Re: [Devel] pixel size, hinting and scaling

[Artur Zaprzała]

Graham Asher wrote:
> Here's some working code that decomposes a FreeType matrix into scale and
> the rest. I'd be grateful for comments. It converts the matrix's effect on a
> vector pointing rightward into a new matrix representing the inverse of the
> rotation. It then removes the rotation, stores the scale factors, removes
> the scales, and adds the rotation back. The scales are forced positive so
> that they can be used to set pixel sizes without further manipulation (apart
> from converting to 1/64 pixels).
>
> I developed this code as part of my work for Artifex on the
> GhostScript-to-FreeType bridge.


Decomposing affine transform to scaling and the rest is ambiguous. 
Notice that you can docompose each rotation (except when a=0||b=0) to 
shearing and scaling:
|a b|    |a 0|   | 1  b/a|
|   | =  |   | * |       |
|c d|    |0 d|   |c/d  1 |

so you cannot get scaling only part and rotation-and-shear only part.

Using [1,0] vector to find rotation you miss x-axis skew. If you use 
e.g. [0,1] vector in you, you'll get different scales.


--
Artur Zaprzała