// densify a line segment
MapPoint startPt = MapPointBuilderEx.CreateMapPoint(1.0, 1.0);
MapPoint endPt = MapPointBuilderEx.CreateMapPoint(1, 21);
LineSegment line = LineBuilderEx.CreateLineSegment(startPt, endPt);
Polyline polyline = PolylineBuilderEx.CreatePolyline(line);
Geometry geom = GeometryEngine.Instance.DensifyByLength(polyline, 2);
Polyline result = geom as Polyline;
// densify a circular arc
MapPoint fromPt = MapPointBuilderEx.CreateMapPoint(2, 1);
MapPoint toPt = MapPointBuilderEx.CreateMapPoint(1, 2);
Coordinate2D interiorPt = new Coordinate2D(1 + Math.Sqrt(2) / 2, 1 + Math.Sqrt(2) / 2);
EllipticArcBuilderEx cab = new EllipticArcBuilderEx(fromPt, toPt, interiorPt);
EllipticArcSegment circularArc = cab.ToSegment();
polyline = PolylineBuilderEx.CreatePolyline(circularArc);
geom = GeometryEngine.Instance.DensifyByLength(polyline, 2);
result = geom as Polyline;