/// <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)
{
var vertices = pl.GetVertices().ToArray();
var last = vertices.Length - 1;
var vertex = vertices[0];
var p0 = vertex.Position.Convert2D();
_ = pl.Elevation;
var cen = new Point2d(0.0, 0.0);
var area = 0.0;
var bulge = vertex.Bulge;
double tmpArea;
Point2d tmpPt;
var tri = new Triangle2D();
var 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 (var i = 1; i < last; i++)
{
var p1 = vertices[i].Position.Convert2D();
var 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)
{
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)));
}