Hi Chris - if you are asking about flashlight-car-skull etc scene, I think you will be hard pressed to do this in a convincing way with surfaces.
To answer your question… it depends. The tedious way would be to run ClosestPoint : select the curve, start ClosestPoint and then snap to the points, one by one. To make this go faster, use
With the curve preselected, this will repeat the command so you can click one by one and just keep going
Then move the points with Point osnap
Another way is to start the Move command with a control point selected, snap to the point as a point to move From and then use the OnCrv and Perp osnaps to set the To point.
Your choice, as to tedium.
Let me see if I can make you a quick script to ease the pain.
@chris.prinsen2 - here is a python that should make this easy enough…
GripToCurveClosestPoint.py (2.0 KB)
To use the Python script use
RunPythonScript, or a macro:
_-RunPythonScript "Full path to py file inside double-quotes"