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Architectural surface panelling often requires fabricating molds for panels, a process that can be cost-inefficient and material-wasteful when using traditional methods such as CNC milling. In this paper, we introduce a novel solution to generating molds for efficiently fabricating architectural panels. At the core of our method is a machine that utilizes a deflatable membrane as a flexible mold. By adjusting the deflation level and boundary element positions, the membrane can be reconfigured into various shapes, allowing for mass customization with significantly lower overhead costs. We devise an efficient algorithm that works in sync with our flexible mold machine that optimizes the placement of customizable boundary element positions, ensuring the fabricated panel matches the geometry of a given input shape: (1) Using a quadratic Weingarten surface arising from a natural assumption on the membrane's stress, we can approximate the initial placement of the boundary element from the input shape's geometry; (2) we solve the inverse problem with a simulator-in-the-loop optimizer by searching for the optimal placement of boundary curves with sensitivity analysis. We validate our approach by fabricating baseline panels and a facade with a wide range of curvature profiles, providing a detailed numerical analysis on simulation and fabrication, demonstrating significant advantages in cost and flexibility. [ABSTRACT FROM AUTHOR]

We propose a reduced-space elastodynamic solver that is well suited for augmenting rigged character animations with secondary motion. At the core of our method is a novel deformation subspace based on Linear Blend Skinning that overcomes many of the shortcomings prior subspace methods face. Our skinning subspace is parameterized entirely by a set of scalar weights, which we can obtain through a small, material-aware and rig-sensitive generalized eigenvalue problem. The resulting subspace can easily capture rotational motion and guarantees that the resulting simulation is rotation equivariant. We further propose a simple local-global solver for linear co-rotational elasticity and propose a clustering method to aggregate per-tetrahedra nonlinear energetic quantities. The result is a compact simulation that is fully decoupled from the complexity of the mesh. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Standard liquid simulators apply operator splitting to independently solve for pressure and viscous stresses, a decoupling that induces incorrect free surface boundary conditions. Such methods are unable to simulate fluid phenomena reliant on the balance of pressure and viscous stresses, such as the liquid rope coil instability exhibited by honey. By contrast, unsteady Stokes solvers retain coupling between pressure and viscosity, thus resolving these phenomena, albeit using a much larger and thus more computationally expensive linear system compared to the decoupled approach. To accelerate solving the unsteady Stokes problem, we propose a reduced fluid model wherein interior regions are represented with incompressible polynomial vector fields. Sets of standard grid cells are consolidated into super-cells, each of which are modelled using a quadratic field of 26 degrees of freedom. We demonstrate that the reduced field must necessarily be at least quadratic, with the affine model being unable to correctly capture viscous forces. We reproduce the liquid rope coiling instability, as well as other simulated examples, to show that our reduced model is able to reproduce the same fluid phenomena at a smaller computational cost. Futhermore, we performed a crowdsourced user survey to verify that our method produces imperceptible differences compared to the full unsteady Stokes method. [ABSTRACT FROM AUTHOR]

We present a simple and concise discretization of the covariant derivative vector Dirichlet energy for triangle meshes in 3D using Crouzeix‐Raviart finite elements. The discretization is based on linear discontinuous Galerkin elements, and is simple to implement, without compromising on quality: there are two degrees of freedom for each mesh edge, and the sparse Dirichlet energy matrix can be constructed in a single pass over all triangles using a short formula that only depends on the edge lengths, reminiscent of the scalar cotangent Laplacian. Our vector Dirichlet energy discretization can be used in a variety of applications, such as the calculation of Killing fields, parallel transport of vectors, and smooth vector field design. Experiments suggest convergence and suitability for applications similar to other discretizations of the vector Dirichlet energy. [ABSTRACT FROM AUTHOR]

Current quadratic smoothness energies for curved surfaces either exhibit distortions near the boundary due to zero Neumann boundary conditions or they do not correctly account for intrinsic curvature, which leads to unnatural-looking behavior away from the boundary. This leads to an unfortunate trade-off: One can either have natural behavior in the interior or a distortion-free result at the boundary, but not both. We introduce a generalized Hessian energy for curved surfaces, expressed in terms of the covariant one-form Dirichlet energy, the Gaussian curvature, and the exterior derivative. Energy minimizers solve the Laplace-Beltrami biharmonic equation, correctly accounting for intrinsic curvature, leading to natural-looking isolines. On the boundary, minimizers are as-linear-as-possible, which reduces the distortion of isolines at the boundary. We discretize the covariant one-form Dirichlet energy using Crouzeix-Raviart finite elements, arriving at a discrete formulation of the Hessian energy for applications on curved surfaces. We observe convergence of the discretization in our experiments. [ABSTRACT FROM AUTHOR]

