  In this paper, we establish two necessary conditions for a joint
triangulation of two sets of $n$ points in the plane and conjecture that they
are sufficient. We show that these necessary conditions can be tested in
$O(n^3)$ time. For the problem of a joint triangulation of two simple polygons
of $n$ vertices, we propose an $O(n^3)$ time algorithm for constructing a joint
triangulation using dynamic programming.
