Abstract We propose a method for designing inflatable shells made of superimposed quasi‐inextensible membranes sealed according to specific welding patterns. The shapes of the patterns are defined on unit triangular cells and allow us to locally control the contraction of the cells from rest to inflated configuration. By paving the patterns on the surface of the structure and properly grading their parameters, we are able to generate inflatables of prescribed deployed shapes through metric frustration. Our triangular cells exhibit isotropic contraction. Our inverse design algorithm can thus leverage conformal parametrization to compute local contraction ratios that are converted to pattern geometries. Key to our approach is to define the arrangement of the patterns using an unstructured triangulation of the target surface. Compared to more traditional arrangements laid out on regular grids, our approach allows us to easily cut or segment the structure without visible seams and to decrease the contraction range necessary to reproduce a given surface, thus enlarging our design space. Additionally, unstructured arrangements lead to inflatable structures whose cells conform to the boundary of the target surface and therefore better covers it. We demonstrate the capabilities of our approach in simulation and by fabricating various prototypes, made of one or multiple components.

Abstract Inflatable pads, such as those used as mattresses or protective equipment, are structures made of two planar membranes sealed according to periodic patterns, typically parallel lines or dots. In this work, we propose to treat these inflatables as metamaterials. By considering novel sealing patterns with 6‐fold symmetry, we are able to generate a family of inflatable materials whose macroscale contraction is isotropic and can be modulated by controlling the parameters of the seals. We leverage this property of our inflatable materials family to propose a simple and effective algorithm based on conformal mapping that allows us to design the layout of inflatable structures that can be fabricated flat and whose inflated shapes approximate those of given target freeform surfaces.

We present how we co-designed with a connoisseur a system that visualizes a star-like ribbon joining at the solar plexus and animated it from motion capture data to perform Isadora Duncan’s dances. Additionally, the system visualizes the trace of the solar plexus and specific keyframes of the choreography as key poses placed in the 3D space. We display the visualization in a Hololens headset and provide features that allow to manipulate it in order to understand and learn Duncan’s qualities and choreographic style. Through a workshop with dancers, we ran a structured observation where we compared qualitatively how the dancers were able to perceive Duncan’s qualities and embody them using the system set according to two different conditions: displaying all the future keyframes or displaying a limited number of keyframes. We discuss the results of our workshop and the use of augmented reality in the studio for pedagogical purposes.

We propose a new approach for representing wrinkles, designed to capture complex and detailed wrinkle behavior on coarse triangle meshes, called Complex Wrinkle Fields. Complex Wrinkle Fields consist of an almost-everywhere-unit complex-valued phase function over the surface; a frequency one-form; and an amplitude scalar, with a soft compatibility condition coupling the frequency and phase. We develop algorithms for interpolating between two such wrinkle fields, for visualizing them as displacements of a Loop-subdivided refinement of the base mesh, and for making smooth local edits to the wrinkle amplitude, frequency, and/or orientation. These algorithms make it possible, for the first time, to create and edit animations of wrinkles on triangle meshes that are smooth in space, evolve smoothly through time, include singularities along with their complex interactions, and that represent frequencies far finer than the surface resolution.

We present a new abstract representation of choreographic motion that conveys the movement quality of fluidity that is central to the style of modern dance pioneer Isadora Duncan. We designed our model through a collaboration with an expert Duncanian dancer, using five flexible ribbons joining at the solar plexus and animated it from motion capture data using a tailored optimization-based algorithm. We display our model in a Hololens headset and provide features that allow to visualize and manipulate it in order to understand and learn Duncan’s choreographic style. Through a series of workshops, we explored our system with professional dancers and were able to observe how it provides them with an immersive experience of a novel visualization of Duncan movement qualities in a way that was not possible with traditional human-like or skeleton-based representations.

Abstract We introduce a new mechanism for self‐actuating deployable structures, based on printing a dense pattern of closely‐spaced plastic ribbons on sheets of pre‐stretched elastic fabric. We leverage two shape‐changing effects that occur when such an assembly is printed and allowed to relax: first, the incompressible plastic ribbons frustrate the contraction of the fabric back to its rest state, forcing residual strain in the fabric and creating intrinsic curvature. Second, the differential compression at the interface between the plastic and fabric layers yields abilayer effectin the direction of the ribbons, making each ribbon buckle into an arc at equilibrium state and creating extrinsic curvature. We describe an inverse design tool to fabricate low‐cost, lightweight prototypes of freeform surfaces using the controllable directional distortion and curvature offered by this mechanism. The core of our method is a parameterization algorithm that bounds surface distortions along and across principal curvature directions, along with a pattern synthesis algorithm that covers a surface with ribbons to match the target distortions and curvature given by the aforementioned parameterization. We demonstrate the flexibility and accuracy of our method by fabricating and measuring a variety of surfaces, including nearly‐developable surfaces as well as surfaces with positive and negative mean curvature, which we achieve thanks to a simple hardware setup that allows printing on both sides of the fabric.

