First, adjust the plane direction with the variable. Then press "S." Next, click to make a new point in the shape. Press space to clip a side off.
This project is a demonstration of Sutherland-Hodgman shape clipping. It uses vectors and the dot product to clip the part of the shape on the back of the plane off. Credit to Randy Gaul for writing an article on the Sutherland-Hodgman Clipping algorithm where I learned this. http://tutsplus.com/authors/randy-gaul