I have a list of vertices of simple polygons, and I would like to test whether or not a polygon is fully contained in another polygon in the list.
Is it sufficient to do something like:
Let $p_0$ be the candidate polygon.
Let $r_i, ~le_i, ~u_i, ~l_i$ denote the right most, left most, upper most and lower most vertex of the ith polygon in the list.
For all polygons in the list, if any polygon has:
- $r_i(x) \ge r_0(x)$ AND
- $le_i(x) \le le_0(x)$ AND
- $u_i(y) \ge u_0(y)$ AND
- $l_i(y) \le l_0(y)$
where for example $r_i(x)$ denotes the $x$-coordinate of the rightmost vertex of the $i$-th polygon, then we may conclude that $p_0$ is fully contained within $p_i$.
Does this make sense, and is there a counter example for which this algorithm doesn't work?