We propose a new model and algorithm to capture the high-definition statics of thin shells via coarse meshes. This model predicts global, fine-scale wrinkling at frequencies much higher than the resolution of the coarse mesh; moreover, it is grounded in the geometric analysis of elasticity, and does not require manual guidance, a corpus of training examples, nor tuning of ad hoc parameters. We first approximate the coarse shape of the shell using tension field theory, in which material forces do not resist compression. We then augment this base mesh with wrinkles, parameterized by an amplitude and phase field that we solve for over the base mesh, which together characterize the geometry of the wrinkles. We validate our approach against both physical experiments and numerical simulations, and we show that our algorithm produces wrinkles qualitatively similar to those predicted by traditional shell solvers requiring orders of magnitude more degrees of freedom.

We present a method for designing mechanical metamaterials based on the novel concept of Voronoi diagrams induced by star-shaped metrics. As one of its central advantages, our approach supports interpolation between arbitrary metrics. This capability opens up a rich space of structures with interesting aesthetics and a wide range of mechanical properties, including isotropic, tetragonal, orthotropic, as well as smoothly graded materials. We evaluate our method by creating large sets of example structures, provided as accompanying material. We validate the mechanical properties predicted by simulation through tensile tests on a set of physical prototypes.

We present an inverse design tool for fabric formwork - a process where flat panels are sewn together to form a fabric container for casting a plaster sculpture. Compared to 3D printing techniques, the benefit of fabric formwork is its properties of low-cost and easy transport. The process of fabric formwork is akin to molding and casting but having a soft boundary. Deformation of the fabric container is governed by force equilibrium between the pressure forces from liquid fill and tension in the stretched fabric. The final result of fabrication depends on the shapes of the flat panels, the fabrication orientation and the placement of external supports. Our computational framework generates optimized flat panels and fabrication orientation with reference to a target shape, and determines effective locations for external supports. We demonstrate the function of this design tool on a variety of models with different shapes and topology. Physical fabrication is also demonstrated to validate our approach.

We propose an inverse strategy for modeling thin elastic shells physically, just from the observation of their geometry. Our algorithm takes as input an arbitrary target mesh, and interprets this configuration automatically as a stable equilibrium of a shell simulator under gravity and frictional contact constraints with a given external object. Unknowns are the natural shape of the shell (i.e., its shape without external forces) and the frictional contact forces at play, while the material properties (mass density, stiffness, friction coefficients) can be freely chosen by the user. Such an inverse problem formulates as an ill-posed nonlinear system subject to conical constraints. To select and compute a plausible solution, our inverse solver proceeds in two steps. In a first step, contacts are reduced to frictionless bilateral constraints and a natural shape is retrieved using the adjoint method. The second step uses this result as an initial guess and adjusts each bilateral force so that it projects onto the admissible Coulomb friction cone, while preserving global equilibrium. To better guide minimization towards the target, these two steps are applied iteratively using a degressive regularization of the shell energy. We validate our approach on simulated examples with reference material parameters, and show that our method still converges well for material parameters lying within a reasonable range around the reference, and even in the case of arbitrary meshes that are not issued from a simulation. We finally demonstrate practical inversion results on complex shell geometries freely modeled by an artist or automatically captured from real objects, such as posed garments or soft accessories.

In this paper we present a novel two-scale framework to optimize the structure and the material distribution of an object given its functional specifications. Our approach utilizes multi-material microstructures as low-level building blocks of the object. We start by precomputing the material property gamut -- the set of bulk material properties that can be achieved with all material microstructures of a given size. We represent the boundary of this material property gamut using a level set field. Next, we propose an efficient and general topology optimization algorithm that simultaneously computes an optimal object topology and spatially-varying material properties constrained by the precomputed gamut. Finally, we map the optimal spatially-varying material properties onto the microstructures with the corresponding properties in order to generate a high-resolution printable structure. We demonstrate the efficacy of our framework by designing, optimizing, and fabricating objects in different material property spaces on the level of a trillion voxels, i.e several orders of magnitude higher than what can be achieved with current systems.

