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module com {  module sun {  module star {  module geometry {

/** This structure defines a 3 by 4 affine matrix.<p>

    The matrix defined by this structure constitutes an affine mapping
    of a point in 3D to another point in 3D. The last line of a
    complete 4 by 4 matrix is omitted, since it is implicitly assumed
    to be [0,0,0,1].<p>

    An affine mapping, as performed by this matrix, can be written out
    as follows, where <code>xs, ys</code> and <code>zs</code> are the source, and
    <code>xd, yd</code> and <code>zd</code> the corresponding result coordinates:

    <code>
        xd = m00*xs + m01*ys + m02*zs + m03;
        yd = m10*xs + m11*ys + m12*zs + m13;
        zd = m20*xs + m21*ys + m22*zs + m23;
    </code><p>

    Thus, in common matrix language, with M being the
    AffineMatrix3D and vs=[xs,ys,zs]^T, vd=[xd,yd,zd]^T two 3D
    vectors, the affine transformation is written as
    vd=M*vs. Concatenation of transformations amounts to
    multiplication of matrices, i.e. a translation, given by T,
    followed by a rotation, given by R, is expressed as vd=R*(T*vs) in
    the above notation. Since matrix multiplication is associative,
    this can be shortened to vd=(R*T)*vs=M'*vs. Therefore, a set of
    consecutive transformations can be accumulated into a single
    AffineMatrix3D, by multiplying the current transformation with the
    additional transformation from the left.<p>

    Due to this transformational approach, all geometry data types are
    points in abstract integer or real coordinate spaces, without any
    physical dimensions attached to them. This physical measurement
    units are typically only added when using these data types to
    render something onto a physical output device. For 3D coordinates
    there is also a projection from 3D to 2D device coordinates needed.
    Only then the total transformation matrix (including projection to 2D)
    and the device resolution determine the actual measurement unit in 3D.<p>

    @since OOo 2.0
 */
struct AffineMatrix3D
{
    /// The top, left matrix entry.
    double m00;

    /// The top, left middle matrix entry.
    double m01;

    /// The top, right middle matrix entry.
    double m02;

    /// The top, right matrix entry.
    double m03;

    /// The middle, left matrix entry.
    double m10;

    /// The middle, middle left matrix entry.
    double m11;

    /// The middle, middle right matrix entry.
    double m12;

    /// The middle, right matrix entry.
    double m13;

    /// The bottom, left matrix entry.
    double m20;

    /// The bottom, middle left matrix entry.
    double m21;

    /// The bottom, middle right matrix entry.
    double m22;

    /// The bottom, right matrix entry.
    double m23;
};

}; }; }; };

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