A FAST AND COMPLETE CONVEX-HULL ALGORITHM ARCHITECTURE BASED ON ELLIPSE AND ELASTIC ELLIPSE METHODS

The number of inner points excluded in an initial convex hull (ICH) is vital to the efficiency getting the convex hull (CH) in a planar point set. The maximum inscribed circle method proposed recently is effective to remove inner points in ICH. However, limited by density distribution of a planar point set, it does not always work well. Although the affine transformation method can be used, it is still hard to have a better performance. Furthermore, the algorithm mentioned above fails to deal with the exceptional distribution: the gravity centroid (GC) of a planar point set is outside or on the edge formed by the extreme points in ICH. This paper considers how to remove more inner points in ICH when GC is inside of ICH and completely process the case which mentioned above. Further, we presented a complete algorithm architecture: (1) using the ellipse and elasticity ellipse methods (EM and EEM) to remove more inner points in ICH and process the cases: GC is inside or outside of ICH. (2) Using the traditional methods to process the situation: the initial centroid is on the edge in ICH. It is adaptive to more data sets than other algorithms. The experiments under seven distributions show that the proposed method performs better than other traditional algorithms in saving time and space.