I have been struggling with a bizzare problem in Protel PCB.
It refuses to accept that some pads (with reliefs to an internal plane) are actually connected.
This illustrates the issue
A connects to B but does not connect to C. This is obviously nonsense!
Protel requires that for a split plane to be DRC-correct, the split must be done by placing a POLYGON PLANE onto the plane, without a fill, so you get just the outline track. So obviously their algorithm is a bit "simple". Yet, no matter how many times I re-do this process of placing that polygon, I cannot make it see C as connected to A and B. In the end I fixed it by connecting B-C with a track... The polygon principle definitely works in other scenarios.
It raises the specific question of how PCB software handles split planes. How does it determine which pads (with reliefs to the plane) are actually connected to each other, if there is a weird geometry in the split? (the above case has no weird geometry; it is blindingly obvious that A B and C are connected!)
One obvious way to determine topological connectivity is by dividing the whole plane into squares and "colouring in" each square around a particular pad, and working outwards until you reach the external boundary, and if there is a contiguous line of coloured-in squares between two pads, then those two pads are connected.
That will break down if the grid used for the squares is bigger than a narrow channel in a split plane.
I don't know if there are algorithms which can determine connectivity without doing this i.e. which will pick up a conductive channel of any width or complexity, no matter how narrow?