When designers want more than just a pretty picture of the complex 3D geometric model shown on their computer screens, they are increasingly turning to "layered manufacturing" technologies to automatically produce a prototype part. In this talk I will describe geometric algorithms for increasing the efficiency of layered manufacturing. As in many other solid modeling systems, we use a topological data structure to capture the connectivity of the boundary of the part. Unfortunately, the standard layered manufacturing interchange format consists of unorganized "triangle-soup" from which we must derive connectivity ourselves. For very large data sets, the topological data structure itself can be bigger than core memory, and a naive algorithm for building it becomes prohibitively slow due to memory thrashing. I will present an out-of-core algorithm for building such a data structure efficiently from large, unorganized polygonal data sets. I will also describe a new sweep-plane algorithm built on this data structure that "slices" a model into horizontal, 2.5-D layers of uniform thickness for input to layered manufacturing. This algorithm exploits both geometric and topological inter-slice coherence to increase efficiency compared to calculating each slice as an individual intersection with a plane. Finally, I will outline a graphics hardware accelerated algorithm that produces a modified process plan that can significantly reduce build times and material usage for calligraphic layered manufacturing systems.