Find coverage for plane from half-planes The document (see pic. below) states that it is possible to find a cover of the plane by a subset of 3 half-planes. It proposes to use linear programming for this. How to formulate such a program?



The original document can be found here: On the Separation of a Polyhedron from Its Single-Part Mold.

EDIT: For clarity: i need to understand how can i use LP to find subcoverage of size 3 from coverage of bigger size.
I believe the connection between Helly's theorem and linear programming
stems from this paper:


  Amenta, Nina. "Helly-type theorems and generalized linear programming." Discrete &amp; Computational Geometry 12, no. 3 (1994): 241-261.
  (Springer link.)


This arose from Nina Amenta's Ph.D. thesis (PDF download),
under the direction of Raimund Seidel.