LibreOffice 7.4 SDK API Reference
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AffineMatrix2D Struct Reference

This structure defines a 2 by 3 affine matrix. More...


Public Attributes

double m00
 The top, left matrix entry. More...
double m01
 The top, middle matrix entry. More...
double m02
 The top, right matrix entry. More...
double m10
 The bottom, left matrix entry. More...
double m11
 The bottom, middle matrix entry. More...
double m12
 The bottom, right matrix entry. More...

Detailed 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.

OOo 2.0

Member Data Documentation

◆ m00

double m00

The top, left matrix entry.

◆ m01

double m01

The top, middle matrix entry.

◆ m02

double m02

The top, right matrix entry.

◆ m10

double m10

The bottom, left matrix entry.

◆ m11

double m11

The bottom, middle matrix entry.

◆ m12

double m12

The bottom, right matrix entry.

The documentation for this struct was generated from the following file: