@article{14628, abstract = {We introduce a compact, intuitive procedural graph representation for cellular metamaterials, which are small-scale, tileable structures that can be architected to exhibit many useful material properties. Because the structures’ “architectures” vary widely—with elements such as beams, thin shells, and solid bulks—it is difficult to explore them using existing representations. Generic approaches like voxel grids are versatile, but it is cumbersome to represent and edit individual structures; architecture-specific approaches address these issues, but are incompatible with one another. By contrast, our procedural graph succinctly represents the construction process for any structure using a simple skeleton annotated with spatially varying thickness. To express the highly constrained triply periodic minimal surfaces (TPMS) in this manner, we present the first fully automated version of the conjugate surface construction method, which allows novices to create complex TPMS from intuitive input. We demonstrate our representation’s expressiveness, accuracy, and compactness by constructing a wide range of established structures and hundreds of novel structures with diverse architectures and material properties. We also conduct a user study to verify our representation’s ease-of-use and ability to expand engineers’ capacity for exploration.}, author = {Makatura, Liane and Wang, Bohan and Chen, Yi-Lu and Deng, Bolei and Wojtan, Christopher J and Bickel, Bernd and Matusik, Wojciech}, issn = {0730-0301}, journal = {ACM Transactions on Graphics}, keywords = {Computer Graphics and Computer-Aided Design}, number = {5}, publisher = {Association for Computing Machinery}, title = {{Procedural metamaterials: A unified procedural graph for metamaterial design}}, doi = {10.1145/3605389}, volume = {42}, year = {2023}, } @article{13188, abstract = {The Kirchhoff rod model describes the bending and twisting of slender elastic rods in three dimensions, and has been widely studied to enable the prediction of how a rod will deform, given its geometry and boundary conditions. In this work, we study a number of inverse problems with the goal of computing the geometry of a straight rod that will automatically deform to match a curved target shape after attaching its endpoints to a support structure. Our solution lets us finely control the static equilibrium state of a rod by varying the cross-sectional profiles along its length. We also show that the set of physically realizable equilibrium states admits a concise geometric description in terms of linear line complexes, which leads to very efficient computational design algorithms. Implemented in an interactive software tool, they allow us to convert three-dimensional hand-drawn spline curves to elastic rods, and give feedback about the feasibility and practicality of a design in real time. We demonstrate the efficacy of our method by designing and manufacturing several physical prototypes with applications to interior design and soft robotics.}, author = {Hafner, Christian and Bickel, Bernd}, issn = {1557-7368}, journal = {ACM Transactions on Graphics}, keywords = {Computer Graphics, Computational Design, Computational Geometry, Shape Modeling}, number = {5}, publisher = {Association for Computing Machinery}, title = {{The design space of Kirchhoff rods}}, doi = {10.1145/3606033}, volume = {42}, year = {2023}, } @article{12972, abstract = {Embroidery is a long-standing and high-quality approach to making logos and images on textiles. Nowadays, it can also be performed via automated machines that weave threads with high spatial accuracy. A characteristic feature of the appearance of the threads is a high degree of anisotropy. The anisotropic behavior is caused by depositing thin but long strings of thread. As a result, the stitched patterns convey both color and direction. Artists leverage this anisotropic behavior to enhance pure color images with textures, illusions of motion, or depth cues. However, designing colorful embroidery patterns with prescribed directionality is a challenging task, one usually requiring an expert designer. In this work, we propose an interactive algorithm that generates machine-fabricable embroidery patterns from multi-chromatic images equipped with user-specified directionality fields.We cast the problem of finding a stitching pattern into vector theory. To find a suitable stitching pattern, we extract sources and sinks from the divergence field of the vector field extracted from the input and use them to trace streamlines. We further optimize the streamlines to guarantee a smooth and connected stitching pattern. The generated patterns approximate the color distribution constrained by the directionality field. To allow for further artistic control, the trade-off between color match and directionality match can be interactively explored via an intuitive slider. We showcase our approach by fabricating several embroidery paths.