I just want to give you the name

voronoi diagram.

I've only seen the case where the "influence" of a point is the euclidean distance. That is, for each point p

of an input set you get a corresponding "section" (cell) which contains all points which distance to p is not greater

than to every other point of the input set.

So it doesn't actually fit your problem but I imagine there are other forms of the vornoi diagram which solve your problem.

Or maybe you find a way to make the borders fuzzy, don't know.

You're picture reminded me of this, so just use this term to google

Note, however, that most algorithms for voronoi diagrams compute a representation of the borders of the section, like a graph, for

instance. I could imagine that's not what you need.

If you just want to draw such sections, why not draw several predefined sections on top of each other? This should even work

with picking.

You could use

metaballs to generate sections.

What are you trying to do, anyways?