@article{20628, abstract = {The realistic simulation of sand, soil, powders, rubble piles, and large collections of rigid bodies is a common and important problem in the fields of computer graphics, computational physics, and engineering. Direct simulation of these individual bodies quickly becomes expensive, so we often approximate the entire group as a continuum material that can be more easily computed using tools for solving partial differential equations, like the material point method (MPM). In this paper, we present a method for automatically extracting continuum material properties from a collection of rigid bodies. We use numerical homogenization with periodic boundary conditions to simulate an effectively infinite number of rigid bodies in contact. We then record the effective stress-strain relationships from these simulations and convert them into elastic properties and yield criteria for the continuum simulations. Our experiments validate existing theoretical models like the Mohr-Coulomb yield surface by extracting material behaviors from a collection of spheres in contact. We further generalize these existing models to more exotic materials derived from diverse and non-convex shapes. We observe complicated jamming behaviors from non-convex grains, and we introduce a new material model for materials with extremely high levels of internal friction and cohesion. We simulate these new continuum models using MPM with an improved return mapping technique. The end result is a complete system for turning an input rigid body simulation into an efficient continuum simulation with the same effective mechanical properties.}, author = {Chen, Yi-Lu and Ly, Mickaël and Wojtan, Christopher J}, issn = {1557-7368}, journal = {ACM Transactions on Graphics}, location = {Hong Kong, China}, number = {6}, publisher = {Association for Computing Machinery}, title = {{Numerical homogenization of sand from grain-level simulations}}, doi = {10.1145/3763344}, volume = {44}, year = {2025}, } @article{17203, abstract = {The behavior of a rigid body primarily depends on its mass moments, which consist of the mass, center of mass, and moments of inertia. It is possible to manipulate these quantities without altering the geometric appearance of an object by introducing cavities in its interior. Algorithms that find cavities of suitable shapes and sizes have enabled the computational design of spinning tops, yo-yos, wheels, buoys, and statically balanced objects. Previous work is based, for example, on topology optimization on voxel grids, which introduces a large number of optimization variables and box constraints, or offset surface computation, which cannot guarantee that solutions to a feasible problem will always be found. In this work, we provide a mathematical analysis of constrained topology optimization problems that depend only on mass moments. This class of problems covers, among others, all applications mentioned above. Our main result is to show that no matter the outer shape of the rigid body to be optimized or the optimization objective and constraints considered, the optimal solution always features a quadric-shaped interface between material and cavities. This proves that optimal interfaces are always ellipsoids, hyperboloids, paraboloids, or one of a few degenerate cases, such as planes. This insight lets us replace a difficult topology optimization problem with a provably equivalent non-linear equation system in a small number (<10) of variables, which represent the coefficients of the quadric. This system can be solved in a few seconds for most examples, provides insights into the geometric structure of many specific applications, and lets us describe their solution properties. Finally, our method integrates seamlessly into modern fabrication workflows because our solutions are analytical surfaces that are native to the CAD domain.}, author = {Hafner, Christian and Ly, Mickaël and Wojtan, Christopher J}, issn = {1557-7368}, journal = {Transactions on Graphics}, keywords = {Topology Optimization, Mass Moments, Computational Geometry}, location = {Denver, Colorado}, number = {4}, publisher = {Association for Computing Machinery}, title = {{Spin-it faster: Quadrics solve all topology optimization problems that depend only on mass moments}}, doi = {10.1145/3658194}, volume = {43}, year = {2024}, } @article{17219, abstract = {We introduce a multi-material non-manifold mesh-based surface tracking algorithm that converts self-intersections into topological changes. Our algorithm generalizes prior work on manifold surface tracking with topological changes: it preserves surface features like mesh-based methods, and it robustly handles topological changes like level set methods. Our method also offers improved efficiency and robustness over the state of the art. We demonstrate the effectiveness of the approach on a range of examples, including complex soap film simulations with thousands of interacting bubbles, and boolean unions of non-manifold meshes consisting of millions of triangles.