/// <summary>
        /// Divide a sub polygon by a line segment.
        /// </summary>
        /// <param name="lineSegment">the line segment.</param>
        /// <param name="poly">the polygon to divide.</param>
        /// <returns>one of the sub polygon divided from the polygon.</returns>
        internal Polygon2D DividedBy(LineSegment2D lineSegment, Polygon2D poly)
        {
            if (poly.isDiagonal(lineSegment))
            {
                int a = poly.HasVertex(lineSegment.FirstPoint);
                int b = poly.HasVertex(lineSegment.LastPoint);

                if (a > b)
                {
                    int tmp = a;
                    a = b;
                    b = tmp;
                }

                Point2DCollection p2 = new Point2DCollection(b - a + 1);
                Point2DCollection p1 = new Point2DCollection(poly.VertexCount - p2.Size + 2);

                for (int i = 0; i < poly.VertexCount; i++)
                {
                    if (i <= a || i >= b)
                    {
                        p1.Add(poly.GetPoint(i));
                    }
                    if (i >= a && i <= b)
                    {
                        p2.Add(poly.GetPoint(i));
                    }
                }

                if (p1.Count > p2.Count)
                {
                    SubDivision.Add(new Polygon2D(p1));
                    return(new Polygon2D(p2));
                }
                else
                {
                    SubDivision.Add(new Polygon2D(p2));
                    return(new Polygon2D(p1));
                }
            }
            else if (lineSegment.Intersects(poly))
            {
                Point2DCollection Points = new Point2DCollection(2);

                for (int i = 0; i < poly.VertexCount; i++)
                {
                    LineSegment2D border = poly.GetEdge(i);

                    Point2D p = lineSegment.GetIntersectPoint(border);

                    if (p.isRegular)
                    {
                        Points.DistinctAdd(p);
                    }
                }

                Debug.Assert(Points.Count == 2);

                if (poly.HasVertex(Points[0]) == Polygon2D.NoSuchPoint)
                {
                    poly.Add(Points[0], poly.OnEdge(Points[0]));
                    Parent.AddInner(Points[0]);
                    this.InnerPoints.DistinctAdd(Points[0]);
                }

                if (poly.HasVertex(Points[1]) == Polygon2D.NoSuchPoint)
                {
                    poly.Add(Points[1], poly.OnEdge(Points[1]));
                    Parent.AddInner(Points[1]);
                    this.InnerPoints.DistinctAdd(Points[1]);
                }

                LineSegment2D line = new LineSegment2D(Points[0], Points[1]);

                return(DividedBy(line, poly));
            }
            else
            {
                return(poly);
            }
        }
 /// <summary>
 /// Add an inner point to the polygon.
 /// </summary>
 /// <param name="point">the new inner point.</param>
 public void AddInnerPoint(Point2D point)
 {
     Polygon.AddInner(point);
 }