oscillating field with prescribed main frequencies and preserved contrast oscillations. In addition, the profile of each oscillation is directly controllable (e.g. sine wave, sawtooth, rectangular or any 1D profile). Our technique builds upon a reformulation of Gabor noise in terms of a phasor field that affords for a clear separation between local intensity and phase. Applications range from texturing to modeling surface displacements, as well as multi-material microstructures in the context of additive manufacturing. CCS Concepts: • Computing methodologies → Texturing.

Fig. 1. Our technique synthesizes fiber-like microstructures that can be additively manufactured. This induces an elastic response that we call rigid-transverse: the fibrous microstructures are very rigid along their elongated axis while being comparatively very flexible in the (local) orthogonal plane. Left: Without any spatial gradation, our microstructures are formed by square diamond profiles defined in the , plane and extruded along the axis. Right: 3D printed object embedding our synthesized microstructures. The designer directly manipulates the fiber orientations, controlling how the cube volume reshapes under large deformations. Here, the top face collapses while gripping the bar, as the fibers prevent stretch along their main direction (see orange dashed line). Note the more disorganized structures at the bottom, which cancels the directional effect in this area. Nature offers a marvel of astonishing and rich deformation behaviors. Yet, most of the objects we fabricate are comparatively rather inexpressive, either rigid or exhibiting simple homogeneous deformations when interacted with. We explore the synthesis and fabrication of novel microstructures that mimic the effects of having oriented rigid fibers in an otherwise flexible material: the result is extremely rigid along a transverse direction while being comparatively very flexible in the locally orthogonal plane. By allowing free gradation of the rigidity direction orientation within the object, the microstructures can be designed such that, under deformation, distances along fibers in the volume are preserved while others freely change. Through a simple painting tool, this allows a designer to influence the way the volume reshapes when deformed, and results in a wide range of novel possibilities. Many gradations are possible: local free orientation of the fibers; local control

Additive manufacturing techniques form an object by accumulating layers of material on top of one another. Each layer has to be supported by the one below for the fabrication process to succeed. To reduce print time and material usage, especially in the context of prototyping, it is often desirable to fabricate hollow objects. This exacerbates the requirement of support between consecutive layers: standard hollowing produces surfaces in overhang that cannot be directly fabricated anymore. Therefore, these surfaces require internal support structures. These are similar to external supports for overhangs, with the key difference that internal supports remain invisible within the object after fabrication. A fundamental challenge is to generate structures that provide a dense support while using little material. In this paper, we propose a novel type of support inspired by rib structures. Our approach guarantees that any point in a layer is supported by a point below, within a given threshold distance. Despite providing strong guarantees for printability, our supports remain lightweight and reliable to print. We propose a greedy support generation algorithm that creates compact hierarchies of rib‐like walls. The walls are progressively eroded away and straightened, eventually merging with the interior object walls. We demonstrate our technique on a variety of models and provide performance figures in the context of fused filament fabrication 3D printing.

Fig. 1. Our technique generates dense planar infill trajectories, precisely following an input direction field. Through the anisotropy of the deposition process, the direction field controls the appearance and the physical properties of the 3D printed object. The trajectories are arranged in a staggered layout across layers. Left: A 3D printed gear where the direction of the trajectories is parameterized to adapt to the functionality of the part. Here, trajectories are mostly circular in the rim and hub while being aligned with the spokes. Note the staggered layout in the side views. Right: The anisotropy of the deposition results in anisotropy in the specular reflectance.Here, this is controlled to pattern the appearance of an otherwise flat part, resulting in a brushed metal effect.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.