Drawing a Curve on an Object
Maya 2012 Tutorial
How to Draw a Curve on an Object in Maya
Let's say you wanted to draw a line in 3D space that followed the contour of an object. By making the object live, the curve's Control Vertices stick to the object as you create your CV Curve.
Add a polygon sphere to the workspace by choosing Create > Polygon Primitives > Sphere.
Select the sphere and choose Modify > Make Live. The object dims.
Choose Create > CV Curve and set the Degree to 3 Cubic in the tool options.
Click multiple times on the sphere and notice how the curve points follow the sphere. Press Enter to accept your curve.
To turn off the Live feature, click the sphere and choose Modify > Make Not Live.