paint a straight line in view

I want to put my view in an orthographic view, like the left view, and draw a straight line in that view that paints a line all away around a model, Is this possible? I've been trying to do it, but it won't paint on the back side of the model. I also have to touch the model to get it to paint, where I want to start a line off of the model, hold shift, and end off of the model. 

This isn't something I can do in the UV view because the object has an odd shape, but I want the line to be straight, even though the mesh is "hilly".