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
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
|
/*************************************************************************
*
* DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.
*
* Copyright 2008 by Sun Microsystems, Inc.
*
* OpenOffice.org - a multi-platform office productivity suite
*
* $RCSfile: AffineMatrix3D.idl,v $
*
* $Revision: 1.2 $
*
* This file is part of OpenOffice.org.
*
* OpenOffice.org is free software: you can redistribute it and/or modify
* it under the terms of the GNU Lesser General Public License version 3
* only, as published by the Free Software Foundation.
*
* OpenOffice.org is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
* GNU Lesser General Public License version 3 for more details
* (a copy is included in the LICENSE file that accompanied this code).
*
* You should have received a copy of the GNU Lesser General Public License
* version 3 along with OpenOffice.org. If not, see
* <http://www.openoffice.org/license.html>
* for a copy of the LGPLv3 License.
*
************************************************************************/
#ifndef __com_sun_star_geometry_AffineMatrix3D_idl__
#define __com_sun_star_geometry_AffineMatrix3D_idl__
module com { module sun { module star { module geometry {
/** This structure defines a 3 by 4 affine matrix.<p>
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 implicitely assumed
to be [0,0,0,1].<p>
An affine mapping, as performed by this matrix, can be written out
as follows, where <code>xs, ys</code> and <code>zs</code> are the source, and
<code>xd, yd</code> and <code>zd</code> the corresponding result coordinates:
<code>
xd = m00*xs + m01*ys + m02*zs + m03;
yd = m10*xs + m11*ys + m12*zs + m13;
zd = m20*xs + m21*ys + m22*zs + m23;
</code><p>
Thus, in common matrix language, with M being the
<type>AffineMatrix3D</type> 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.<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. For 3D coordinates
there is also a projection from 3D to 2D device coordiantes needed.
Only then the total transformation matrix (oncluding projection to 2D)
and the device resolution determine the actual measurement unit in 3D.<p>
@since OOo 2.0.0
*/
struct AffineMatrix3D
{
/// The top, left matrix entry.
double m00;
/// The top, left middle matrix entry.
double m01;
/// The top, right middle matrix entry.
double m02;
/// The top, right matrix entry.
double m03;
/// The middle, left matrix entry.
double m10;
/// The middle, middle left matrix entry.
double m11;
/// The middle, middle right matrix entry.
double m12;
/// The middle, right matrix entry.
double m13;
/// The bottom, left matrix entry.
double m20;
/// The bottom, middle left matrix entry.
double m21;
/// The bottom, middle right matrix entry.
double m22;
/// The bottom, right matrix entry.
double m23;
};
}; }; }; };
#endif
|
