On the convex layers of a planar set

B. Chazelle
1985 IEEE Transactions on Information Theory  
Let S be a set of n points in the Euclidean plane. The convex layers of S are the convex polygons obtained by iterating on the following procedure: compute the convex hull of S and remove its vertices from S. This process of peeling a planar point set is central in the study of robust estimators in statistics. It also provides valuable information on the morphology of a set of sites and has proven to be an efficient preconditioning for range search problems. An optimal algorithm is described
more » ... computing the convex layers of S. The algorithm runs in O( n log n) time and requires O(n) space. Also addressed is the problem of determining the depth of a query point within the convex layers of S, i.e., the number of layers that enclose the query point. This is essentially a planar point location problem, for which optimal solutions are therefore known. Taking advantage of structural properties of the problem, however, a much simpler optimal solution is derived.
doi:10.1109/tit.1985.1057060 fatcat:yaon7b76g5g23mkufm2dusw3ky