This diagram tests our ability to compute insets from the original paisley. This is necessary to create the multiple shells.

The red lines represent the bezier control points for the "patch" we use to bridge from the spiral to the semicircle. Using cubic beziers gives us the control necessary to keep the tangents aligned at all the junctions between the curve segments. The two lines stretching out from the origin represent the theta span where the bezier patch is used instead of the spiral.