A Note on Approximate Convex Hulls

Bentley, Faust and Preparata [1] presented a linear time algorithm for computing an approximate convex hull in two-dimensional space. They compute a polygon with vertices in the given set of points in the plane such that the polygon is arbitrarily close to the convex hull of the point set. Soisalon-Soininen [2] modified the approximation scheme of [1] and, among other things, gave a criterion which depends on the required accuracy and which selects edges of the computed approximate hull such that no points can lie 'behind' these edges. However, the criterion given in [2] is not quite correct and an additional condition is required for the edges to be selected. In this note we present a correct form of this criterion.