I'm currently partitioning a big area $A$ into $n$ areas $B_i$ such that $$\bigcup_{i=1}^n B_i = A$$
I have geo-coordinates which I know are in $A$ (also with the finite precision of floats).
Obviously, for every point $p$ in $A$ there has to be an area $B_i$ such that the point is in $B_i$. Formally:
$$p \in A \Rightarrow \exists i: p \in B_i$$
But due to floating point precision, I wonder if it could happen that for all $B_i$ the B_i.intersects(p)
method returns false. Formally:
$$\forall i: \neg B_i.\texttt{intersects}(p)$$
All areas are polygons and neighboring polygons share some points which define the polygons.
If the answer is yes, then an example would be good. It would be awesome if one could also quantify the probability of this.
(In my current case, I use shapely.)