Convex hull problem with imprecise input

In this paper, we study the computation of a-dimensional convex hull of a set of points whose positions are inaccurate, that is, known only up to a given accuracy. To compute accuracy guaranteed results from such an imprecise input, we consider two types of convex hull, inner convex hull and outer convex hull which are defined as the intersection and the union of all possible convex hulls. The gap of these two hulls explicitly represents the accuracy of a possible convex hull. Under an assumption that the size of error is given for each input point, we show that the inner convex hull and the outer convex hull are calculated in O(n log n) time for n points in the plane.