I need to create curves through sets of input points with the number of control points equal to the number of input points. Also for multispan curves the divisions between spans need to aligned with input points or midway between input points.

This is what SrfPtGrid does for surfaces. I need the analogous capability for curves. [Correction: SrfPtGrid does not put the divisions between spans on input points in general.] Neither InterpCrv, CurveThroughPt nor CurveThroughPolyline does this.