}, author = {Synak, Peter and Kalinov, Aleksei and Strugaru, Irina-Malina and Etemadihaghighi, Arian and Yang, Huidong and Wojtan, Christopher J}, issn = {1557-7368}, journal = {ACM Transactions on Graphics}, keywords = {surface tracking, topology change, non- manifold meshes, multi-material flows, solid modeling}, number = {4}, publisher = {Association for Computing Machinery}, title = {{Multi-material mesh-based surface tracking with implicit topology changes}}, doi = {10.1145/3658223}, volume = {43}, year = {2024}, } @article{17424, abstract = {Surface-based inflatables are composed of two thin layers of nearly inextensible sheet material joined together along carefully selected fusing curves. During inflation, pressure forces separate the two sheets to maximize the enclosed volume. The fusing curves restrict this expansion, leading to a spatially varying in-plane contraction and hence metric frustration. The inflated structure settles into a 3D equilibrium that balances pressure forces with the internal elastic forces of the sheets. We present a computational framework for analyzing and designing surface-based inflatable structures with arbitrary fusing patterns. Our approach employs numerical homogenization to characterize the behavior of parametric families of periodic inflatable patch geometries, which can then be combined to tessellate the sheet with smoothly varying patterns. We propose a novel parametrization of the underlying deformation space that allows accurate, efficient, and systematical analysis of the stretching and bending behavior of inflated patches with potentially open boundaries. We apply our homogenization algorithm to create a database of geometrically diverse fusing patterns spanning a wide range of material properties and deformation characteristics. This database is employed in an inverse design algorithm that solves for fusing curves to best approximate a given input target surface. Local patches are selected and blended to form a global network of curves based on a geometric flattening algorithm. These fusing curves are then further optimized to minimize the distance of the deployed structure to target surface. We show that this approach offers greater flexibility to approximate given target geometries compared to previous work while significantly improving structural performance.}, author = {Ren, Yingying and Panetta, Julian and Suzuki, Seiichi and Kusupati, Uday and Isvoranu, Florin and Pauly, Mark}, issn = {1557-7368}, journal = {ACM Transactions on Graphics}, number = {4}, publisher = {Association for Computing Machinery}, title = {{Computational homogenization for inverse design of surface-based inflatables}}, doi = {10.1145/3658125}, volume = {43}, year = {2024}, } @article{14240, abstract = {This paper introduces a novel method for simulating large bodies of water as a height field. At the start of each time step, we partition the waves into a bulk flow (which approximately satisfies the assumptions of the shallow water equations) and surface waves (which approximately satisfy the assumptions of Airy wave theory). We then solve the two wave regimes separately using appropriate state-of-the-art techniques, and re-combine the resulting wave velocities at the end of each step. This strategy leads to the first heightfield wave model capable of simulating complex interactions between both deep and shallow water effects, like the waves from a boat wake sloshing up onto a beach, or a dam break producing wave interference patterns and eddies. We also analyze the numerical dispersion created by our method and derive an exact correction factor for waves at a constant water depth, giving us a numerically perfect re-creation of theoretical water wave dispersion patterns.}, author = {Jeschke, Stefan and Wojtan, Christopher J}, issn = {1557-7368}, journal = {ACM Transactions on Graphics}, number = {4}, publisher = {Association for Computing Machinery}, title = {{Generalizing shallow water simulations with dispersive surface waves}}, doi = {10.1145/3592098}, volume = {42}, year = {2023}, } @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 = {1557-7368}, 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{12984, abstract = {Tattoos are a highly popular medium, with both artistic and medical applications. Although the mechanical process of tattoo application has evolved historically, the results are reliant on the artisanal skill of the artist. This can be especially challenging for some skin tones, or in cases where artists lack experience. We provide the first systematic overview of tattooing as a computational fabrication technique. We built an automated tattooing rig and a recipe for the creation of silicone sheets mimicking realistic skin tones, which allowed us to create an accurate model predicting tattoo appearance. This enables several exciting applications including tattoo previewing, color retargeting, novel ink spectra optimization, color-accurate prosthetics, and more.}, author = {Piovarci, Michael and Chapiro, Alexandre and Bickel, Bernd}, issn = {1557-7368}, journal = {ACM Transactions on Graphics}, keywords = {appearance, modeling, reproduction, tattoo, skin color, gamut mapping, ink-optimization, prosthetic}, location = {Los Angeles, CA, United States}, number = {4}, publisher = {Association for Computing Machinery}, title = {{Skin-Screen: A computational fabrication framework for color tattoos}}, doi = {10.1145/3592432}, 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{13265, abstract = {In this study, we propose a computational framework for optimizing the continuity of the toolpath in fabricating surface models on an extrusion-based 3D printer. Toolpath continuity is a critical issue that influences both the quality and the efficiency of extrusion-based fabrication. Transfer moves lead to rough and bumpy surfaces, where this phenomenon worsens for materials with large viscosity, like clay. The effects of continuity on the surface models are even more severe in terms of the quality of the surface and the stability of the model. We introduce a criterion called the one–path patch (OPP) to represent a patch on the surface of the shell that can be traversed along one path by considering the constraints on fabrication. We study the properties of the OPPs and their merging operations to propose a bottom-up OPP merging procedure to decompose the given shell surface into a minimal number of OPPs, and to generate the “as-continuous-as-possible” (ACAP) toolpath. Furthermore, we augment the path planning algorithm with a curved-layer printing scheme that reduces staircase defects and improves the continuity of the toolpath by connecting multiple segments. We evaluated the ACAP algorithm on ceramic and thermoplastic materials, and the results showed that it improves the fabrication of surface models in terms of both efficiency and surface quality.}, author = {Zhong, Fanchao and Xu, Yonglai and Zhao, Haisen and Lu, Lin}, issn = {1557-7368}, journal = {ACM Transactions on Graphics}, number = {3}, publisher = {Association for Computing Machinery}, title = {{As-Continuous-As-Possible extrusion-based fabrication of surface models}}, doi = {10.1145/3575859}, volume = {42}, year = {2023}, } @article{17379, abstract = {We introduce a computational pipeline for simulating and designing C-shells, a new class of planar-to-spatial deployable linkage structures. A C-shell is composed of curved flexible beams connected at rotational joints that can be assembled in a stress-free planar configuration. When actuated, the elastic beams deform and the assembly deploys towards the target 3D shape. We propose two alternative computational design approaches for C-shells: (i) Forward exploration simulates the deployed shape from a planar beam layout provided by the user. Once a satisfactory overall shape is found, a subsequent design optimization adapts the beam geometry to reduce the elastic energy of the linkage while preserving the target shape. (ii) Inverse design is facilitated by a new geometric flattening method that takes a design surface as input and computes an initial layout of piecewise straight linkage beams. Our design optimization algorithm then calculates the smooth curved beams to best reproduce the target shape at minimal elastic energy. We find that C-shells offer a rich space for design and show several studies that highlight new shape topologies that cannot be achieved with existing deployable linkage structures.