Create convex polygon

Polygon is the closed curve on a plane, formed by a piece of direct lines. The pieces connecting boundary points of polygon, constructed by this rule, conclude inside of polygon all points from the marked set. In the program the variant of construction of convex polygon by Grehem method is realized. Any star-shaped polygon first is constructed, and then it is brought up to convex, by reconstruction of the triangles having at least one external side.  

   It is necessary for user to select on a map the pickets, which must be joint, and then to press the button of a mode. For marking it is possible to use standard operations of marking or to use modes from the panel «Mark pickets» .  As a result of operation by the pickets selected on a map a creation of polygon object will be made, according to a code specified in parameters of settings. The structure of boundary points of convex polygon includes not all points from the selected set.  

  Set of points inside of polygon, from which all boundary points of polygon are visible, is named as a kernel of polygon. Speak, that polygon is a star-shaped one, if its kernel is nonempty. The polygon is named a fan-shaped polygon if its nonempty kernel contains one or more tops (each such top is named as a root of polygon). If the fan-shaped polygon contains all tops it is convex polygon. In other words, if from any boundary point of polygon all other boundary points of polygon are visible such polygon is named convex one.