Abstract We present a computational approach for unfolding 3D shapes isometrically into the plane as a single patch without overlapping triangles. This is a hard, sometimes impossible, problem, which existing methods are forced to soften by allowing for map distortions or multiple patches. Instead, we propose a geometric relaxation of the problem: We modify the input shape until it admits an overlap‐free unfolding. We achieve this by locally displacing vertices and collapsing edges, guided by the unfolding process. We validate our algorithm quantitatively and qualitatively on a large dataset of complex shapes and show its proficiency by fabricating real shapes from paper.

Abstract Fused filament fabrication (FFF) enables users to quickly design and fabricate parts with unprecedented geometric complexity, fine‐tuning both the structural and aesthetic properties of each object. Nevertheless, the full potential of this technology has yet to be realized, as current slicing methods fail to fully exploit the deposition freedom offered by modern 3D printers. In this work, we introduce a novel approach to toolpath generation that moves beyond the traditional layer‐based concept. We use frames, referred to as atoms , as solid elements instead of slices. We optimize the distribution of atoms within the part volume to ensure even spacing and smooth orientation while accurately capturing the part's geometry. Although these atoms collectively represent the complete object, they do not inherently define a fabrication plan. To address this, we compute an extrusion toolpath as an ordered sequence of atoms that, when followed, provides a collision‐free fabrication strategy. This general approach is robust, requires minimal user intervention compared to existing techniques, and integrates many of the best features into a unified framework: precise deposition conforming to non‐planar surfaces, effective filling of narrow features – down to a single path – and the capability to locally print vertical structures before transitioning elsewhere. Additionally, it enables entirely new capabilities, such as anisotropic appearance fabrication on curved surfaces.

We present a method to 3D print surfaces exhibiting a prescribed varying field of anisotropic appearance using only standard fused filament fabrication printers. This enables the fabrication of patterns triggering reflections similar to that of brushed metal with direct control over the directionality of the reflections. Our key insight, on which we ground the method, is that the direction of the deposition paths leads to a certain degree of surface roughness, which yields a visual anisotropic appearance. Therefore, generating dense cyclic infills aligned with a line field allows us to grade the anisotropic appearance of the printed surface. To achieve this, we introduce a highly parallelizable algorithm for optimizing oriented, cyclic paths. Our algorithm outperforms existing approaches regarding efficiency, robustness, and result quality. We demonstrate the effectiveness of our technique in conveying an anisotropic appearance on several challenging test cases, ranging from patterns to photographs reinterpreted as anisotropic appearances.

We propose a computational design approach for covering a surface with individually addressable RGB LEDs, effectively forming a low-resolution surface screen. To achieve a low-cost and scalable approach, we propose creating designs from flat PCB panels bent in-place along the surface of a 3D printed core. Working with standard rigid PCBs enables the use of established PCB manufacturing services, allowing the fabrication of designs with several hundred LEDs. Our approach optimizes the PCB geometry for folding, and then jointly optimizes the LED packing, circuit and routing, solving a challenging layout problem under strict manufacturing requirements. Unlike paper, PCBs cannot bend beyond a certain point without breaking. Therefore, we introduce parametric cut patterns acting as hinges, designed to allow bending while remaining compact. To tackle the joint optimization of placement, circuit and routing, we propose a specialized algorithm that splits the global problem into one sub-problem per triangle, which is then individually solved. Our technique generates PCB blueprints in a completely automated way. After being fabricated by a PCB manufacturing service, the boards are bent and glued by the user onto the 3D printed support. We demonstrate our technique on a range of physical models and virtual examples, creating intricate surface light patterns from hundreds of LEDs. The code and data for this paper are available at https://github.com/mfremer/pcbend.

While 3D printing enables the customization and home fabrication of a wide range of shapes, fabricating freeform thin-shells remains challenging. As layers misalign with the curvature, they incur structural deficiencies, while the curved shells require large support structures, typically using more material than the part itself. We present a computational framework for optimizing the internal structure of 3D printed plates such that they morph into a desired freeform shell when heated. This exploits the shrinkage effect of thermoplastics such as PLA, which store internal stresses along the deposition directions. These stresses get released when the material is heated again above its glass transition temperature, causing an anisotropic deformation that induces curvature. Our inverse design method takes as input a freeform surface and finds an optimized set of deposition trajectories in each layer such that their anisotropic shrinkage deforms the plate into the prescribed surface geometry. We optimize for a continuous vector field that varies across the plate and within its thickness. The algorithm then extracts a set of deposition trajectories from the vector field in order to fabricate the flat plates on standard FFF printers. We validate our algorithm on freeform, doubly-curved surfaces.

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 of the overall material rigidity (structure density); local canceling of the effect of the fibers, obtaining a more isotropic material. Our algorithm to synthesize the structures builds upon procedural texturing. It produces a cellular geometry that can be fabricated reliably despite 3D printing walls at a minimal thickness, allowing prints to be very flexible. The synthesis algorithm is efficient and scales to large volumes.