# Affine transformation

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## Definition of the noun affine transformation

What does affine transformation mean as a name of something?

**noun**

- (mathematics) a transformation that is a combination of single transformations such as translation or rotation or reflection on an axis
- domain: math / mathematics / maths
- lexical domain: Relations - nouns denoting relations between people or things or ideas
- more generic word: transformation = a function that changes the position or direction of the axes of a coordinate system

### Alternative definition of the noun affine transformation

**noun**

- [
*geometry, linear algebra*] a linear transformation between vector spaces followed by a translation.

## Explanation

**Affine transformation**: In geometry, an affine transformation, affine map or an affinity 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.

- also known as Affin transformation, 仿射变换

## Printed dictionaries and other books with definitions for Affine transformation

Click on a title to look inside that book (if available):

### The Mathematics Dictionary (1992)

by R.C. James, Glenn James

Afflne Alexander affine transformations on a vector space, one often refers to the
vector space as an affine space. **affine transformation**. /// the plane, a
transformation of the form x' = , y' = a2x +b2y + c2. It is singular or nonsingular
according as ...

### Encyclopaedia of Mathematics (2012)

by Michiel Hazewinkel

AMS 1980 Subject
Classification: 53A15 **AFFINE TRANSFORMATION** of a Euclidean space - A one-
to-one ...

### The Penguin Dictionary of Mathematics (2008)

Fourth edition by David Nelson

However, some familiar geometric concepts such as the circle are not relevant to
affine geometry, because a circle can be transformed to an ellipse by certain
affine transformations. **affine transformation** A mapping of a *vector space that is
the ...

### CRC Concise Encyclopedia of Mathematics, Second Edition (2002)

by Eric W. Weisstein

GROUP, AFFINE HULL, AFFINE SPACE, **AFFINE TRANSFORMATION**, AFFINITY
, PROJECTIVE PLANE References Lindner, C. C. and Rodger, C. A. Design
Theory. Boca Raton, FL: CRC Press, 1997. Affine Scheme Let P be the set of
PRIME ...

### Dictionary of Computer Vision and Image Processing (2013)

by Robert B. Fisher, Toby P. Breckon, Kenneth Dawson-Howe, Andrew Fitzgibbon, Craig Robertson, Emanuele Trucco, Christopher K. I. Williams

affine flow: A methodof findingthe movement of a surface patch
by estimating **the affine transformation** parameters required to transform the ...

### Geostatistical Glossary and Multilingual Dictionary (1991)

by Ricardo A. Olea, International Association for Mathematical Geology. Committee on Geostatistics

**affine Transformation**. affinity
transformation. Akkumulation. accumulation. allgemeines relatives
Semivariogramm.

### Dictionary of Mathematical Geosciences (2017)

With Historical Notes by Richard J. Howarth

**Affine transformation** Any transformation which preserves
collinearity: when applied to positional data, such transformations can alter
distances and ...

### International GIS Dictionary (1995)

by Rachael McDonnell

**AFFINE TRANSFORMATION** ALONG- TRACK SCANNING
**AFFINE TRANSFORMATION** After DIGITIZING it is necessary to transform the
SPATIAL DATA from digitizer co-ordinates to real-world ones prior to any
analysis.

### Encyclopedia of Distances (2016)

by Michel Marie Deza, Elena Deza

**An affine transformation** (or affinity) is a bijection of An onto itself which preserves
collinearity and ratios of distances In this sense, affine indicates a special class of
projective transformations that do not move any objects from the affine space ...

### Encyclopedia of Geography (2010)

by Barney Warf

**Affine Transformation** An affine transform is the most basic linear transformation
model and is defined by the following equations: u = β0 + β1x + β2y v = β3 + β4x
+ β5y, where (u, v) are coordinates in the target system, (x, y) are the coordinates
...

### Encyclopedia of GIS (2007)

by Shashi Shekhar, Hui Xiong

**An affine transformation** can preserve
collinearity and ...

## Online dictionaries and encyclopedias with entries for Affine transformation

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## Video about Affine transformation

**Affine transformation Meaning**

Video shows what affine transformation means. a linear transformation between vector spaces followed by a translation.. Affine transformation Meaning. How to ...

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