Layered Manufacturing (LM) is an emerging technology that is gaining importance in the manufacturing industry. (See e.g. the book by Jacobs [7].) This technology makes it possible to rapidly build three-dimensional objects directly from their computer representations on a desktop-sized machine connected to a workstation. A specific process of LM, that is widely in use, is StereoLithography. The input to this process is the triangulated boundary of a polyhedral CAD model. This model is first sliced by horizontal planes into layers. Then, the object is built layer by layer in the following way. The StereoLithography apparatus consists of a vat of photocurable liquid resin, a platform, and a laser. Initially, the platform is below the surface of the resin at a depth equal to the layer thickness. The laser traces out the contour of the first slice on the surface and then hatches the interior, which hardens to a depth equal to the layer thickness. In this way, the first layer is created; it rests on the platform. Then, the platform is lowered by the layer thickness and the just-vacated region is re-coated with resin. The subsequent layers are then built in the same way.