Thanks, I should have reminded myself that my intuitions are often non-mathematical. I don't even know how I decided that a change in angle would have a non-linear effect on density.

I also had an intuition that the aspect ratio change would squish the distribution. I guess this aspect ratio doesn't matter for the density distribution of dimensionless points.

But, if doing something like splatting a pixel/sprite at each point coordinate, would the sprite shape need to be transformed to match...?