The widget shows the smooth interpolated curve, so you may be able to get the points you need from the widget or representation object.
If you have trouble figuring this out then you may switch from VTK core to the higher-level VTK classes provided by 3D Slicer. You can use these classes in C++, Python scripting, and/or graphical user interface.
Probing with curve is implemented in Line profile module in Sandbox extension.