Re: [Freetype] A question about rotated glyph metrics

[Alexander Gelfenbain]

Hi David,

thank you for your help!

On Thu, Aug 30, 2001 at 10:13:39AM +0200, David Turner wrote:
> > 
> > Question: what is the proper way to calculate glyph metrics for a 
> > transformed
> > glyph? If the transformed glyph is unhinted, my guess would be to load
> > an unscaled glyph, convert FUnits to floating point coordinates  and apply 
> > the affine
> > transform to them in my code. Or should I scale the untransformed glyph with
> > TT_Set_Instance_CharSize(1<<6), get its metrics and apply my affine 
> > transform to it?
> >
> 
> Generally speaking, you should decompose your affine transform into
> a scale then another rotation/skewing transform.

I don't have the _Graphics Gems III_ book that has an article on decomposing
affine transforms handy. It seems that if I have an 2x2 matrix that defines
an affine transform:

a11 a12
a21 a22


I can decompose it into  the scale matrix S

sx 0
0 sy

and the other affine transform matrix B using the following formulae:

sx = sqrt(a11**2 + a12**2);
sy = det(A)/sx;  where det(A) is a11*a22 - a12*a21.


b11 = a11/sx
b12 = a12/sx
b21 = a21/sy
b22 = a22/sy

does that sound correct?

Thanks,

AG


-- 
Alexander Gelfenbain, Sun Microsystems, Inc.
+1 (408) 635-0612