Find coverage for plane from half-planes
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.