In geometry, an affine transformation or affine map or an affinity (from the Latin, affinis, "connected with") between two vector spaces (strictly speaking, two affine spaces) consists of a linear transformation followed by a translation:

x -> Ax + b

In the finite-dimensional case each affine transformation is given by a matrix A and a vector b, which can be written as the matrix A with an extra column b.

Physically, an affine transform is one that preserves

Collinearity between points, i.e., three points which lie on a line continue to be collinear after the transformation
Ratios of distances along a line, i.e., for distinct colinear points p_1, p_2, p_3, the ratio | p_2 − p_1 | / | p_3 − p_2 | is preserved
In general, an affine transform is composed of zero or more linear transformations (rotation, scaling or shear) and translation (shift). Several linear transformations can be combined into a single matrix, thus the general formula given above is still applicable.


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  1. Michael Kors outlet 2013.07.28 23:34  댓글주소  수정/삭제  댓글쓰기

    태양이 바다에 미광을 비추면,나는 너를 생각한다.