In this article, we present a novel two-scale framework to optimize the structure and the material distribution of an object given its functional specifications. Our approach utilizes multi-material microstructures as low-level building blocks of the object. We start by precomputing the material property gamut—the set of bulk material properties that can be achieved with all material microstructures of a given size. We represent the boundary of this material property gamut using a level set field. Next, we propose an efficient and general topology optimization algorithm that simultaneously computes an optimal object topology and spatially varying material properties constrained by the precomputed gamut. Finally, we map the optimal spatially varying material properties onto the microstructures with the corresponding properties to generate a high-resolution printable structure. We demonstrate the efficacy of our framework by designing, optimizing, and fabricating objects in different material property spaces on the level of a trillion voxels, that is, several orders of magnitude higher than what can be achieved with current systems.

This paper presents a design, simulation, and fabrication pipeline for making transforming inflatables with various materials. We introduce a bending mechanism that creates multiple, programmable shape-changing behaviors with inextensible materials, including paper, plastics and fabrics. We developed a software tool that generates these bending mechanism for a given geometry, simulates its transformation, and exports the compound geometry as digital fabrication files. We show a range of fabrication methods, from manual sealing, to heat pressing with custom stencils and a custom heat-sealing head that can be mounted on usual 3-axis CNC machines to precisely fabricate the designed transforming material. Finally, we present three applications to show how this technology could be used for designing interactive wearables, toys, and furniture.

We present an interactive tool for designing physical surfaces made from flexible interlocking quadrilateral elements of a single size and shape. With the element shape fixed, the design task becomes one of finding a discrete structure---i.e., element connectivity and binary orientations---that leads to a desired geometry. In order to address this challenging problem of combinatorial geometry, we propose a forward modeling tool that allows the user to interactively explore the space of feasible designs. Paralleling principles from conventional modeling software, our approach leverages a library of base shapes that can be instantiated, combined, and extended using two fundamental operations: merging and extrusion. In order to assist the user in building the designs, we furthermore propose a method to automatically generate assembly instructions. We demonstrate the versatility of our method by creating a diverse set of digital and physical examples that can serve as personalized lamps or decorative items.

We propose an interactive, optimization-in-the-loop tool for designing inflatable structures. Given a target shape, the user draws a network of seams defining desired segment boundaries in 3D. Our method computes optimally-shaped flat panels for the segments, such that the inflated structure is as close as possible to the target while satisfying the desired seam positions. Our approach is underpinned by physics-based pattern optimization, accurate coarse-scale simulation using tension field theory, and a specialized constraint-optimization method. Our system is fast enough to warrant interactive exploration of different seam layouts, including internal connections, and their effects on the inflated shape. We demonstrate the resulting design process on a varied set of simulation examples, some of which we have fabricated, demonstrating excellent agreement with the design intent.

We present a method for fabrication-oriented design of actuated deformable characters that allows a user to automatically create physical replicas of digitally designed characters using rapid manufacturing technologies. Given a deformable character and a set of target poses as input, our method computes a small set of actuators along with their locations on the surface and optimizes the internal material distribution such that the resulting character exhibits the desired deformation behavior. We approach this problem with a dedicated algorithm that combines finite-element analysis, sparse regularization, and constrained optimization. We validate our pipeline on a set of two- and three-dimensional example characters and present results in simulation and physically-fabricated prototypes.

Abstract This paper presents an automatic process for fabrication‐oriented design of custom‐shaped rubber balloons. We cast computational balloon design as an inverse problem: given a target shape, we compute an optimal balloon that, when inflated, approximates the target as closely as possible. To solve this problem numerically, we propose a novel physics‐driven shape optimization method, which combines physical simulation of inflatable elastic membranes with a dedicated constrained optimization algorithm. We validate our approach by fabricating balloons designed with our method and comparing their inflated shapes to the results predicted by simulation. An extensive set of manufactured sample balloons demonstrates the shape diversity that can be achieved by our method.

We propose a complete process for designing, simulating, and fabricating synthetic skin for an animatronics character that mimics the face of a given subject and its expressions. The process starts with measuring the elastic properties of a material used to manufacture synthetic soft tissue. Given these measurements we use physics-based simulation to predict the behavior of a face when it is driven by the underlying robotic actuation. Next, we capture 3D facial expressions for a given target subject. As the key component of our process, we present a novel optimization scheme that determines the shape of the synthetic skin as well as the actuation parameters that provide the best match to the target expressions. We demonstrate this computational skin design by physically cloning a real human face onto an animatronics figure.