# 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

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### 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 ...

### 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 ...

### Encyclopaedia of Mathematics (set) (1994)

by Michiel Hazewinkel

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

### Concise Dictionary of Mathematics (2012)

**Affine Transformation** ¥ Shearing Orientation and Handedness ¥ Orientation and
Handedness. uniform way by using matrices. The result (,)xy′′ of applying a
Euclidean transformation to a point (,)xy is given by the formula (,) (,) xy xyAb ...

### Encyclopedia of Distances (2014)

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 Operations Research and Management Science (2012)

by Saul I. Gass, Carl M. Harris

**AFFINE TRANSFORMATION** A
shifted linear transformation. **An affine transformation** on an n-dimensional vector
...

### 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
...

### 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 ...

### Encyclopedia of Geographic Information Science (2008)

by Karen Kemp

**The affine transformation**
model ...

### Encyclopaedia of Mathematics (2013)

A-Integral — Coordinates by M. Hazewinkel

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

### 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 ...

### Academic Press Dictionary of Science and Technology (1992)

by Christopher G. Morris, Academic Press

aerospace engineering **affine transformation** aerospace engineering
Engineering, the development and study of various technologies relating to
aircraft, spacecraft, and missiles that are designed for flight in the earth's
atmosphere and in outer ...

## 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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