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

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  27 #ifndef __com_sun_star_geometry_AffineMatrix2D_idl__
  28 #define __com_sun_star_geometry_AffineMatrix2D_idl__
  29
  30 module com {  module sun {  module star {  module geometry {
  31
  32 /** This structure defines a 2 by 3 affine matrix.<p>
  33
  34     The matrix defined by this structure constitutes an affine mapping
  35     of a point in 2D to another point in 2D. The last line of a
  36     complete 3 by 3 matrix is omitted, since it is implicitely assumed
  37     to be [0,0,1].<p>
  38
  39     An affine mapping, as performed by this matrix, can be written out
  40     as follows, where <code>xs</code> and <code>ys</code> are the source, and
  41     <code>xd</code> and <code>yd</code> the corresponding result coordinates:
  42
  43     <code>
  44         xd = m00*xs + m01*ys + m02;
  45         yd = m10*xs + m11*ys + m12;
  46     </code><p>
  47
  48     Thus, in common matrix language, with M being the
  49     <type>AffineMatrix2D</type> and vs=[xs,ys]^T, vd=[xd,yd]^T two 2D
  50     vectors, the affine transformation is written as
  51     vd=M*vs. Concatenation of transformations amounts to
  52     multiplication of matrices, i.e. a translation, given by T,
  53     followed by a rotation, given by R, is expressed as vd=R*(T*vs) in
  54     the above notation. Since matrix multiplication is associative,
  55     this can be shortened to vd=(R*T)*vs=M'*vs. Therefore, a set of
  56     consecutive transformations can be accumulated into a single
  57     AffineMatrix2D, by multiplying the current transformation with the
  58     additional transformation from the left.<p>
  59
  60     Due to this transformational approach, all geometry data types are
  61     points in abstract integer or real coordinate spaces, without any
  62     physical dimensions attached to them. This physical measurement
  63     units are typically only added when using these data types to
  64     render something onto a physical output device, like a screen or a
  65     printer, Then, the total transformation matrix and the device
  66     resolution determine the actual measurement unit.<p>
  67
  68     @since OOo 2.0.0
  69  */
  70 struct AffineMatrix2D
  71 {
  72     /// The top, left matrix entry.
  73     double m00;
  74
  75     /// The top, middle matrix entry.
  76     double m01;
  77
  78     /// The top, right matrix entry.
  79     double m02;
  80
  81     /// The bottom, left matrix entry.
  82     double m10;
  83
  84     /// The bottom, middle matrix entry.
  85     double m11;
  86
  87     /// The bottom, right matrix entry.
  88     double m12;
  89 };
  90
  91 }; }; }; };
  92
  93 #endif