offapi/com/sun/star/geometry/AffineMatrix3D.idl

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  19
  20 module com {  module sun {  module star {  module geometry {
  21
  22 /** This structure defines a 3 by 4 affine matrix.<p>
  23
  24     The matrix defined by this structure constitutes an affine mapping
  25     of a point in 3D to another point in 3D. The last line of a
  26     complete 4 by 4 matrix is omitted, since it is implicitly assumed
  27     to be [0,0,0,1].<p>
  28
  29     An affine mapping, as performed by this matrix, can be written out
  30     as follows, where <code>xs, ys</code> and <code>zs</code> are the source, and
  31     <code>xd, yd</code> and <code>zd</code> the corresponding result coordinates:
  32
  33     <code>
  34         xd = m00*xs + m01*ys + m02*zs + m03;
  35         yd = m10*xs + m11*ys + m12*zs + m13;
  36         zd = m20*xs + m21*ys + m22*zs + m23;
  37     </code><p>
  38
  39     Thus, in common matrix language, with M being the
  40     AffineMatrix3D and vs=[xs,ys,zs]^T, vd=[xd,yd,zd]^T two 3D
  41     vectors, the affine transformation is written as
  42     vd=M*vs. Concatenation of transformations amounts to
  43     multiplication of matrices, i.e. a translation, given by T,
  44     followed by a rotation, given by R, is expressed as vd=R*(T*vs) in
  45     the above notation. Since matrix multiplication is associative,
  46     this can be shortened to vd=(R*T)*vs=M'*vs. Therefore, a set of
  47     consecutive transformations can be accumulated into a single
  48     AffineMatrix3D, by multiplying the current transformation with the
  49     additional transformation from the left.<p>
  50
  51     Due to this transformational approach, all geometry data types are
  52     points in abstract integer or real coordinate spaces, without any
  53     physical dimensions attached to them. This physical measurement
  54     units are typically only added when using these data types to
  55     render something onto a physical output device. For 3D coordinates
  56     there is also a projection from 3D to 2D device coordinates needed.
  57     Only then the total transformation matrix (including projection to 2D)
  58     and the device resolution determine the actual measurement unit in 3D.<p>
  59
  60     @since OOo 2.0
  61  */
  62 struct AffineMatrix3D
  63 {
  64     /// The top, left matrix entry.
  65     double m00;
  66
  67     /// The top, left middle matrix entry.
  68     double m01;
  69
  70     /// The top, right middle matrix entry.
  71     double m02;
  72
  73     /// The top, right matrix entry.
  74     double m03;
  75
  76     /// The middle, left matrix entry.
  77     double m10;
  78
  79     /// The middle, middle left matrix entry.
  80     double m11;
  81
  82     /// The middle, middle right matrix entry.
  83     double m12;
  84
  85     /// The middle, right matrix entry.
  86     double m13;
  87
  88     /// The bottom, left matrix entry.
  89     double m20;
  90
  91     /// The bottom, middle left matrix entry.
  92     double m21;
  93
  94     /// The bottom, middle right matrix entry.
  95     double m22;
  96
  97     /// The bottom, right matrix entry.
  98     double m23;
  99 };
 100
 101 }; }; }; };
 102
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