}, author = {Liu, Zhenyuan and Piovarci, Michael and Hafner, Christian and Charrondiere, Raphael and Bickel, Bernd}, issn = {1467-8659}, journal = {Computer Graphics Forum}, keywords = {embroidery, design, directionality, density, image}, location = {Saarbrucken, Germany}, number = {2}, pages = {397--409}, publisher = {Wiley}, title = {{Directionality-aware design of embroidery patterns}}, doi = {10.1111/cgf.14770 }, volume = {42}, year = {2023}, } @article{13049, abstract = {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.}, author = {Freire, Marco and Bhargava, Manas and Schreck, Camille and Hugron, Pierre-Alexandre and Bickel, Bernd and Lefebvre, Sylvain}, issn = {1557-7368}, journal = {Transactions on Graphics}, keywords = {PCB design and layout, Mesh geometry models}, location = {Los Angeles, CA, United States}, number = {4}, publisher = {Association for Computing Machinery}, title = {{PCBend: Light up your 3D shapes with foldable circuit boards}}, doi = {10.1145/3592411}, volume = {42}, year = {2023}, } @article{11993, abstract = {Moulding refers to a set of manufacturing techniques in which a mould, usually a cavity or a solid frame, is used to shape a liquid or pliable material into an object of the desired shape. The popularity of moulding comes from its effectiveness, scalability and versatility in terms of employed materials. Its relevance as a fabrication process is demonstrated by the extensive literature covering different aspects related to mould design, from material flow simulation to the automation of mould geometry design. In this state-of-the-art report, we provide an extensive review of the automatic methods for the design of moulds, focusing on contributions from a geometric perspective. We classify existing mould design methods based on their computational approach and the nature of their target moulding process. We summarize the relationships between computational approaches and moulding techniques, highlighting their strengths and limitations. Finally, we discuss potential future research directions.}, author = {Alderighi, Thomas and Malomo, Luigi and Auzinger, Thomas and Bickel, Bernd and Cignoni, Paulo and Pietroni, Nico}, issn = {1467-8659}, journal = {Computer Graphics Forum}, keywords = {Computer Graphics and Computer-Aided Design}, number = {6}, pages = {435--452}, publisher = {Wiley}, title = {{State of the art in computational mould design}}, doi = {10.1111/cgf.14581}, volume = {41}, year = {2022}, } @article{9376, abstract = {This paper presents a method for designing planar multistable compliant structures. Given a sequence of desired stable states and the corresponding poses of the structure, we identify the topology and geometric realization of a mechanism—consisting of bars and joints—that is able to physically reproduce the desired multistable behavior. In order to solve this problem efficiently, we build on insights from minimally rigid graph theory to identify simple but effective topologies for the mechanism. We then optimize its geometric parameters, such as joint positions and bar lengths, to obtain correct transitions between the given poses. Simultaneously, we ensure adequate stability of each pose based on an effective approximate error metric related to the elastic energy Hessian of the bars in the mechanism. As demonstrated by our results, we obtain functional multistable mechanisms of manageable complexity that can be fabricated using 3D printing. Further, we evaluated the effectiveness of our method on a large number of examples in the simulation and fabricated several physical prototypes.}, author = {Zhang, Ran and Auzinger, Thomas and Bickel, Bernd}, issn = {1557-7368}, journal = {ACM Transactions on Graphics}, keywords = {multistability, mechanism, computational design, rigidity}, number = {5}, publisher = {Association for Computing Machinery}, title = {{Computational design of planar multistable compliant structures}}, doi = {10.1145/3453477}, volume = {40}, year = {2021}, } @phdthesis{8366, abstract = {Fabrication of curved shells plays an important role in modern design, industry, and science. Among their remarkable properties are, for example, aesthetics of organic shapes, ability to evenly distribute loads, or efficient flow separation. They find applications across vast length scales ranging from sky-scraper architecture to microscopic devices. But, at the same time, the design of curved shells and their manufacturing process pose a variety of challenges. In this thesis, they are addressed from several perspectives. In particular, this thesis presents approaches based on the transformation of initially flat sheets into the target curved surfaces. This involves problems of interactive design of shells with nontrivial mechanical constraints, inverse design of complex structural materials, and data-driven modeling of delicate and time-dependent physical properties. At the same time, two newly-developed self-morphing