:: com :: sun :: star :: geometry ::

 unpublished struct AffineMatrix2D
Usage Restrictions
not published
Description
This structure defines a 2 by 3 affine matrix.

The matrix defined by this structure constitutes an affine mapping of a point in 2D to another point in 2D. The last line of a complete 3 by 3 matrix is omitted, since it is implicitly assumed to be [0,0,1].

An affine mapping, as performed by this matrix, can be written out as follows, where `xs` and `ys` are the source, and `xd` and `yd` the corresponding result coordinates: ``` xd = m00*xs + m01*ys + m02; yd = m10*xs + m11*ys + m12; ```

Thus, in common matrix language, with M being the AffineMatrix2D and vs=[xs,ys]^T, vd=[xd,yd]^T two 2D vectors, the affine transformation is written as vd=M*vs. Concatenation of transformations amounts to multiplication of matrices, i.e. a translation, given by T, followed by a rotation, given by R, is expressed as vd=R*(T*vs) in the above notation. Since matrix multiplication is associative, this can be shortened to vd=(R*T)*vs=M'*vs. Therefore, a set of consecutive transformations can be accumulated into a single AffineMatrix2D, by multiplying the current transformation with the additional transformation from the left.

Due to this transformational approach, all geometry data types are points in abstract integer or real coordinate spaces, without any physical dimensions attached to them. This physical measurement units are typically only added when using these data types to render something onto a physical output device, like a screen or a printer, Then, the total transformation matrix and the device resolution determine the actual measurement unit.

Since
OOo 2.0

 Elements' Summary m00 The top, left matrix entry. m01 The top, middle matrix entry. m02 The top, right matrix entry. m10 The bottom, left matrix entry. m11 The bottom, middle matrix entry. m12 The bottom, right matrix entry.
Elements' Details
m00
 double m00; Description The top, left matrix entry.
m01
 double m01; Description The top, middle matrix entry.
m02
 double m02; Description The top, right matrix entry.
m10
 double m10; Description The bottom, left matrix entry.
m11
 double m11; Description The bottom, middle matrix entry.
m12
 double m12; Description The bottom, right matrix entry.
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