[cairo] Adding cairo_shear and family

[Behdad Esfahbod]

Hey,

I think the API is mainly designed to be used with either nonzero sx or sy,
not both.  I like having the exact matrix in there.  We don't do that for
rotate, scale, and translate because they are obvious.  I don't like the idea
of separate calls.

behdad

M Joonas Pihlaja wrote:
> 
> Hi,
> 
> I think calling a 2x2 multiplication by
> 
> [ 1  sx]
> [ sy  1]
> 
> a shear is slightly misleading since shears don't commute. While it's
> true that shears along the coordinate axes are given respectively by
> 
> [1 sx], [1  0],
> [0  1]  [sy 1]
> 
> it matters whether one does an x-shear first or a y-shear first, and [1
> sx; sy 1] isn't a simple combination of x- and y-shears alone.  Also,
> the inverse of the [1 sx; sy 1] matrix is
> 
>      1       [1  -sx]
> -----------  [-sy  1].
> (1 - sx sy)
> 
> Finally, I think the docs shouldn't give the equations in matrix form
> but rather in words and scalar equations like the others do. None of the
> other cairo_t or cairo_matrix_t functions use matrix form.
> 
> Cheers,
> 
> Joonas
>