Is there a known/existing algorithm for taking a 2D canvas covered in  arbitrarily/randomly distributed points and dividing it entirely into a set of non-overlapping polygons? An example of the kind of result I'm looking for:
Is there a computationally reasonable algorithm for generating a set of polygons from a set of 2d points?
algorithms;graphs
You might be looking for a Voronoi diagram.  Given a set $S$ of points, it creates one cell per point, where the cell for point $p$ contains everything that is closer to $p$ than to any other point in $S$.  There are algorithms to compute a Voronoi diagram in $O(n \lg n)$ time, where $n$ is the number of points in your set.