trasformazione affine".
- Affine_transformation label "Аффинное преобразование".
- Affine_transformation label "تحويل تآلفي".
- Affine_transformation label "アフィン写像".
- Affine_transformation label "仿射变换".
- Affine_transformation sameAs Afinní_zobrazení.
- Affine_transformation sameAs Affine_Abbildung.
- Affine_transformation sameAs Transformación_afín.
- Affine_transformation sameAs Application_affine.
- Affine_transformation sameAs Trasformazione_affine.
- Affine_transformation sameAs アフィン写像.
- Affine_transformation sameAs 아핀_변환.
- Affine_transformation sameAs Affiene_transformatie.
- Affine_transformation sameAs Przekształcenie_afiniczne.
- Affine_transformation sameAs Transformação_afim.
- Affine_transformation sameAs m.09l17.
- Affine_transformation sameAs Q382497.
- Affine_transformation sameAs Q382497.
- Affine_transformation wasDerivedFrom Affine_transformation?oldid=606778292.
- Affine_transformation depiction Fractal_fern_explained.png.
- Affine_transformation isPrimaryTopicOf Affine_transformation.