offapi/com/sun/star/geometry/Matrix2D.idl

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  19
  20 module com {  module sun {  module star {  module geometry {
  21
  22 /** This structure defines a 2 by 2 matrix.<p>
  23
  24     This constitutes a linear mapping of a point in 2D to another
  25     point in 2D.<p>
  26
  27     The matrix defined by this structure constitutes a linear
  28     mapping of a point in 2D to another point in 2D. In contrast to
  29     the com.sun.star.geometry.AffineMatrix2D, this
  30     matrix does not include any translational components.<p>
  31
  32     A linear mapping, as performed by this matrix, can be written out
  33     as follows, where <code>xs</code> and <code>ys</code> are the source, and
  34     <code>xd</code> and <code>yd</code> the corresponding result coordinates:
  35
  36     <code>
  37         xd = m00*xs + m01*ys;
  38         yd = m10*xs + m11*ys;
  39     </code><p>
  40
  41     Thus, in common matrix language, with M being the
  42     Matrix2D and vs=[xs,ys]^T, vd=[xd,yd]^T two 2D
  43     vectors, the linear mapping is written as
  44     vd=M*vs. Concatenation of transformations amounts to
  45     multiplication of matrices, i.e. a scaling, given by S,
  46     followed by a rotation, given by R, is expressed as vd=R*(S*vs) in
  47     the above notation. Since matrix multiplication is associative,
  48     this can be shortened to vd=(R*S)*vs=M'*vs. Therefore, a set of
  49     consecutive transformations can be accumulated into a single
  50     Matrix2D, by multiplying the current transformation with the
  51     additional transformation from the left.<p>
  52
  53     Due to this transformational approach, all geometry data types are
  54     points in abstract integer or real coordinate spaces, without any
  55     physical dimensions attached to them. This physical measurement
  56     units are typically only added when using these data types to
  57     render something onto a physical output device, like a screen or a
  58     printer. Then, the total transformation matrix and the device
  59     resolution determine the actual measurement unit.<p>
  60
  61     @since OOo 2.0
  62  */
  63 struct Matrix2D
  64 {
  65     /// The top, left matrix entry.
  66     double m00;
  67
  68     /// The top, right matrix entry.
  69     double m01;
  70
  71     /// The bottom, left matrix entry.
  72     double m10;
  73
  74     /// The bottom, right matrix entry.
  75     double m11;
  76 };
  77
  78 }; }; }; };
  79
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