[cairo] Downing scaling images

[Bill Spitzak]

A different possible algorithm is to do downscaling in two steps. The 
second step uses a scale close enough to 1:1 that bilinear sampling is 
acceptable. Advantages of this are:

- The pixman code can be reused without changes
- The integer box filter is by far the fastest possible variable sized 
filter you can do.
- The result of the first step can be saved by Cairo, making redrawing 
the same transform (or similar ones such as rotations) much faster.

Disadvantages are:

- More blurring due to two filtering passes
- Blur will vary depending on the translation
- Space needed to store the intermediate surface (never more than 1/2 
the full size surface).
- If the source is on the server it will have to be copied to cairo's 
memory.

The algorithm is to reduce the transform to an integer scaling-only 
transform and a remainder matrix which scales by more or equal to a 
cutoff value. The cutoff needs to be chosen somewhere between .5 and 1, 
larger values will make it blurrier but reduce bilinear sampling artifacts.

The integer scale is then used to do very fast box-filtering of the 
image into a down-sized one (if it is 1:1 then this is skipped and the 
original image is used). This is very fast: for a 1/N by 1/M scale each 
output pixel is the average of a NxM rectangle of pixels and these 
rectangles do not overlap.

The remainder transform is then used by the pixman bilinear filter to 
sample this temporary image.

The temporary image is saved with the source surface, and invalidated 
only if that surface is changed or if a different-sized temporary 
surface is used.

Note that this is only an idea. I am worried about the blurring 
artifacts. A direct comparison to the filtering I described before shows 
that it has problems, though it is a lot better than some OpenGL mipmap 
scaling I compared it to.