}, author = {Becker, Quentin and Suzuki, Seiichi and Ren, Yingying and Pellis, Davide and Panetta, Julian and Pauly, Mark}, issn = {1557-7368}, journal = {ACM Transactions on Graphics}, number = {6}, publisher = {Association for Computing Machinery}, title = {{C-shells: Deployable gridshells with curved beams}}, doi = {10.1145/3618366}, volume = {42}, year = {2023}, } @article{17381, abstract = {We present an algorithmic approach to discover, study, and design multistable elastic knots. Elastic knots are physical realizations of closed curves embedded in 3-space. When endowed with the material thickness and bending resistance of a physical wire, these knots settle into equilibrium states that balance the forces induced by elastic deformation and self-contacts of the wire. In general, elastic knots can have many distinct equilibrium states, i.e. they are multistable mechanical systems. We propose a computational pipeline that combines randomized spatial sampling and physics simulation to efficiently find stable equilibrium states of elastic knots. Leveraging results from knot theory, we run our pipeline on thousands of different topological knot types to create an extensive data set of multistable knots. By applying a series of filters to this data, we discover new transformable knots with interesting geometric and physical properties. A further analysis across knot types reveals geometric and topological patterns, yielding constructive principles that generalize beyond the currently tabulated knot types. We show how multistable elastic knots can be used to design novel deployable structures and engaging recreational puzzles. Several physical prototypes at different scales highlight these applications and validate our simulation.}, author = {Vidulis, Michele and Ren, Yingying and Panetta, Julian and Grinspun, Eitan and Pauly, Mark}, issn = {1557-7368}, journal = {ACM Transactions on Graphics}, number = {4}, publisher = {Association for Computing Machinery}, title = {{Computational exploration of multistable elastic knots}}, doi = {10.1145/3592399}, 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{11442, abstract = {Enabling additive manufacturing to employ a wide range of novel, functional materials can be a major boost to this technology. However, making such materials printable requires painstaking trial-and-error by an expert operator, as they typically tend to exhibit peculiar rheological or hysteresis properties. Even in the case of successfully finding the process parameters, there is no guarantee of print-to-print consistency due to material differences between batches. These challenges make closed-loop feedback an attractive option where the process parameters are adjusted on-the-fly. There are several challenges for designing an efficient controller: the deposition parameters are complex and highly coupled, artifacts occur after long time horizons, simulating the deposition is computationally costly, and learning on hardware is intractable. In this work, we demonstrate the feasibility of learning a closed-loop control policy for additive manufacturing using reinforcement learning. We show that approximate, but efficient, numerical simulation is sufficient as long as it allows learning the behavioral patterns of deposition that translate to real-world experiences. In combination with reinforcement learning, our model can be used to discover control policies that outperform baseline controllers. Furthermore, the recovered policies have a minimal sim-to-real gap. We showcase this by applying our control policy in-vivo on a single-layer, direct ink writing printer. }, author = {Piovarci, Michael and Foshey, Michael and Xu, Jie and Erps, Timothy and Babaei, Vahid and Didyk, Piotr and Rusinkiewicz, Szymon and Matusik, Wojciech and Bickel, Bernd}, issn = {1557-7368}, journal = {ACM Transactions on Graphics}, number = {4}, publisher = {Association for Computing Machinery}, title = {{Closed-loop control of direct ink writing via reinforcement learning}}, doi = {10.1145/3528223.3530144}, volume = {41}, year = {2022}, } @article{11735, abstract = {Interlocking puzzles are intriguing geometric games where the puzzle pieces are held together based on their geometric arrangement, preventing the puzzle from falling apart. High-level-of-difficulty, or simply high-level, interlocking puzzles are a subclass of interlocking puzzles that require multiple moves to take out the first subassembly from the puzzle. Solving a high-level interlocking puzzle is a challenging task since one has to explore many different configurations of the puzzle pieces until reaching a configuration where the first subassembly can be taken out. Designing a high-level interlocking puzzle with a user-specified level of difficulty is even harder since the puzzle pieces have to be interlocking in all the configurations before the first subassembly is taken out. In this paper, we present a computational approach to design high-level interlocking puzzles. The core idea is to represent all possible configurations of an interlocking puzzle as well as transitions among these configurations using a rooted, undirected graph called a disassembly graph and leverage this graph to find a disassembly plan that requires a minimal number of moves to take out the first subassembly from the puzzle. At the design stage, our algorithm iteratively constructs the geometry of each puzzle piece to expand the disassembly graph incrementally, aiming to achieve a user-specified level of difficulty. We show that our approach allows efficient generation of high-level interlocking puzzles of various shape complexities, including new solutions not attainable by state-of-the-art approaches.