Use the following options to set what happens when you select Curves > Extend > Extend Curve on Surface.
Specifies how to extend the curve in the surface’s UV space:
Linear extends the curve in a straight line.
Circular extends the curve in an arc direction.
Extrapolate extends the curve by deducing the direction and tangency of the curve.
The Parametric Distance value specifies the length of the extension. The value specifies a percentage of the surface length in the direction the curve runs. For instance, a value of 0.5 extends the curve length by roughly half the length of the surface in the direction the curve runs.
Lets you specify an extend position in the UV Point To Extend To entry box. To use actual UV values rather than estimates, select Create > Measure Tools > Parameter Tool, drag on the surface, and release the mouse button to display the UV coordinates at the pointer.