We develop a new kind of "space-filling" curves, connected Fermat spirals , and show their compelling properties as a tool path fill pattern for layered fabrication. Unlike classical space-filling curves such as the Peano or Hilbert curves, which constantly wind and bind to preserve locality, connected Fermat spirals are formed mostly by long, low-curvature paths. This geometric property, along with continuity, influences the quality and efficiency of layered fabrication. Given a connected 2D region, we first decompose it into a set of sub-regions, each of which can be filled with a single continuous Fermat spiral. We show that it is always possible to start and end a Fermat spiral fill at approximately the same location on the outer boundary of the filled region. This special property allows the Fermat spiral fills to be joined systematically along a graph traversal of the decomposed sub-regions. The result is a globally continuous curve. We demonstrate that printing 2D layers following tool paths as connected Fermat spirals leads to efficient and quality fabrication, compared to conventional fill patterns.

We reduce the material of a 3D kitten (left), by carving porous in the solid (mid-left), to yield a honeycomb-like interior structure which provides an optimal strength-to-weight ratio, and relieves the overall stress illustrated on a cross-section (mid-right). The 3D printed hollowed solid is built-to-last using our interior structure (right).

Traditional manufacturing workflows strongly decouple design and fabrication phases. As a result, fabrication-related objectives such as manufacturing time and precision are difficult to optimize in the design space, and vice versa. This paper presents HL-HELM, a high-level, domain-specific language for expressing abstract, parametric fabrication plans; it also introduces LL-HELM, a low-level language for expressing concrete fabrication plans that take into account the physical constraints of available manufacturing processes. We present a new compiler that supports the real-time, unoptimized translation of high-level, geometric fabrication operations into concrete, tool-specific fabrication instructions; this gives users immediate feedback on the physical feasibility of plans as they design them. HELM offers novel optimizations to improve accuracy and reduce fabrication time as well as material costs. Finally, optimized low-level plans can be interpreted as step-by-step instructions for users to actually fabricate a physical product. We provide a variety of example fabrication plans in the carpentry domain that are designed using our high-level language, show how the compiler translates and optimizes these plans to generate concrete low-level instructions, and present the final physical products fabricated in wood.

We present a technique for designing 3D-printed perforated lampshades, which project continuous grayscale images onto the surrounding walls. Given the geometry of the lampshade and a target grayscale image, our method computes a distribution of tiny holes over the shell, such that the combined footprints of the light emanating through the holes form the target image on a nearby diffuse surface. Our objective is to approximate the continuous tones and the spatial detail of the target image, to the extent possible within the constraints of the fabrication process.To ensure structural integrity, there are lower bounds on the thickness of the shell, the radii of the holes, and the minimal distances between adjacent holes. Thus, the holes are realized as thin tubes distributed over the lampshade surface. The amount of light passing through a single tube may be controlled by the tube's radius and by its direction (tilt angle). The core of our technique thus consists of determining a suitable configuration of the tubes: their distribution across the relevant portion of the lampshade, as well as the parameters (radius, tilt angle) of each tube. This is achieved by computing a capacity-constrained Voronoi tessellation over a suitably defined density function, and embedding a tube inside the maximal inscribed circle of each tessellation cell. The density function for a particular target image is derived from a series of simulated images, each corresponding to a different uniform density tube pattern on the lampshade.

Minor physical damage can reduce the insulation performance of epoxy resin, which seriously threatens the reliability of electrical equipment. In this paper, the epoxy resin insulating composite was prepared by a microcapsule system to achieve its self-healing goal. The repair performance to physical damage was analyzed by the tests of scratch, cross-section damage, electric tree, and breakdown strength. The results show that compared with pure epoxy resin, the composite has the obvious self-healing performance. For mechanical damage, the maximum repair rate of physical structure is 100%, and the breakdown strength can be restored to 83% of the original state. For electrical damage, microcapsule can not only attract the electrical tree and inhibit its propagation process, but also repair the tubules of electrical tree effectively. Moreover, the repair rate is fast, which meets the application requirements of epoxy resin insulating material. In addition, the repair behavior is dominated by capillarity and molecular diffusion on the defect surface. Furthermore, the electrical properties of repaired part are greatly affected by the characteristics of damage interface and repair product. In a word, the composite shows better repair performance to physical damage, which is conducive to improving the reliability of electrical insulating materials.