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

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  19
  20 module com {  module sun {  module star {  module geometry {
  21
  22 /** This structure defines a 2 by 3 affine matrix.<p>
  23
  24     The matrix defined by this structure constitutes an affine mapping
  25     of a point in 2D to another point in 2D. The last line of a
  26     complete 3 by 3 matrix is omitted, since it is implicitly assumed
  27     to be [0,0,1].<p>
  28
  29     An affine mapping, as performed by this matrix, can be written out
  30     as follows, where <code>xs</code> and <code>ys</code> are the source, and
  31     <code>xd</code> and <code>yd</code> the corresponding result coordinates:
  32
  33     <code>
  34         xd = m00*xs + m01*ys + m02;
  35         yd = m10*xs + m11*ys + m12;
  36     </code><p>
  37
  38     Thus, in common matrix language, with M being the
  39     AffineMatrix2D and vs=[xs,ys]^T, vd=[xd,yd]^T two 2D
  40     vectors, the affine transformation is written as
  41     vd=M*vs. Concatenation of transformations amounts to
  42     multiplication of matrices, i.e. a translation, given by T,
  43     followed by a rotation, given by R, is expressed as vd=R*(T*vs) in
  44     the above notation. Since matrix multiplication is associative,
  45     this can be shortened to vd=(R*T)*vs=M'*vs. Therefore, a set of
  46     consecutive transformations can be accumulated into a single
  47     AffineMatrix2D, by multiplying the current transformation with the
  48     additional transformation from the left.<p>
  49
  50     Due to this transformational approach, all geometry data types are
  51     points in abstract integer or real coordinate spaces, without any
  52     physical dimensions attached to them. This physical measurement
  53     units are typically only added when using these data types to
  54     render something onto a physical output device, like a screen or a
  55     printer, Then, the total transformation matrix and the device
  56     resolution determine the actual measurement unit.<p>
  57
  58     @since OOo 2.0
  59  */
  60 struct AffineMatrix2D
  61 {
  62     /// The top, left matrix entry.
  63     double m00;
  64
  65     /// The top, middle matrix entry.
  66     double m01;
  67
  68     /// The top, right matrix entry.
  69     double m02;
  70
  71     /// The bottom, left matrix entry.
  72     double m10;
  73
  74     /// The bottom, middle matrix entry.
  75     double m11;
  76
  77     /// The bottom, right matrix entry.
  78     double m12;
  79 };
  80
  81 }; }; }; };
  82
  83 /* vim:set shiftwidth=4 softtabstop=4 expandtab: */