We propose a framework for simulating the complex dynamics of strands interacting with compressible, shear-dependent liquids, such as oil paint, mud, cream, melted chocolate, and pasta sauce. Our framework contains three main components: the strands modeled as discrete rods, the bulk liquid represented as a continuum (material point method), and a reduced-dimensional flow of liquid on the surface of the strands with detailed elastoviscoplastic behavior. These three components are tightly coupled together. To enable discrete strands interacting with continuum-based liquid, we develop models that account for the volume change of the liquid as it passes through strands and the momentum exchange between the strands and the liquid. We also develop an extended constraint-based collision handling method that supports cohesion between strands. Furthermore, we present a principled method to preserve the total momentum of a strand and its surface flow, as well as an analytic plastic flow approach for Herschel-Bulkley fluid that enables stable semi-implicit integration at larger time steps. We explore a series of challenging scenarios, involving splashing, shaking, and agitating the liquid which causes the strands to stick together and become entangled. [ABSTRACT FROM AUTHOR]

We propose a technique to simulate granular materials that exploits the dual strengths of discrete and continuum treatments. Discrete element simulations provide unmatched levels of detail and generality, but prove excessively costly when applied to large scale systems. Continuum approaches are computationally tractable, but limited in applicability due to built-in modeling assumptions; e.g., models suitable for granular flows typically fail to capture clogging, bouncing and ballistic motion. In our hybrid approach, an oracle dynamically partitions the domain into continuum regions where safe, and discrete regions where necessary. The domains overlap along transition zones, where a Lagrangian dynamics mass-splitting coupling principle enforces agreement between the two simulation states. Enrichment and homogenization operations allow the partitions to evolve over time. This approach accurately and efficiently simulates scenarios that previously required an entirely discrete treatment. [ABSTRACT FROM AUTHOR]

Robotic manipulation of deformable objects is a difficult problem especially because of the complexity of the many different ways an object can deform. Searching such a high-dimensional state space makes it difficult to recognize, track, and manipulate deformable objects. In this paper, we introduce a predictive, model-driven approach to address this challenge, using a precomputed, simulated database of deformable object models. Mesh models of common deformable garments are simulated with the garments picked up in multiple different poses under gravity, and stored in a database for fast and efficient retrieval. To validate this approach, we developed a comprehensive pipeline for manipulating clothing as in a typical laundry task. First, the database is used for category and the pose estimation is used for a garment in an arbitrary position. A fully featured 3-D model of the garment is constructed in real time, and volumetric features are then used to obtain the most similar model in the database to predict the object category and pose. Second, the database can significantly benefit the manipulation of deformable objects via nonrigid registration, providing accurate correspondences between the reconstructed object model and the database models. Third, the accurate model simulation can also be used to optimize the trajectories for the manipulation of deformable objects, such as the folding of garments. Extensive experimental results are shown for the above tasks using a variety of different clothings. Note to Practitioners—This paper provides an open source, extensible, 3-D database for dissemination to the robotics and graphics communities. Model-driven methods are proliferating, and they need to be applied, tested, and validated in real environments. A key idea we have exploited is to have an innovative and novel use of simulation. This database will serve as infrastructure for developing advanced robotic machine learning algorithms. We want to address this machine learning idea ourselves, but we expect the dissemination of the database to other researchers with different agendas and task applications, which will bring wide progress in this area. Our proposed methods, as mentioned earlier, can be easily applied to interrelated areas. One example is that the 3-D shape-based matching algorithm can be used for other objects, such as bottles, papers, and food. After integrating with other robotic systems, the use of the robot can be easily extended to other tasks, such as making food, cleaning room, and fetching objects, to assist our daily life. [ABSTRACT FROM AUTHOR]

While folds and pleats add interest to garments and cloth objects, incorporating them into an existing design manually or using existing software requires expertise and time. We present FoldSketch, a new system that supports simple and intuitive fold and pleat design. FoldSketch users specify the fold or pleat configuration they seek using a simple schematic sketching interface; the system then algorithmically generates both the fold-enhanced 3D garment geometry that conforms to user specifications, and the corresponding 2D patterns that reproduce this geometry within a simulation engine. While previous work aspired to compute the desired patterns for a given target 3D garment geometry, our main algorithmic challenge is that we do not have target geometry to start with. Real-life garment folds have complex profile shapes, and their exact geometry and location on a garment are intricately linked to a range of physical factors such as fabric properties and the garment's interaction with the wearer's body; it is therefore virtually impossible to predict the 3D shape of a fold-enhanced garment using purely geometric means. At the same time, using physical simulation to model folds requires appropriate 2D patterns and initial drape, neither of which can be easily provided by the user. We obtain both the 3D fold-enhanced garment and its corresponding patterns and initial drape via an alternating 2D-3D algorithm. We first expand the input patterns by allocating excess material for the expected fold formation; we then use these patterns to produce an estimated fold-enhanced drape geometry that balances designer expectations against physical reproducibility. We use the patterns and the estimated drape as input to a simulation generating an initial reproducible output. We improve the output's alignment with designer expectations by progressively refining the patterns and the estimated drape, converging to a final fully physically reproducible fold-enhanced garment. Our experiments confirm that FoldSketch reliably converges to a desired garment geometry and corresponding patterns and drape, and works well with different physical simulators. We demonstrate the versatility of our approach by showcasing a collection of garments augmented with diverse fold and pleat layouts specified via the FoldSketch interface, and further validate our approach via comparisons to alternative solutions and feedback from potential users. [ABSTRACT FROM AUTHOR]

