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