[cairo] Adding cairo_shear and family

[Bill Spitzak]

Behdad Esfahbod wrote:
> M Joonas Pihlaja wrote:
> 
>> FWIW, I liked Bill's and Paolo's approach of an area preserving mapping
>> (this being one of the properties of a shear) and along those lines I
>> would propose using
>>
>> [1 +- sqrt(-sx*sy)    sx
>> sy            1 -+ sqrt(-sx*sy)],
> 
> I initially liked it too.  But it's too hard to see what that's doing.  The
> good thing about [1 sx sy 1] is that combined with a cairo_scale, you can map
> your two coordinates onto arbitrary vectors *easily* just by a cairo_scale and
> a cairo_shear.  That's not the case with the area-preserving variant.

You can get two arbitrary vectors "easily" by putting the values right 
into the matrix: [xx xy yx yy 0 0] where the vector for the x axis is 
[xx xy] and the vector for the y axis is [yx yy].

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Bill Spitzak, Senior Software Engineer
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