}, author = {Chen, Rulin and Wang, Ziqi and Song, Peng and Bickel, Bernd}, issn = {1557-7368}, journal = {ACM Transactions on Graphics}, number = {4}, publisher = {Association for Computing Machinery}, title = {{Computational design of high-level interlocking puzzles}}, doi = {10.1145/3528223.3530071}, volume = {41}, year = {2022}, } @article{11736, abstract = {This paper introduces a methodology for inverse-modeling of yarn-level mechanics of cloth, based on the mechanical response of fabrics in the real world. We compiled a database from physical tests of several different knitted fabrics used in the textile industry. These data span different types of complex knit patterns, yarn compositions, and fabric finishes, and the results demonstrate diverse physical properties like stiffness, nonlinearity, and anisotropy. We then develop a system for approximating these mechanical responses with yarn-level cloth simulation. To do so, we introduce an efficient pipeline for converting between fabric-level data and yarn-level simulation, including a novel swatch-level approximation for speeding up computation, and some small-but-necessary extensions to yarn-level models used in computer graphics. The dataset used for this paper can be found at http://mslab.es/projects/YarnLevelFabrics.}, author = {Sperl, Georg and Sánchez-Banderas, Rosa M. and Li, Manwen and Wojtan, Christopher J and Otaduy, Miguel A.}, issn = {1557-7368}, journal = {ACM Transactions on Graphics}, number = {4}, publisher = {Association for Computing Machinery}, title = {{Estimation of yarn-level simulation models for production fabrics}}, doi = {10.1145/3528223.3530167}, volume = {41}, year = {2022}, } @article{12431, abstract = {This paper presents a new representation of curve dynamics, with applications to vortex filaments in fluid dynamics. Instead of representing these filaments with explicit curve geometry and Lagrangian equations of motion, we represent curves implicitly with a new co-dimensional 2 level set description. Our implicit representation admits several redundant mathematical degrees of freedom in both the configuration and the dynamics of the curves, which can be tailored specifically to improve numerical robustness, in contrast to naive approaches for implicit curve dynamics that suffer from overwhelming numerical stability problems. Furthermore, we note how these hidden degrees of freedom perfectly map to a Clebsch representation in fluid dynamics. Motivated by these observations, we introduce untwisted level set functions and non-swirling dynamics which successfully regularize sources of numerical instability, particularly in the twisting modes around curve filaments. A consequence is a novel simulation method which produces stable dynamics for large numbers of interacting vortex filaments and effortlessly handles topological changes and re-connection events.}, author = {Ishida, Sadashige and Wojtan, Christopher J and Chern, Albert}, issn = {1557-7368}, journal = {ACM Transactions on Graphics}, number = {6}, publisher = {Association for Computing Machinery}, title = {{Hidden degrees of freedom in implicit vortex filaments}}, doi = {10.1145/3550454.3555459}, volume = {41}, year = {2022}, } @article{17065, abstract = {Past work on optimizing fabrication plans given a carpentry design can provide Pareto-optimal plans trading off between material waste, fabrication time, precision, and other considerations. However, when developing fabrication plans, experts rarely restrict to a single design, instead considering families of design variations, sometimes adjusting designs to simplify fabrication. Jointly exploring the design and fabrication plan spaces for each design is intractable using current techniques. We present a new approach to jointly optimize design and fabrication plans for carpentered objects. To make this bi-level optimization tractable, we adapt recent work from program synthesis based on equality graphs (e-graphs), which encode sets of equivalent programs. Our insight is that subproblems within our bi-level problem share significant substructures. By representing both designs and fabrication plans in a new bag of parts (BOP) e-graph, we amortize the cost of optimizing design components shared among multiple candidates. Even using BOP e-graphs, the optimization space grows quickly in practice. Hence, we also show how a feedback-guided search strategy dubbed Iterative Contraction and Expansion on E-graphs (ICEE) can keep the size of the e-graph manageable and direct the search towards promising candidates. We illustrate the advantages of our pipeline through examples from the carpentry domain.