Vectric Customer

I would like to make a vase like this on my rotary axis. After I profile the basic shape, how can I make the small V-Bit grooves the length of the curved vase?

After you create a 3D model of the basic shape, set the V-Carve toolpath of the lines to "Project toolpath onto the 3D model".

How will VCP handle the cut width as the cutter moves down a steeply sloped object?

The Z axis is always perpendicular to the center point thus the "parallel" lines will converge toward each other as they get closer to the center point of the object - much like the lines on a globe.
Here is a portion of the G-code for profiling one of the lines as generated by the Wrap PP:
N250 G00 X-1.9990 A0.0000 Z0.0500
N260 G1 X-1.9990 A0.0000 Z-0.2863 F60.0
N270 G1 X-1.9908 A0.0000 Z-0.2712
N280 G1 X-1.9746 A0.0000 Z-0.2573
N290 G1 X-1.9583 A0.0000 Z-0.2468
N300 G1 X-1.9340 A0.0000 Z-0.2342

Note how as X advances Z changes its depth to compensate for the curve it is following. The A angular variable stays constant.

If we run the parallel lines perpendicular to X on a curved surface:
and look at the G-code:

LINE 1
N270 G1 X0.0122 A18.5346 Z-0.0500 F40.0
N280 G1 X0.0122 A-8.4375 Z-0.0500 F60.0

LINE 2
N320 G1 X1.8499 A18.5346 Z-0.2061 F40.0
N330 G1 X1.8499 A-8.4375 Z-0.2061 F60.0


Note that the A angular values vary but X and Z stay constant within a line but are different from each other because one is on top of the curved surface and the other is down the slope.

As PaulRoundtree suggests the actual width of the lines will vary if the lines are perpendicular to X and go down a slope. This is because the bit is always perpendicular to the center point of the round material even if the surface of the material varies. If the lines being cut are parallel to X then this will not happen as much. In either case it should not be noticeable if using a V bit to simply being used to scribe shallow lines.