Convex Hulls of Finite Planar and Spatial Sets of Points

Abstract : The convex hulls of planar and spatial sets of n points can be determined with O(n lg n) operations. The presented algorithms use the 'divide and conquer' technique and recursively apply a merge procedure for two nonintersecting convex hulls. It is also shown that any convex hull algorithm requires at least O(n lg n) operations, so that the time complexity of the proposed algorithms is optimal within a multiplicative constant.