Additive manufacturing is typically conducted in a layer-by-layer fashion. A key step of the process is to define, within each planar layer, the trajectories along which material is deposited to form the final shape. The direction of these trajectories triggers an anisotropy in the fabricated parts, which directly affects their properties, from their mechanical behavior to their appearance. Controlling this anisotropy paves the way to novel applications, from stronger parts to controlled deformations and surface patterning. This work introduces a method to generate trajectories that precisely follow an input direction field while simultaneously avoiding intra- and inter-layer defects. Our method results in spatially coherent trajectories - all follow the specified direction field throughout the layers - while providing precise control over their inter-layer arrangement. This allows us to generate a staggered layout of trajectories across layers, preventing unavoidable tiny gaps from forming tunnel-shaped voids throughout a part volume. Our approach is simple, robust, easy to implement, and scales linearly with the input volume. It builds upon recent results in procedural generation of oscillating patterns, generating a signal in the 3D domain that oscillates with a frequency matching the deposition beads width while following the input direction field. Trajectories are extracted with a process akin to a marching square.