Thin shells —- solids that are thin in one dimension compared to the other two —- often emit rich nonlinear sounds when struck. Strong excitations can even cause chaotic thin-shell vibrations, producing sounds whose energy spectrum diffuses from low to high frequencies over time —- a phenomenon known as wave turbulence. It is all these nonlinearities that grant shells such as cymbals and gongs their characteristic "glinting" sound. Yet, simulation models that efficiently capture these sound effects remain elusive. We propose a physically based, multi-scale reduced simulation method to synthesize nonlinear thin-shell sounds. We first split nonlinear vibrations into two scales, with a small low-frequency part simulated in a fully nonlinear way, and a high-frequency part containing many more modes approximated through time-varying linearization. This allows us to capture interesting nonlinearities in the shells' deformation, tens of times faster than previous approaches. Furthermore, we propose a method that enriches simulated sounds with wave turbulent sound details through a phenomenological diffusion model in the frequency domain, and thereby sidestep the expensive simulation of chaotic high-frequency dynamics. We show several examples of our simulations, illustrating the efficiency and realism of our model. [ABSTRACT FROM AUTHOR]

Developable surfaces are those that can be made by smoothly bending flat pieces without stretching or shearing. We introduce a definition of developability for triangle meshes which exactly captures two key properties of smooth developable surfaces, namely flattenability and presence of straight ruling lines. This definition provides a starting point for algorithms in developable surface modeling—-we consider a variational approach that drives a given mesh toward developable pieces separated by regular seam curves. Computation amounts to gradient descent on an energy with support in the vertex star, without the need to explicitly cluster patches or identify seams. We briefly explore applications to developable design and manufacturing. [ABSTRACT FROM AUTHOR]

We propose a method for simulating the complex dynamics of partially and fully saturated woven and knit fabrics interacting with liquid, including the effects of buoyancy, nonlinear drag, pore (capillary) pressure, dripping, and convection-diffusion. Our model evolves the velocity fields of both the liquid and solid relying on mixture theory, as well as tracking a scalar saturation variable that affects the pore pressure forces in the fluid. We consider the porous microstructure implied by the fibers composing individual threads, and use it to derive homogenized drag and pore pressure models that faithfully reflect the anisotropy of fabrics. In addition to the bulk liquid and fabric motion, we derive a quasi-static flow model that accounts for liquid spreading within the fabric itself. Our implementation significantly extends standard numerical cloth and fluid models to support the diverse behaviors of wet fabric, and includes a numerical method tailored to cope with the challenging nonlinearities of the problem. We explore a range of fabric-water interactions to validate our model, including challenging animation scenarios involving splashing, wringing, and collisions with obstacles, along with qualitative comparisons against simple physical experiments. [ABSTRACT FROM AUTHOR]

In geometry processing, smoothness energies are commonly used to model scattered data interpolation, dense data denoising, and regularization during shape optimization. The squared Laplacian energy is a popular choice of energy and has a corresponding standard implementation: squaring the discrete Laplacian matrix. For compact domains, when values along the boundary are not known in advance, this construction bakes in low-order boundary conditions. This causes the geometric shape of the boundary to strongly bias the solution. For many applications, this is undesirable. Instead, we propose using the squared Frobenius norm of the Hessian as a smoothness energy. Unlike the squared Laplacian energy, this energy’s natural boundary conditions (those that best minimize the energy) correspond to meaningful high-order boundary conditions. These boundary conditions model free boundaries where the shape of the boundary should not bias the solution locally. Our analysis begins in the smooth setting and concludes with discretizations using finite-differences on 2D grids or mixed finite elements for triangle meshes. We demonstrate the core behavior of the squared Hessian as a smoothness energy for various tasks. [ABSTRACT FROM AUTHOR]