}, author = {Zhao, Haisen and Willsey, Max and Zhu, Amy and Nandi, Chandrakana and Tatlock, Zachary and Solomon, Justin and Schulz, Adriana}, issn = {1557-7368}, journal = {ACM Transactions on Graphics}, number = {3}, publisher = {Association for Computing Machinery}, title = {{Co-optimization of design and fabrication plans for carpentry}}, doi = {10.1145/3508499}, volume = {41}, year = {2022}, } @article{17383, abstract = {We present a computational inverse design framework for a new class of volumetric deployable structures that have compact rest states and deploy into bending-active 3D target surfaces. Umbrella meshes consist of elastic beams, rigid plates, and hinge joints that can be directly printed or assembled in a zero-energy fabrication state. During deployment, as the elastic beams of varying heights rotate from vertical to horizontal configurations, the entire structure transforms from a compact block into a target curved surface. Umbrella Meshes encode both intrinsic and extrinsic curvature of the target surface and in principle are free from the area expansion ratio bounds of past auxetic material systems. We build a reduced physics-based simulation framework to accurately and efficiently model the complex interaction between the elastically deforming components. To determine the mesh topology and optimal shape parameters for approximating a given target surface, we propose an inverse design optimization algorithm initialized with conformal flattening. Our algorithm minimizes the structure's strain energy in its deployed state and optimizes actuation forces so that the final deployed structure is in stable equilibrium close to the desired surface with few or no external constraints. We validate our approach by fabricating a series of physical models at various scales using different manufacturing techniques.}, author = {Ren, Yingying and Kusupati, Uday and Panetta, Julian and Isvoranu, Florin and Pellis, Davide and Chen, Tian and Pauly, Mark}, issn = {1557-7368}, journal = {ACM Transactions on Graphics}, number = {4}, pages = {1--15}, publisher = {Association for Computing Machinery}, title = {{Umbrella meshes: Elastic mechanisms for freeform shape deployment}}, doi = {10.1145/3528223.3530089}, volume = {41}, year = {2022}, } @article{17384, abstract = {Basket weaving is a traditional craft for creating curved surfaces as an interwoven array of thin, flexible, and initially straight ribbons. The three-dimensional shape of a woven structure emerges through a complex interplay of the elastic bending behavior of the ribbons and the contact forces at their crossings. Curvature can be injected by carefully placing topological singularities in the otherwise regular weaving pattern. However, shape control through topology is highly non-trivial and inherently discrete, which severely limits the range of attainable woven geometries. Here, we demonstrate how to construct arbitrary smooth free-form surface geometries by weaving carefully optimized curved ribbons. We present an optimization-based approach to solving the inverse design problem for such woven structures. Our algorithm computes the ribbons' planar geometry such that their interwoven assembly closely approximates a given target design surface in equilibrium. We systematically validate our approach through a series of physical prototypes to show a broad range of new woven geometries that is not achievable by existing methods. We anticipate our computational approach to significantly enhance the capabilities for the design of new woven structures. Facilitated by modern digital fabrication technology, we see potential applications in material science, bio- and mechanical engineering, art, design, and architecture.}, author = {Ren, Yingying and Panetta, Julian and Chen, Tian and Isvoranu, Florin and Poincloux, Samuel and Brandt, Christopher and Martin, Alison and Pauly, Mark}, issn = {1557-7368}, journal = {ACM Transactions on Graphics}, number = {4}, pages = {1--15}, publisher = {Association for Computing Machinery}, title = {{3D weaving with curved ribbons}}, doi = {10.1145/3450626.3459788}, volume = {40}, year = {2021}, } @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}, }