ArcGIS Pro 2.8 API Reference Guide
Centroid Method (IGeometryEngine)
Example 

ArcGIS.Core.Geometry Namespace > IGeometryEngine Interface : Centroid Method
The input geometry.
Gets the centroid (center of gravity) of the geometry.
Syntax
MapPoint Centroid( 
   Geometry geometry
)
Function Centroid( _
   ByVal geometry As Geometry _
) As MapPoint

Parameters

geometry
The input geometry.

Return Value

Returns the centroid of the geometry.
Exceptions
ExceptionDescription
Geometry is null or empty.
The method is not implemented for GeometryBag.
Remarks
If the geometry is a MapPoint, then the centroid returned is the same as the source; including Z and M values (if any exist on the source geometry). The centroid of any other geometry type is a point with HasZ = false, HasM = false.
Example
// simple polygon
List<Coordinate2D> list2D = new List<Coordinate2D>();
list2D.Add(new Coordinate2D(0, 0));
list2D.Add(new Coordinate2D(0, 2));
list2D.Add(new Coordinate2D(2, 2));
list2D.Add(new Coordinate2D(2, 0));

Polygon polygon = PolygonBuilder.CreatePolygon(list2D, SpatialReferences.WGS84);

// verify it is simple
bool isSimple = GeometryEngine.Instance.IsSimpleAsFeature(polygon);
// find the centroid
MapPoint centroid = GeometryEngine.Instance.Centroid(polygon);
// centroid.X = 1
// centroid.Y = 1

// map Point
MapPoint pt1 = MapPointBuilder.CreateMapPoint(1, 2, 3, 4, SpatialReferences.WGS84);
MapPoint pt2 = MapPointBuilder.CreateMapPoint(5, 2, double.NaN, 7);

// pt1.HasZ = true
// pt1.HasM = true
centroid = GeometryEngine.Instance.Centroid(pt1);
// centroid.HasZ = true
// centroid.HasM = true
// pt1.IsEqual(centroid) = true

// multipoint
List<MapPoint> list = new List<MapPoint>() { pt1, pt2 };
Multipoint multipoint = MultipointBuilder.CreateMultipoint(list);
// multipoint.HasZ = true
// multipoint.HasM = true

centroid = GeometryEngine.Instance.Centroid(multipoint);
// centroid.X = 3
// centroid.Y = 2
// centroid.HasZ = false
// centroid.HasM = false
Requirements

Target Platforms: Windows 10, Windows 8.1

See Also

Reference

IGeometryEngine Interface
IGeometryEngine Members