Creo Interactive Surface Design (Style) > Curves > Creating Curves > Curves on a Surface (COS) > About Curves on Surfaces
  
About Curves on Surfaces
You can create a curve on surface (COS) in the following ways:
Specify points through which the curve passes on a surface
Drop or project a curve onto a surface or datum plane
However, all points on a COS are constrained to lie on a single surface so that the curve is also on the surface. The curve is a child of the surface.
When you drop a curve on a composite surface, individual COS curves are created for each component of the composite surface. Similarly, you can a create a COS by specifying points on the individual components of a composite surface.