RE: [Devel] Freetype 2.1.2 & rotated text - no change necessary from FreeType 2.1.0

[Graham Asher]

David,

as far as I can see the transformation problem is notational. Using the
PostScript convention (see p. 187 of the PostScript Language Reference
Manual, 3rd Ed.) we have 6 coefficients - the variable members of a 3 x 3
matrix:

A B 0
C D 0
X Y 1

and the formula for applying a transformation is

x' = Ax + Cy + X
y' = Bx + Dy + Y

It seems that FreeType has borrowed the xx, yx, xy, yy notation from Donald
Knuth's METAFONT (see p. 142 of The METAFONTbook), which uses the notation,
given here in matrix form

XX YX 0
XY YY 0
X Y 1

and states that the formula is

x' = X + x * XX + y * XY
y' = Y + x * YX + y * YY

In PostScript these values are stored in the order A B C D X Y, but in
FreeType we have:

xx = A
yx = B
xy = C
yy = D,

so we are storing them in the order A C B D. Hence the confusion.

BUT - this is PURELY a notational question. FT_Matrix is not buggy, and
neither is FT_Vector_Transform. So please don't change them. To change them
would screw up the notation and destroy the correspondence of the names of
the members of FT_Matrix with the coefficients defined by METAFONT and
probably elsewhere.

Best regards,

Graham