On an Isomorphic Direction of Improving and Optimizing an Algorithm for Determining the Convex Hull of 2D Point Set or Line Segment Set

In this paper, the common weakness of the current algorithms for seeking the convex hull of a finite 2D points set or Line Segment Set (include: polygons, closure broken lines, semi-closure broken lines,opening line segments, etc. is pointed out up to day; the isomorphic fundamental theorem of the convex hull is raised, with which an algorithm for determining the convex hull would be improved and optimized. Further, based on the isomorphic fundamental theorem of the convex hull, an isomorphic direction of improving and optimizing an algorithm for determining the convex hull of a finite 2D points set or line segments set is clarified, which should be: 1. a minimum distributed domain of the poles of the convex hull, i.e., make that the domain including all poles of the convex hull is as small as possible; a immediate objects-judged for all poles of the convex hull, i.e., make all objects-judged are as near by the current poles of the convex hull to be determined as possible. 2 try one's best to improve the excellent sequential algorithms, which would be reformed, for finding the convex hull into their parallel algorithms, or create other new parallel algorithms.