Key points are not available for this paper at this time.
Given a set of points P = p1, p2, …, pn in three dimensions, the width of P, W (P), is defined as the minimum distance between parallel planes of support of P. It is shown that W (P) can be computed in Ο (n log n + I) time and Ο (n) space, where I is the number of antipodal pairs of edges of the convex hull of P, and in the worst case I - Ο (n2). If P is a set of points in the plane, this complexity can be reduced to Ο (n log n). Finally, for simple polygons linear time suffices.
Houle et al. (Tue,) studied this question.