A CONVEX HULL ALGORITHM FOR POINTS WITH APPROXIMATELY KNOWN POSITIONS

Abstract

We consider the problem of deriving good approximations of the convex hull of a set of points in the plane in the realistic case that only arbitrary finite approximations of the real valued coordinates can be known. In particular, the algorithm we introduce derives sequences of improved certified approximations converging to the exact solution, at the same time allowing the insertion of new points to the problem instance. The complexity analysis of the algorithm is performed by referring to a suitable computation model, based on a RAM with logarithmic costs, and the derived space and time bounds are shown to be competitive with respect to current off-line algorithms.