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

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  31 #ifndef __com_sun_star_geometry_AffineMatrix3D_idl__
  32 #define __com_sun_star_geometry_AffineMatrix3D_idl__
  33
  34 module com {  module sun {  module star {  module geometry {
  35
  36 /** This structure defines a 3 by 4 affine matrix.<p>
  37
  38     The matrix defined by this structure constitutes an affine mapping
  39     of a point in 3D to another point in 3D. The last line of a
  40     complete 4 by 4 matrix is omitted, since it is implicitely assumed
  41     to be [0,0,0,1].<p>
  42
  43     An affine mapping, as performed by this matrix, can be written out
  44     as follows, where <code>xs, ys</code> and <code>zs</code> are the source, and
  45     <code>xd, yd</code> and <code>zd</code> the corresponding result coordinates:
  46
  47     <code>
  48         xd = m00*xs + m01*ys + m02*zs + m03;
  49         yd = m10*xs + m11*ys + m12*zs + m13;
  50         zd = m20*xs + m21*ys + m22*zs + m23;
  51     </code><p>
  52
  53     Thus, in common matrix language, with M being the
  54     <type>AffineMatrix3D</type> and vs=[xs,ys,zs]^T, vd=[xd,yd,zd]^T two 3D
  55     vectors, the affine transformation is written as
  56     vd=M*vs. Concatenation of transformations amounts to
  57     multiplication of matrices, i.e. a translation, given by T,
  58     followed by a rotation, given by R, is expressed as vd=R*(T*vs) in
  59     the above notation. Since matrix multiplication is associative,
  60     this can be shortened to vd=(R*T)*vs=M'*vs. Therefore, a set of
  61     consecutive transformations can be accumulated into a single
  62     AffineMatrix3D, by multiplying the current transformation with the
  63     additional transformation from the left.<p>
  64
  65     Due to this transformational approach, all geometry data types are
  66     points in abstract integer or real coordinate spaces, without any
  67     physical dimensions attached to them. This physical measurement
  68     units are typically only added when using these data types to
  69     render something onto a physical output device. For 3D coordinates
  70     there is also a projection from 3D to 2D device coordiantes needed.
  71     Only then the total transformation matrix (oncluding projection to 2D)
  72     and the device resolution determine the actual measurement unit in 3D.<p>
  73
  74     @since OOo 2.0.0
  75  */
  76 struct AffineMatrix3D
  77 {
  78     /// The top, left matrix entry.
  79     double m00;
  80
  81     /// The top, left middle matrix entry.
  82     double m01;
  83
  84     /// The top, right middle matrix entry.
  85     double m02;
  86
  87     /// The top, right matrix entry.
  88     double m03;
  89
  90     /// The middle, left matrix entry.
  91     double m10;
  92
  93     /// The middle, middle left matrix entry.
  94     double m11;
  95
  96     /// The middle, middle right matrix entry.
  97     double m12;
  98
  99     /// The middle, right matrix entry.
 100     double m13;
 101
 102     /// The bottom, left matrix entry.
 103     double m20;
 104
 105     /// The bottom, middle left matrix entry.
 106     double m21;
 107
 108     /// The bottom, middle right matrix entry.
 109     double m22;
 110
 111     /// The bottom, right matrix entry.
 112     double m23;
 113 };
 114
 115 }; }; }; };
 116
 117 #endif