1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
|
/* -*- Mode: C++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
/*
* This file is part of the LibreOffice project.
*
* This Source Code Form is subject to the terms of the Mozilla Public
* License, v. 2.0. If a copy of the MPL was not distributed with this
* file, You can obtain one at http://mozilla.org/MPL/2.0/.
*
* This file incorporates work covered by the following license notice:
*
* Licensed to the Apache Software Foundation (ASF) under one or more
* contributor license agreements. See the NOTICE file distributed
* with this work for additional information regarding copyright
* ownership. The ASF licenses this file to you under the Apache
* License, Version 2.0 (the "License"); you may not use this file
* except in compliance with the License. You may obtain a copy of
* the License at http://www.apache.org/licenses/LICENSE-2.0 .
*/
#ifndef __com_sun_star_geometry_AffineMatrix2D_idl__
#define __com_sun_star_geometry_AffineMatrix2D_idl__
module com { module sun { module star { module geometry {
/** This structure defines a 2 by 3 affine matrix.<p>
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].<p>
An affine mapping, as performed by this matrix, can be written out
as follows, where <code>xs</code> and <code>ys</code> are the source, and
<code>xd</code> and <code>yd</code> the corresponding result coordinates:
<code>
xd = m00*xs + m01*ys + m02;
yd = m10*xs + m11*ys + m12;
</code><p>
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.<p>
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.<p>
@since OOo 2.0
*/
struct AffineMatrix2D
{
/// The top, left matrix entry.
double m00;
/// The top, middle matrix entry.
double m01;
/// The top, right matrix entry.
double m02;
/// The bottom, left matrix entry.
double m10;
/// The bottom, middle matrix entry.
double m11;
/// The bottom, right matrix entry.
double m12;
};
}; }; }; };
#endif
/* vim:set shiftwidth=4 softtabstop=4 expandtab: */
|
