Abstract: In this paper a new algorithm to generate random
simple polygons from a given set of points in a two dimensional
plane is designed. The proposed algorithm uses a genetic algorithm to
generate polygons with few vertices. A new merge algorithm is
presented which converts any two polygons into a simple polygon.
This algorithm at first changes two polygons into a polygonal chain
and then the polygonal chain is converted into a simple polygon. The
process of converting a polygonal chain into a simple polygon is
based on the removal of intersecting edges. The experiments results
show that the proposed algorithm has the ability to generate a great
number of different simple polygons and has better performance in
comparison to celebrated algorithms such as space partitioning and
steady growth.
Abstract: A chord of a simple polygon P is a line segment [xy]
that intersects the boundary of P only at both endpoints x and y. A
chord of P is called an interior chord provided the interior of [xy] lies
in the interior of P. P is weakly visible from [xy] if for every point v
in P there exists a point w in [xy] such that [vw] lies in P. In this
paper star-shaped, L-convex, and convex polygons are characterized
in terms of weak visibility properties from internal chords and starshaped
subsets of P. A new Krasnoselskii-type characterization of
isothetic star-shaped polygons is also presented.
Abstract: We consider the methods of construction simple
polygons for a set S of n points and applying them for searching the
minimal area polygon. In this paper we propose the approximate
algorithm, which generates the simple polygonalizations of a fixed
set of points and finds the minimal area polygon, in O (n3) time and
using O(n2) memory.
Abstract: In this study we survey the method for fast finding a minimum link path between two arbitrary points within a simple polygon, which can pass only through the vertices, with preprocessing.