Hi Andrei, the main way is to do a 2D drawing and then use boolean difference to use that 2D curve as the cutting object which does then do a projection of the planar object onto the surface.

You can place points snapped directly on to surfaces, but for curved surfaces just placing a few points of a curve does not make the full curve itself to on the surface unless the surface is planar. So usually direct drawing of curves on surfaces is only done for planar surfaces and not on curved surfaces.

There is a different kind of projection called "Closest point" projection which would probably help you with some of these cases - currently closest point projection in MoI does not work very well though so until that is fixed up you usually will need to use planar projection and just arrange the planar curves as needed to make the cuts you want.

When closest point projection is working better then you'll be able to use a somewhat different method of drawing curves with control points directly snapped on to surfaces, and then using that 3D bent curve as a cutting curve in trim to cut a surface (even though it's not all the way on the surface), then you'd thicken the cut surface using Shell. Right now that method does not work all that well though because of the closest point (in Rhino called "pullback") projection is problematic.

- Michael