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

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  27 #ifndef __com_sun_star_geometry_AffineMatrix3D_idl__
  28 #define __com_sun_star_geometry_AffineMatrix3D_idl__
  29
  30 module com {  module sun {  module star {  module geometry {
  31
  32 /** This structure defines a 3 by 4 affine matrix.<p>
  33
  34     The matrix defined by this structure constitutes an affine mapping
  35     of a point in 3D to another point in 3D. The last line of a
  36     complete 4 by 4 matrix is omitted, since it is implicitely assumed
  37     to be [0,0,0,1].<p>
  38
  39     An affine mapping, as performed by this matrix, can be written out
  40     as follows, where <code>xs, ys</code> and <code>zs</code> are the source, and
  41     <code>xd, yd</code> and <code>zd</code> the corresponding result coordinates:
  42
  43     <code>
  44         xd = m00*xs + m01*ys + m02*zs + m03;
  45         yd = m10*xs + m11*ys + m12*zs + m13;
  46         zd = m20*xs + m21*ys + m22*zs + m23;
  47     </code><p>
  48
  49     Thus, in common matrix language, with M being the
  50     <type>AffineMatrix3D</type> and vs=[xs,ys,zs]^T, vd=[xd,yd,zd]^T two 3D
  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     AffineMatrix3D, 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. For 3D coordinates
  66     there is also a projection from 3D to 2D device coordiantes needed.
  67     Only then the total transformation matrix (oncluding projection to 2D)
  68     and the device resolution determine the actual measurement unit in 3D.<p>
  69
  70     @since OOo 2.0.0
  71  */
  72 struct AffineMatrix3D
  73 {
  74     /// The top, left matrix entry.
  75     double m00;
  76
  77     /// The top, left middle matrix entry.
  78     double m01;
  79
  80     /// The top, right middle matrix entry.
  81     double m02;
  82
  83     /// The top, right matrix entry.
  84     double m03;
  85
  86     /// The middle, left matrix entry.
  87     double m10;
  88
  89     /// The middle, middle left matrix entry.
  90     double m11;
  91
  92     /// The middle, middle right matrix entry.
  93     double m12;
  94
  95     /// The middle, right matrix entry.
  96     double m13;
  97
  98     /// The bottom, left matrix entry.
  99     double m20;
 100
 101     /// The bottom, middle left matrix entry.
 102     double m21;
 103
 104     /// The bottom, middle right matrix entry.
 105     double m22;
 106
 107     /// The bottom, right matrix entry.
 108     double m23;
 109 };
 110
 111 }; }; }; };
 112
 113 #endif