Curves-on-surface are special curves that are primarily used to define the regions on a NURBS surface for trimming. Curves-on-surface reside in the UV space of a surface, rather than in the XYZ space of the scene.
You can create curves-on-surface by:
For a region to trim successfully, the curve-on-surface must fully enclose a region on the surface to be trimmed, or bisect the surface to be trimmed.
Curves-on-surface are primarily used to trim surfaces, and can also be used as an edge for new surfaces.
Curves on surface (along with their edit points) have a special Move manipulator. When you move a curve on surface, the manipulator constrains the curve on surface to the surface and allows movement across the surface in U and V.