I'm interested in calculating the Hausdorff Distance between 2 polygons (specifically quadrilaterals which are almost rectangles) defined by their vertices. They may overlap.
Recall $d_H(A,B) = \max(d(A,B), d(B,A))$ where $d$ is the Hausdorff semi-metric $d(A,B) = \sup_{a\in A}\inf_{b\in B}d(a,b)$.
Is it true that, given a finite disjoint covering of $A$, $\{A_i\}$, $d(A,B)=\max\{d(A_i,B)\}$? A corollary of which is that $d(A,B)=d(A\setminus B,B)$.
I have found a paper by Atallah 1 (PDF). I'm interested in working in Python and would be open to any preprogrammed solutions.
Yes, if $\cup A_i = A$. This follows from transitivity of comparison operators. It does not matter how you divide your points, $\max\{\sup A, \sup B\} = \sup A \cup B$.