While additive manufacturing and 3D printing have achieved notoriety for their abilities to manufacture complex three-dimensional parts, the state of the art is not truly three-dimensional. Rather, the process plans rely on a stack of discretized two-dimensional layers. Discretization of smooth, freeform features results in printed parts with stair-stepped surfaces, increasing the total volumetric error of the part and potentially diminishing the intended performance of functional surfaces. By performing process planning in a fully three-dimensional domain, as opposed to the 2.5D status quo, the capabilities of additive manufacturing are enhanced and the technologies can be more fully leveraged by designers and manufacturers.