This constitutes a linear mapping of a point in 2D to another
point in 2D.
The matrix defined by this structure constitutes a linear
mapping of a point in 2D to another point in 2D. In contrast to
the ::com.sun.star.geometry.AffineMatrix2D, this
matrix does not include any translational components.
A linear mapping, as performed by this matrix, can be written out
as follows, where
ys are the source, and
yd the corresponding result coordinates:
xd = m00*xs + m01*ys;
yd = m10*xs + m11*ys;
Thus, in common matrix language, with M being the
Matrix2D and vs=[xs,ys]^T, vd=[xd,yd]^T two 2D
vectors, the linear mapping is written as
vd=M*vs. Concatenation of transformations amounts to
multiplication of matrices, i.e. a scaling, given by S,
followed by a rotation, given by R, is expressed as vd=R*(S*vs) in
the above notation. Since matrix multiplication is associative,
this can be shortened to vd=(R*S)*vs=M'*vs. Therefore, a set of
consecutive transformations can be accumulated into a single
Matrix2D, by multiplying the current transformation with the
additional transformation from the left.
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, like a screen or a
printer. Then, the total transformation matrix and the device
resolution determine the actual measurement unit.