[CONNECT C++] How to Obtain the Vertices of a LineString at a given Location (Fraction)?

If I have a LineString (as a CurveVectorPtr) and some point on that LineString, I can retrieve the direction (i.e. Tangent) at that specific location. If I have a CurveLocationDetail, I also know the index of the segment that some point lies on. How can I obtain the LineString vertices that "enclose" that  point? If the LineString contain 3 "segments" (i.e. has 4 vertices) and my point lies on "segment" index 1 (between vertice[1] and vertice[2]). how can I return the DPoint3d of vertice[1] and vertice[2]?

Thanks

Bruce