This .NET class wraps the AcGeExternalCurve3d ObjectARX class. 

ExternalCurve3d class is a representation for a 3D curve geometry that has its definition external to gelib. Since ExternalCurve3d is an Curve3d, these external entities can be treated as any other gelib 3D curves. Certain external curve points sets may have corresponding native representations in GeLib. In such cases, it is possible to obtain such GeLib representations. However, the curve definitions of native GeLib curves would differ from the definition of external entities. An example of such a difference is differing curve parameterizations. A typical example of a use of ExternalCurve3d is to represent a ShapeManager curve. 

Clearly, an instance of ExternalCurve3d can be used as any other Curve3d. Alternatively, knowledge of the precise definition of the external entity allows direct access to the external entity in its native form. This access is more efficient because it avoids the level of indirection that is incurred when accessing the external entity through GeLib interface.

Autodesk.AutoCAD.Geometry.Entity3d
    Autodesk.AutoCAD.Geometry.Curve3d
        Autodesk.AutoCAD.Geometry.ExternalCurve3d

Public sealed Class ExternalCurve3d
Inherits Curve3d

public sealed class ExternalCurve3d : Curve3d;