Finite blocking property

A translation surface S is said to have the finite blocking property if for every pair (O,A) of points in S, there exists a finite number of blocking points B_1, ... , B_n (different from O and A) such that every geodesic from O to A meets one of the B_i's.

If T is a torus, then T has the finite blocking property and the blocking points can be choosen to be the middles of the geodesics from O to A (even if there are infinitely many geodesics from O to A, there are at most 4 middles).
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