  We consider the problem of finding a net that supports prescribed forces
applied at prescribed points, yet avoids certain obstacles, with all the
elements of the net under compression (strut net) or under tension (cable web).
In the case of masonry structures, for instance, this consists in finding a
strut net that supports the forces, is contained within the physical structure,
and avoids regions that may be not accessible due, for instance, to the
presence of holes. We solve such a problem in the two-dimensional case, where
the prescribed forces are applied at the vertices of a convex polygon, and we
treat the cases of both single and multiple obstacles. By approximating the
obstacles by polygonal regions, the task reduces to identifying the feasible
domain in a linear programming problem. For a single obstacle we show how the
region $\Gamma$ available to the obstacle can be enlarged as much as possible
in the sense that there is no other strut net, having a region $\Gamma_1$
available to the obstacle with $\Gamma_1 \subset\Gamma$. The case where some of
the forces are reactive, unprescribed but reacting to the other prescribed
forces, is also treated. It again reduces to identifying the feasible domain in
a linear programming problem. Finally, one may allow a subset of the reactive
forces to each act not at a prescribed point, but rather at any point on a
prescribed line segment. Then the task reduces to identifying the feasible
domain in a quadratic programming problem.
