Question: Coloring of 2D concave polygons. What process is happening?

Lett_K_etc_Coloring.mws

In the attached program the letters K, M, H are drawn.  These are examples of concave polygons.  (The fact that they happen to be letters is immaterial here.)  I'm interested in the coloring in process.  I experimented with simple shapes, like the letters I and L, which have a small number of points - and the letter I is convex.  These polygons colored in without a hitch.  It seems a general rule is:

    Color the first half dozen points given, then head home towards the first point - then return to the next point.  Does it color in by separating the polygon into pentagons, or hexagons?  

   I'm aware of how to draw & color shapes by splitting them into a smaller number of polygons, so please don't waste time improving my code.   I'dd appreciate my hunch being verified, or a reference to more information.  TIA