Abstract
Abstract. Computing the convex hull of a point set is requirement in the GIS applications. This paper studies on the problem of minimum convex hull and presents an improved algorithm for the minimum convex hull of planar scattered point set. It adopts approach that dividing the point set into several sub regions to get an initial convex hull boundary firstly. Then the points on the boundary, which cannot be vertices of the minimum convex hull, are removed one by one. Finally the concave points on the boundary, which cannot be vertices of the minimum convex hull, are withdrew. Experimental analysis shows the efficiency of the algorithm compared with other methods.
Highlights
A convex polygon, with every internal angle less than or equal to 180 degree, is a simple polygon whose interior is a convex set
We present an improved algorithm to rapidly compute the minimum convex hull of a planar scattered point set in this paper
Algorithm is as follows: (1) All points of the planar scattered point set are sorted in ascending order of x-coordinates to find the minimum point pL0 and the maximum point pR0 of the point set based on their x coordinates, and the x coordinates of two extreme points are identified as the division border, which means the borders of the point set as shown in Figure 3 (1)
Summary
A convex polygon, with every internal angle less than or equal to 180 degree, is a simple polygon whose interior is a convex set. Incremental method is to add points one at a time updating the hull as we proceed Both Graham’s scan and gift-wrapping use a technique called “rotational sweep”, processing vertices in the order of the polar angles they form with a reference vertex. There are some improved algorithms, which can enhance performance though excluding non-convex hull vertexes to reduce the analysis points of the minimum convex hull, such as grouping the set of points (Wang, 2002; Zhang et al, 2009), establishing the auxiliary grid field (Wang, 2010), and obtaining the extreme points (Yu et al, 2005; Wu et al, 2010; Cheng et al, 2009; Liu et al, 2011; Barber et al, 1996). The concave points on the convex hull boundary are deleted to strike the minimum convex hull of the set of points
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