Square Quads Topology for non-complex meshes

Is there any straight-forward way to give a simple mesh, like a plane, a square-grid topology? I’m talking about as square as possible and not rectangles of arbitrary ratios.

This can be important for multiple applications. Apart from texturing, I’m thinking of simulations. In particular, I came across a very interesting blog from Dion Moult, who explores some different fields of using Blender (I have Ladybug simulations in my mind right now). Not that I have not tinkered with it much; my only short experience is through Rhino + Grasshopper. Check this guy out, promising stuff.

Also, back to the topic; say you want to be able to edit the mesh in order to change its proportions. Is there an interactive/ procedural/ whatnot way to retain the “as square as possible grid” topology? This would give the suggested workflows so much more meaning.