Reading the link above, @l. spiro mentioned once you setup your texel adjacency across borders, filtering remains the same as with flat textures. And i remember her to have expertise on this subject.
But it's not really correct to leave it at this. The problem is at the corner regions, where only 3 texels meet not 4. If you use usual bilinear interpolation, what's the proposed solution for the missing 4th texel?
The correct solution would be expensive. It requires to deal with 3 texels, their edges being 120 degrees apart from each other. It's expensive because of the divergent code branch which only a few threads will take. My first idea to calculate weights would be to use mean value weights, which differs wildly from simple bilinear weights.
So i always wondered how this is handled in practice. I assume some compromise, e.g. generating a 4th texel from the average of it's two neighbors.
This would cause a small discontinuity at the 8 corners, but maybe that's acceptable?
If anyone knows, i'm curious since many years about this detail… : )