@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{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{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{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 = {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{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{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}, } @article{10184, abstract = {We introduce a novel technique to automatically decompose an input object’s volume into a set of parts that can be represented by two opposite height fields. Such decomposition enables the manufacturing of individual parts using two-piece reusable rigid molds. Our decomposition strategy relies on a new energy formulation that utilizes a pre-computed signal on the mesh volume representing the accessibility for a predefined set of extraction directions. Thanks to this novel formulation, our method allows for efficient optimization of a fabrication-aware partitioning of volumes in a completely automatic way. We demonstrate the efficacy of our approach by generating valid volume partitionings for a wide range of complex objects and physically reproducing several of them.}, author = {Alderighi, Thomas and Malomo, Luigi and Bickel, Bernd and Cignoni, Paolo and Pietroni, Nico}, issn = {1557-7368 }, journal = {ACM Transactions on Graphics}, number = {6}, publisher = {Association for Computing Machinery}, title = {{Volume decomposition for two-piece rigid casting}}, doi = {10.1145/3478513.3480555}, volume = {40}, year = {2021}, } @article{9817, abstract = {Elastic bending of initially flat slender elements allows the realization and economic fabrication of intriguing curved shapes. In this work, we derive an intuitive but rigorous geometric characterization of the design space of plane elastic rods with variable stiffness. It enables designers to determine which shapes are physically viable with active bending by visual inspection alone. Building on these insights, we propose a method for efficiently designing the geometry of a flat elastic rod that realizes a target equilibrium curve, which only requires solving a linear program. We implement this method in an interactive computational design tool that gives feedback about the feasibility of a design, and computes the geometry of the structural elements necessary to realize it within an instant. The tool also offers an iterative optimization routine that improves the fabricability of a model while modifying it as little as possible. In addition, we use our geometric characterization to derive an algorithm for analyzing and recovering the stability of elastic curves that would otherwise snap out of their unstable equilibrium shapes by buckling. We show the efficacy of our approach by designing and manufacturing several physical models that are assembled from flat elements.}, author = {Hafner, Christian and Bickel, Bernd}, issn = {1557-7368}, journal = {ACM Transactions on Graphics}, keywords = {Computing methodologies, shape modeling, modeling and simulation, theory of computation, computational geometry, mathematics of computing, mathematical optimization}, location = {Virtual}, number = {4}, publisher = {Association for Computing Machinery}, title = {{The design space of plane elastic curves}}, doi = {10.1145/3450626.3459800}, volume = {40}, year = {2021}, } @article{8562, abstract = {Cold bent glass is a promising and cost-efficient method for realizing doubly curved glass facades. They are produced by attaching planar glass sheets to curved frames and require keeping the occurring stress within safe limits. However, it is very challenging to navigate the design space of cold bent glass panels due to the fragility of the material, which impedes the form-finding for practically feasible and aesthetically pleasing cold bent glass facades. We propose an interactive, data-driven approach for designing cold bent glass facades that can be seamlessly integrated into a typical architectural design pipeline. Our method allows non-expert users to interactively edit a parametric surface while providing real-time feedback on the deformed shape and maximum stress of cold bent glass panels. Designs are automatically refined to minimize several fairness criteria while maximal stresses are kept within glass limits. We achieve interactive frame rates by using a differentiable Mixture Density Network trained from more than a million simulations. Given a curved boundary, our regression model is capable of handling multistable configurations and accurately predicting the equilibrium shape of the panel and its corresponding maximal stress. We show predictions are highly accurate and validate our results with a physical realization of a cold bent glass surface.}, author = {Gavriil, Konstantinos and Guseinov, Ruslan and Perez Rodriguez, Jesus and Pellis, Davide and Henderson, Paul M and Rist, Florian and Pottmann, Helmut and Bickel, Bernd}, issn = {1557-7368}, journal = {ACM Transactions on Graphics}, number = {6}, publisher = {Association for Computing Machinery}, title = {{Computational design of cold bent glass façades}}, doi = {10.1145/3414685.3417843}, volume = {39}, year = {2020}, } @article{6650, abstract = {We propose a novel technique for the automatic design of molds to cast highly complex shapes. The technique generates composite, two-piece molds. Each mold piece is made up of a hard plastic shell and a flexible silicone part. Thanks to the thin, soft, and smartly shaped silicone part, which is kept in place by a hard plastic shell, we can cast objects of unprecedented complexity. An innovative algorithm based on a volumetric analysis defines the layout of the internal cuts in the silicone mold part. Our approach can robustly handle thin protruding features and intertwined topologies that have caused previous methods to fail. We compare our results with state of the art techniques, and we demonstrate the casting of shapes with extremely complex geometry.