mechanisms targeting flat-to-curved transformation are presented. In architecture, doubly curved surfaces can be realized as cold bent glass panelizations. Originally flat glass panels are bent into frames and remain stressed. This is a cost-efficient fabrication approach compared to hot bending, when glass panels are shaped plastically. However such constructions are prone to breaking during bending, and it is highly nontrivial to navigate the design space, keeping the panels fabricable and aesthetically pleasing at the same time. We introduce an interactive design system for cold bent glass façades, while previously even offline optimization for such scenarios has not been sufficiently developed. Our method is based on a deep learning approach providing quick and high precision estimation of glass panel shape and stress while handling the shape multimodality. Fabrication of smaller objects of scales below 1 m, can also greatly benefit from shaping originally flat sheets. In this respect, we designed new self-morphing shell mechanisms transforming from an initial flat state to a doubly curved state with high precision and detail. Our so-called CurveUps demonstrate the encodement of the geometric information into the shell. Furthermore, we explored the frontiers of programmable materials and showed how temporal information can additionally be encoded into a flat shell. This allows prescribing deformation sequences for doubly curved surfaces and, thus, facilitates self-collision avoidance enabling complex shapes and functionalities otherwise impossible. Both of these methods include inverse design tools keeping the user in the design loop.}, author = {Guseinov, Ruslan}, isbn = {978-3-99078-010-7}, issn = {2663-337X}, keywords = {computer-aided design, shape modeling, self-morphing, mechanical engineering}, pages = {118}, publisher = {Institute of Science and Technology Austria}, title = {{Computational design of curved thin shells: From glass façades to programmable matter}}, doi = {10.15479/AT:ISTA:8366}, year = {2020}, } @article{7262, abstract = {Advances in shape-morphing materials, such as hydrogels, shape-memory polymers and light-responsive polymers have enabled prescribing self-directed deformations of initially flat geometries. However, most proposed solutions evolve towards a target geometry without considering time-dependent actuation paths. To achieve more complex geometries and avoid self-collisions, it is critical to encode a spatial and temporal shape evolution within the initially flat shell. Recent realizations of time-dependent morphing are limited to the actuation of few, discrete hinges and cannot form doubly curved surfaces. Here, we demonstrate a method for encoding temporal shape evolution in architected shells that assume complex shapes and doubly curved geometries. The shells are non-periodic tessellations of pre-stressed contractile unit cells that soften in water at rates prescribed locally by mesostructure geometry. The ensuing midplane contraction is coupled to the formation of encoded curvatures. We propose an inverse design tool based on a data-driven model for unit cells’ temporal responses.}, author = {Guseinov, Ruslan and McMahan, Connor and Perez Rodriguez, Jesus and Daraio, Chiara and Bickel, Bernd}, issn = {2041-1723}, journal = {Nature Communications}, keywords = {Design, Synthesis and processing, Mechanical engineering, Polymers}, publisher = {Springer Nature}, title = {{Programming temporal morphing of self-actuated shells}}, doi = {10.1038/s41467-019-14015-2}, volume = {11}, year = {2020}, } @article{11667, abstract = {The focus of classic mechanism design has been on truthful direct-revelation mechanisms. In the context of combinatorial auctions, the truthful direct-revelation mechanism that maximizes social welfare is the Vickrey-Clarke-Groves mechanism. For many valuation spaces, computing the allocation and payments of the VCG mechanism, however, is a computationally hard problem. We thus study the performance of the VCG mechanism when bidders are forced to choose bids from a subspace of the valuation space for which the VCG outcome can be computed efficiently. We prove improved upper bounds on the welfare loss for restrictions to additive bids and upper and lower bounds for restrictions to non-additive bids. These bounds show that increased expressiveness can give rise to additional equilibria of poorer efficiency.}, author = {Dütting, Paul and Henzinger, Monika H and Starnberger, Martin}, issn = {2167-8383}, journal = {ACM Transactions on Economics and Computation}, keywords = {Theory of computation, Algorithmic game theory and mechanism design, Applied computing, Economics, Simplified mechanisms, Combinatorial auctions with item bidding, Price of anarchy}, number = {2}, publisher = {Association for Computing Machinery}, title = {{Valuation compressions in VCG-based combinatorial auctions}}, doi = {10.1145/3232860}, volume = {6}, year = {2018}, }