The obstacle problem in no-tension structures and cable nets

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