[cairo] Adding cairo_shear and family

[Behdad Esfahbod]

Bill Spitzak wrote:
> 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].

Well, yeah.  That's the other thing I was thinking about: maybe we don't need
cairo_shear() afterall?

behdad