An optimal real time algorithm for determine the convex hull of a set of points in a plane

Based on the properties of star polygon and that the convex polygon is a special kind of star polygon, with the star point as the origin and the two lines respectively parallel to the x-axis and y-axis as coordinate axis, a relative coordinate system is built and the planar area is divided into four areas. Based on the new equation of relationship of point to orientation line, inner points and externals point of polygon are quickly separated, the embraced vertices (tangent vertices) of external points are rapidly found. An optimal real time algorithm for constructing the convex hull of a set of points in a plane is proposed. (C) 1998 Elsevier Science Ltd. All rights reserved.