algorithmic modeling for Rhino
Another solution would be to divide the curve in points, pull the points to the surface (Pull Point component with C=true) and reconstruct the curve from the pulled points.
May give some weird results sometimes perhaps.
Edit: actually, for a real projection following a direction, better use same strategy with SCX (Surface | Line) with input line= line between each point and each point+projection direction and Lf= true.
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