When we draw, sketch or sculpt a three-dimensional object, what aspects of its geometric structure do we usually choose to depict and how are these depictions executed? More importantly, what can these renderings tell us about our mental representation of these shapes? Despite the wide variety of possible realizations, it is obvious that even the simplest and most na�ve depictions can convey useful information about 3D shape. Our recent work has focused on the invariant properties of the depicted 3D geometry and their relationship to these portrayals. In this talk we'll survey our lab's work in this area as well as some of our inspiration and future plans.