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21
22
23#ifndef __com_sun_star_geometry_Matrix2D_idl__
24#define __com_sun_star_geometry_Matrix2D_idl__
25
26module com {  module sun {  module star {  module geometry {
27
28/** This structure defines a 2 by 2 matrix.<p>
29
30    This constitutes a linear mapping of a point in 2D to another
31    point in 2D.<p>
32
33    The matrix defined by this structure constitutes a linear
34    mapping of a point in 2D to another point in 2D. In contrast to
35    the <type>com.sun.star.geometry.AffineMatrix2D</type>, this
36    matrix does not include any translational components.<p>
37
38    A linear mapping, as performed by this matrix, can be written out
39    as follows, where <code>xs</code> and <code>ys</code> are the source, and
40    <code>xd</code> and <code>yd</code> the corresponding result coordinates:
41
42    <code>
43        xd = m00*xs + m01*ys;
44        yd = m10*xs + m11*ys;
45    </code><p>
46
47    Thus, in common matrix language, with M being the
48    <type>Matrix2D</type> and vs=[xs,ys]^T, vd=[xd,yd]^T two 2D
49    vectors, the linear mapping is written as
50    vd=M*vs. Concatenation of transformations amounts to
51    multiplication of matrices, i.e. a scaling, given by S,
52    followed by a rotation, given by R, is expressed as vd=R*(S*vs) in
53    the above notation. Since matrix multiplication is associative,
54    this can be shortened to vd=(R*S)*vs=M'*vs. Therefore, a set of
55    consecutive transformations can be accumulated into a single
56    Matrix2D, by multiplying the current transformation with the
57    additional transformation from the left.<p>
58
59    Due to this transformational approach, all geometry data types are
60    points in abstract integer or real coordinate spaces, without any
61    physical dimensions attached to them. This physical measurement
62    units are typically only added when using these data types to
63    render something onto a physical output device, like a screen or a
64    printer. Then, the total transformation matrix and the device
65    resolution determine the actual measurement unit.<p>
66
67    @since OOo 2.0
68 */
69published struct Matrix2D
70{
71    /// The top, left matrix entry.
72    double m00;
73
74    /// The top, right matrix entry.
75    double m01;
76
77    /// The bottom, left matrix entry.
78    double m10;
79
80    /// The bottom, right matrix entry.
81    double m11;
82};
83
84}; }; }; };
85
86#endif
87