/// <summary>
        /// Gets the centroid of the polyline 2d.
        /// </summary>
        /// <param name="pl">The instance to which the method applies.</param>
        /// <returns>The centroid of the polyline 2d (WCS coordinates).</returns>
        public static Point3d Centroid(this Polyline2d pl)
        {
            Vertex2d[]    vertices = pl.GetVertices().ToArray();
            int           last     = vertices.Length - 1;
            Vertex2d      vertex   = vertices[0];
            Point2d       p0       = vertex.Position.Convert2d();
            double        elev     = pl.Elevation;
            Point2d       cen      = new Point2d(0.0, 0.0);
            double        area     = 0.0;
            double        bulge    = vertex.Bulge;
            double        tmpArea;
            Point2d       tmpPt;
            Triangle2d    tri = new Triangle2d();
            CircularArc2d arc = new CircularArc2d();

            if (bulge != 0.0)
            {
                arc     = pl.GetArcSegment2dAt(0);
                tmpArea = arc.AlgebricArea();
                tmpPt   = arc.Centroid();
                area   += tmpArea;
                cen    += ((new Point2d(tmpPt.X, tmpPt.Y)) * tmpArea).GetAsVector();
            }
            for (int i = 1; i < last; i++)
            {
                Point2d p1 = vertices[i].Position.Convert2d();
                Point2d p2 = vertices[i + 1].Position.Convert2d();
                tri.Set(p0, p1, p2);
                tmpArea = tri.AlgebricArea;
                area   += tmpArea;
                cen    += (tri.Centroid * tmpArea).GetAsVector();
                bulge   = vertices[i].Bulge;
                if (bulge != 0.0)
                {
                    arc     = pl.GetArcSegment2dAt(i);
                    tmpArea = arc.AlgebricArea();
                    tmpPt   = arc.Centroid();
                    area   += tmpArea;
                    cen    += ((new Point2d(tmpPt.X, tmpPt.Y)) * tmpArea).GetAsVector();
                }
            }
            bulge = vertices[last].Bulge;
            if ((bulge != 0.0) && (pl.Closed == true))
            {
                arc     = pl.GetArcSegment2dAt(last);
                tmpArea = arc.AlgebricArea();
                tmpPt   = arc.Centroid();
                area   += tmpArea;
                cen    += ((new Point2d(tmpPt.X, tmpPt.Y)) * tmpArea).GetAsVector();
            }
            cen = cen.DivideBy(area);
            return(new Point3d(cen.X, cen.Y, pl.Elevation).TransformBy(Matrix3d.PlaneToWorld(pl.Normal)));
        }
        /// <summary>
        /// Gets the centroid of the polyline.
        /// </summary>
        /// <param name="pl">The instance to which the method applies.</param>
        /// <returns>The centroid of the polyline (OCS coordinates).</returns>
        public static Point2d Centroid2d(this Polyline pl)
        {
            Point2d       cen = new Point2d();
            Triangle2d    tri = new Triangle2d();
            CircularArc2d arc = new CircularArc2d();
            double        tmpArea;
            double        area  = 0.0;
            int           last  = pl.NumberOfVertices - 1;
            Point2d       p0    = pl.GetPoint2dAt(0);
            double        bulge = pl.GetBulgeAt(0);

            if (bulge != 0.0)
            {
                arc  = pl.GetArcSegment2dAt(0);
                area = arc.AlgebricArea();
                cen  = arc.Centroid() * area;
            }
            for (int i = 1; i < last; i++)
            {
                tri.Set(p0, pl.GetPoint2dAt(i), pl.GetPoint2dAt(i + 1));
                tmpArea = tri.AlgebricArea;
                cen    += (tri.Centroid * tmpArea).GetAsVector();
                area   += tmpArea;
                bulge   = pl.GetBulgeAt(i);
                if (bulge != 0.0)
                {
                    arc     = pl.GetArcSegment2dAt(i);
                    tmpArea = arc.AlgebricArea();
                    area   += tmpArea;
                    cen    += (arc.Centroid() * tmpArea).GetAsVector();
                }
            }
            bulge = pl.GetBulgeAt(last);
            if ((bulge != 0.0) && (pl.Closed == true))
            {
                arc     = pl.GetArcSegment2dAt(last);
                tmpArea = arc.AlgebricArea();
                area   += tmpArea;
                cen    += (arc.Centroid() * tmpArea).GetAsVector();
            }
            return(cen.DivideBy(area));
        }