Do most games use the premultiply method?

Its format is like a homogeneous division

un premultiplying is like homogeneous division

homogeneous division?

division in homogeneous coords

It's a bit like division in homogeneous coordinates

homogeneous division

homogeneous division

It is structured like homogeneous division

homogeneous division

looks like homogeneous division

Homogeneous division

While it looks most like homogeneous division, the steps at a high level remind me of perspective correct interpolation, if we treat the alpha as invw.

The division is reminiscent of homogenous coordinates where we want to normalize to the last value

Normalization of a vector?

Homogeneous division

Homogeneous division

Homogeneous division

homogenous division

homogenous division

homogenous division

homogeneous division

homogeneous division