offapi/com/sun/star/geometry/AffineMatrix2D.idl

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  28 #ifndef __com_sun_star_geometry_AffineMatrix2D_idl__
  29 #define __com_sun_star_geometry_AffineMatrix2D_idl__
  30
  31 module com {  module sun {  module star {  module geometry {
  32
  33 /** This structure defines a 2 by 3 affine matrix.<p>
  34
  35     The matrix defined by this structure constitutes an affine mapping
  36     of a point in 2D to another point in 2D. The last line of a
  37     complete 3 by 3 matrix is omitted, since it is implicitly assumed
  38     to be [0,0,1].<p>
  39
  40     An affine mapping, as performed by this matrix, can be written out
  41     as follows, where <code>xs</code> and <code>ys</code> are the source, and
  42     <code>xd</code> and <code>yd</code> the corresponding result coordinates:
  43
  44     <code>
  45         xd = m00*xs + m01*ys + m02;
  46         yd = m10*xs + m11*ys + m12;
  47     </code><p>
  48
  49     Thus, in common matrix language, with M being the
  50     <type>AffineMatrix2D</type> and vs=[xs,ys]^T, vd=[xd,yd]^T two 2D
  51     vectors, the affine transformation is written as
  52     vd=M*vs. Concatenation of transformations amounts to
  53     multiplication of matrices, i.e. a translation, given by T,
  54     followed by a rotation, given by R, is expressed as vd=R*(T*vs) in
  55     the above notation. Since matrix multiplication is associative,
  56     this can be shortened to vd=(R*T)*vs=M'*vs. Therefore, a set of
  57     consecutive transformations can be accumulated into a single
  58     AffineMatrix2D, by multiplying the current transformation with the
  59     additional transformation from the left.<p>
  60
  61     Due to this transformational approach, all geometry data types are
  62     points in abstract integer or real coordinate spaces, without any
  63     physical dimensions attached to them. This physical measurement
  64     units are typically only added when using these data types to
  65     render something onto a physical output device, like a screen or a
  66     printer, Then, the total transformation matrix and the device
  67     resolution determine the actual measurement unit.<p>
  68
  69     @since OOo 2.0
  70  */
  71 struct AffineMatrix2D
  72 {
  73     /// The top, left matrix entry.
  74     double m00;
  75
  76     /// The top, middle matrix entry.
  77     double m01;
  78
  79     /// The top, right matrix entry.
  80     double m02;
  81
  82     /// The bottom, left matrix entry.
  83     double m10;
  84
  85     /// The bottom, middle matrix entry.
  86     double m11;
  87
  88     /// The bottom, right matrix entry.
  89     double m12;
  90 };
  91
  92 }; }; }; };
  93
  94 #endif
  95
  96 /* vim:set shiftwidth=4 softtabstop=4 expandtab: */