Siarhei Siamashka wrote:
Bilinear scaling uses weighted average of 2 pixels (in one direction), with weights calculated on the go. Separable convolution uses weighted average of N pixels, with weights obtained by table lookups. Both use subpixel positions (7 phase bits or 128 phases for current bilinear implementation) to lookup or calculate weights. Bilinear filter is naturally a subset of separable convolution.
Also note that the separable filters need different "widths" as well as different phases. This is the distance from the center to the first 0 crossing in a sync filter, note that the non-zero part of the filter is several times the width (3 for a triangle, 5 for most, and 7 for lancos3). If the image is being scaled by 1/N the width is max(1,N).
There probably should be a pre-calculated table of all combinations of width and phase. The minimum width is 1, but there will have to be a maximum chosen. Pixman would use the maximum if a larger size is wanted, which would mean that scales smaller than a certain value would be noisy. However if Cairo prescales by a power of 2 then the maximum scale may be 4.
In Nuke the pre-calculated table is just a very wide filter (I think the width is 64) and that is the maximum filter size. Smaller filters and different offsets are chosen by subsampling this large filter at even intervals (Nuke chose the closest sample, but bilinear sampling would be better). The table was "normalized" so that the width of 1 produced samples that sum to 1, all larger filters needed to a normalization factor calculated by doing 1/sum of the samples.
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