LibreOffice LibreOffice 7.2 SDK API Reference
AffineMatrix3D Struct Reference

This structure defines a 3 by 4 affine matrix. More...

`import"AffineMatrix3D.idl";`

## Public Attributes

double m00
The top, left matrix entry. More...

double m01
The top, left middle matrix entry. More...

double m02
The top, right middle matrix entry. More...

double m03
The top, right matrix entry. More...

double m10
The middle, left matrix entry. More...

double m11
The middle, middle left matrix entry. More...

double m12
The middle, middle right matrix entry. More...

double m13
The middle, right matrix entry. More...

double m20
The bottom, left matrix entry. More...

double m21
The bottom, middle left matrix entry. More...

double m22
The bottom, middle right matrix entry. More...

double m23
The bottom, right matrix entry. More...

## Detailed Description

This structure defines a 3 by 4 affine matrix.

The matrix defined by this structure constitutes an affine mapping of a point in 3D to another point in 3D. The last line of a complete 4 by 4 matrix is omitted, since it is implicitly assumed to be [0,0,0,1].

An affine mapping, as performed by this matrix, can be written out as follows, where `xs, ys` and `zs` are the source, and `xd, yd` and `zd` the corresponding result coordinates:

` xd = m00*xs + m01*ys + m02*zs + m03; yd = m10*xs + m11*ys + m12*zs + m13; zd = m20*xs + m21*ys + m22*zs + m23; `

Thus, in common matrix language, with M being the AffineMatrix3D and vs=[xs,ys,zs]^T, vd=[xd,yd,zd]^T two 3D 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 AffineMatrix3D, 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. For 3D coordinates there is also a projection from 3D to 2D device coordinates needed. Only then the total transformation matrix (including projection to 2D) and the device resolution determine the actual measurement unit in 3D.

Since
OOo 2.0

## ◆ m00

 double m00

The top, left matrix entry.

## ◆ m01

 double m01

The top, left middle matrix entry.

## ◆ m02

 double m02

The top, right middle matrix entry.

## ◆ m03

 double m03

The top, right matrix entry.

## ◆ m10

 double m10

The middle, left matrix entry.

## ◆ m11

 double m11

The middle, middle left matrix entry.

## ◆ m12

 double m12

The middle, middle right matrix entry.

## ◆ m13

 double m13

The middle, right matrix entry.

## ◆ m20

 double m20

The bottom, left matrix entry.

## ◆ m21

 double m21

The bottom, middle left matrix entry.

## ◆ m22

 double m22

The bottom, middle right matrix entry.

## ◆ m23

 double m23

The bottom, right matrix entry.

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