About this alpha quad
selected the center and applied.
Suzanne with 1lv subd, some noise. Applied quads to whole model.
Looks like “false barycentric subdivision”. Obtained quads are a result of connecting every triangle center to the others. It gives out quads, but not the kind we’re looking for, if you know what I mean. The global geometry stays the same.
But let’s see. More test on it. Being python, it’s helluva slow.