}, author = {Alderighi, Thomas and Malomo, Luigi and Giorgi, Daniela and Bickel, Bernd and Cignoni, Paolo and Pietroni, Nico}, issn = {0730-0301}, journal = {ACM Transactions on Graphics}, number = {4}, publisher = {ACM}, title = {{Volume-aware design of composite molds}}, doi = {10.1145/3306346.3322981}, volume = {38}, year = {2019}, } @article{6660, abstract = {Commercially available full-color 3D printing allows for detailed control of material deposition in a volume, but an exact reproduction of a target surface appearance is hampered by the strong subsurface scattering that causes nontrivial volumetric cross-talk at the print surface. Previous work showed how an iterative optimization scheme based on accumulating absorptive materials at the surface can be used to find a volumetric distribution of print materials that closely approximates a given target appearance. In this work, we first revisit the assumption that pushing the absorptive materials to the surface results in minimal volumetric cross-talk. We design a full-fledged optimization on a small domain for this task and confirm this previously reported heuristic. Then, we extend the above approach that is critically limited to color reproduction on planar surfaces, to arbitrary 3D shapes. Our method enables high-fidelity color texture reproduction on 3D prints by effectively compensating for internal light scattering within arbitrarily shaped objects. In addition, we propose a content-aware gamut mapping that significantly improves color reproduction for the pathological case of thin geometric features. Using a wide range of sample objects with complex textures and geometries, we demonstrate color reproduction whose fidelity is superior to state-of-the-art drivers for color 3D printers.}, author = {Sumin, Denis and Weyrich, Tim and Rittig, Tobias and Babaei, Vahid and Nindel, Thomas and Wilkie, Alexander and Didyk, Piotr and Bickel, Bernd and Křivánek, Jaroslav and Myszkowski, Karol}, issn = {0730-0301}, journal = {ACM Transactions on Graphics}, number = {4}, publisher = {ACM}, title = {{Geometry-aware scattering compensation for 3D printing}}, doi = {10.1145/3306346.3322992}, volume = {38}, year = {2019}, } @article{7002, abstract = {Multiple Importance Sampling (MIS) is a key technique for achieving robustness of Monte Carlo estimators in computer graphics and other fields. We derive optimal weighting functions for MIS that provably minimize the variance of an MIS estimator, given a set of sampling techniques. We show that the resulting variance reduction over the balance heuristic can be higher than predicted by the variance bounds derived by Veach and Guibas, who assumed only non-negative weights in their proof. We theoretically analyze the variance of the optimal MIS weights and show the relation to the variance of the balance heuristic. Furthermore, we establish a connection between the new weighting functions and control variates as previously applied to mixture sampling. We apply the new optimal weights to integration problems in light transport and show that they allow for new design considerations when choosing the appropriate sampling techniques for a given integration problem.}, author = {Kondapaneni, Ivo and Vevoda, Petr and Grittmann, Pascal and Skrivan, Tomas and Slusallek, Philipp and Křivánek, Jaroslav}, issn = {0730-0301}, journal = {ACM Transactions on Graphics}, number = {4}, publisher = {ACM}, title = {{Optimal multiple importance sampling}}, doi = {10.1145/3306346.3323009}, volume = {38}, year = {2019}, } @article{7117, abstract = {We propose a novel generic shape optimization method for CAD models based on the eXtended Finite Element Method (XFEM). Our method works directly on the intersection between the model and a regular simulation grid, without the need to mesh or remesh, thus removing a bottleneck of classical shape optimization strategies. This is made possible by a novel hierarchical integration scheme that accurately integrates finite element quantities with sub-element precision. For optimization, we efficiently compute analytical shape derivatives of the entire framework, from model intersection to integration rule generation and XFEM simulation. Moreover, we describe a differentiable projection of shape parameters onto a constraint manifold spanned by user-specified shape preservation, consistency, and manufacturability constraints. We demonstrate the utility of our approach by optimizing mass distribution, strength-to-weight ratio, and inverse elastic shape design objectives directly on parameterized 3D CAD models.}, author = {Hafner, Christian and Schumacher, Christian and Knoop, Espen and Auzinger, Thomas and Bickel, Bernd and Bächer, Moritz}, issn = {0730-0301}, journal = {ACM Transactions on Graphics}, number = {6}, publisher = {ACM}, title = {{X-CAD: Optimizing CAD Models with Extended Finite Elements}}, doi = {10.1145/3355089.3356576}, volume = {38}, year = {2019}, } @article{7418, abstract = {Multiple importance sampling (MIS) has become an indispensable tool in Monte Carlo rendering, widely accepted as a near-optimal solution for combining different sampling techniques. But an MIS combination, using the common balance or power heuristics, often results in an overly defensive estimator, leading to high variance. We show that by generalizing the MIS framework, variance can be substantially reduced. Specifically, we optimize one of the combined sampling techniques so as to decrease the overall variance of the resulting MIS estimator. We apply the approach to the computation of direct illumination due to an HDR environment map and to the computation of global illumination using a path guiding algorithm. The implementation can be as simple as subtracting a constant value from the tabulated sampling density done entirely in a preprocessing step. This produces a consistent noise reduction in all our tests with no negative influence on run time, no artifacts or bias, and no failure cases.}, author = {Karlík, Ondřej and Šik, Martin and Vévoda, Petr and Skrivan, Tomas and Křivánek, Jaroslav}, issn = {1557-7368}, journal = {ACM Transactions on Graphics}, number = {6}, publisher = {ACM}, title = {{MIS compensation: Optimizing sampling techniques in multiple importance sampling}}, doi = {10.1145/3355089.3356565}, volume = {38}, year = {2019}, } @article{5976, abstract = {We propose FlexMaps, a novel framework for fabricating smooth shapes out of flat, flexible panels with tailored mechanical properties. We start by mapping the 3D surface onto a 2D domain as in traditional UV mapping to design a set of deformable flat panels called FlexMaps. For these panels, we design and obtain specific mechanical properties such that, once they are assembled, the static equilibrium configuration matches the desired 3D shape. FlexMaps can be fabricated from an almost rigid material, such as wood or plastic, and are made flexible in a controlled way by using computationally designed spiraling microstructures.}, author = {Malomo, Luigi and Perez Rodriguez, Jesus and Iarussi, Emmanuel and Pietroni, Nico and Miguel, Eder and Cignoni, Paolo and Bickel, Bernd}, issn = {0730-0301}, journal = {ACM Transactions on Graphics}, number = {6}, publisher = {Association for Computing Machinery (ACM)}, title = {{FlexMaps: Computational design of flat flexible shells for shaping 3D objects}}, doi = {10.1145/3272127.3275076}, volume = {37}, year = {2018}, }