This paper aims to democratize the design and fabrication of robots, enabling people of all skill levels to make robots without needing expert domain knowledge. Existing work in computational design and rapid fabrication has explored this question of customization for physical objects but so far has not been able to conquer the complexity of robot designs. We have developed Interactive Robogami, a tool for composition-based design of ground robots that can be fabricated as flat sheets and then folded into 3D structures. This rapid prototyping process enables users to create lightweight, affordable, and materially versatile robots with short turnaround time. Using Interactive Robogami, designers can compose new robot designs from a database of print-and-fold parts. The designs are tested for the users' functional specifications via simulation and fabricated on user satisfaction. We present six robots designed and fabricated using a 3D printing based approach, as well as a larger robot cut from sheet metal. We have also conducted a user study that demonstrates that our tool is intuitive for novice designers and expressive enough to create a wide variety of ground robot designs. [ABSTRACT FROM AUTHOR]

Computer Aided Design (CAD) is a multi-billion dollar industry used by almost every mechanical engineer in the world to create practically every existing manufactured shape. CAD models are not only widely available but also extremely useful in the growing field of fabrication-oriented design because they are parametric by construction and capture the engineer's design intent, including manufacturability. Harnessing this data, however, is challenging, because generating the geometry for a given parameter value requires time-consuming computations. Furthermore, the resulting meshes have different combinatorics, making the mesh data inherently discontinuous with respect to parameter adjustments. In our work, we address these challenges and develop tools that allow interactive exploration and optimization of parametric CAD data. To achieve interactive rates, we use precomputation on an adaptively sampled grid and propose a novel scheme for interpolating in this domain where each sample is a mesh with different combinatorics. Specifically, we extract partial correspondences from CAD representations for local mesh morphing and propose a novel interpolation method for adaptive grids that is both continuous/smooth and local (i.e., the influence of each sample is constrained to the local regions where mesh morphing can be computed). We show examples of how our method can be used to interactively visualize and optimize objects with a variety of physical properties. [ABSTRACT FROM AUTHOR]

Iterative algorithms are frequently used to resolve simultaneous impacts between rigid bodies in physical simulations. However, these algorithms lack formal guarantees of termination, which is sometimes viewed as potentially dangerous, so failsafes are used in practical codes to prevent infinite loops. We show such steps are unnecessary. In particular, we study the broad class of such algorithms that are conservative and satisfy a minimal set of physical correctness properties, and which encompasses recent methods like Generalized Reflections as well as pairwise schemes. We fully characterize finite termination of these algorithms. The only possible failure cases can be detected, and we describe a procedure for modifying the algorithms to provably ensure termination. We also describe modifications necessary to guarantee termination in the presence of numerical error due to the use of floating-point arithmetic. Finally, we discuss the challenges dissipation introduce for finite termination, and describe how dissipation models can be incorporated while retaining the termination guarantee. [ABSTRACT FROM AUTHOR]

The diverse interactions between hair and liquid are complex and span multiple length scales, yet are central to the appearance of humans and animals in many situations. We therefore propose a novel multi-component simulation framework that treats many of the key physical mechanisms governing the dynamics of wet hair. The foundations of our approach are a discrete rod model for hair and a particle-in-cell model for fluids. To treat the thin layer of liquid that clings to the hair, we augment each hair strand with a height field representation. Our contribution is to develop the necessary physical and numerical models to evolve this new system and the interactions among its components. We develop a new reduced-dimensional liquid model to solve the motion of the liquid along the length of each hair, while accounting for its moving reference frame and influence on the hair dynamics. We derive a faithful model for surface tension-induced cohesion effects between adjacent hairs, based on the geometry of the liquid bridges that connect them. We adopt an empirically-validated drag model to treat the effects of coarse-scale interactions between hair and surrounding fluid, and propose new volume-conserving dripping and absorption strategies to transfer liquid between the reduced and particle-in-cell liquid representations. The synthesis of these techniques yields an effective wet hair simulator, which we use to animate hair flipping, an animal shaking itself dry, a spinning car wash roller brush dunked in liquid, and intricate hair coalescence effects, among several additional scenarios. [ABSTRACT FROM AUTHOR]

ACrumpling a thin sheet produces a characteristic sound, comprised of distinct clicking sounds corresponding to buckling events. We propose a physically based algorithm that automatically synthesizes crumpling sounds for a given thin shell animation. The resulting sound is a superposition of individually synthesized clicking sounds corresponding to visually significant and insignificant buckling events. We identify visually significant buckling events on the dynamically evolving thin surface mesh, and instantiate visually insignificant buckling events via a stochastic model that seeks to mimic the power-law distribution of buckling energies observed in many materials. In either case, the synthesis of a buckling sound employs linear modal analysis of the deformed thin shell. Because different buckling events in general occur at different deformed configurations, the question arises whether the calculation of linear modes can be reused. We amortize the cost of the linear modal analysis by dynamically partitioning the mesh into nearly rigid pieces: the modal analysis of a rigidly moving piece is retained over time, and the modal analysis of the assembly is obtained via Component Mode Synthesis (CMS). We illustrate our approach through a series of examples and a perceptual user study, demonstrating the utility of the sound synthesis method in producing realistic sounds at practical computation times. [ABSTRACT FROM AUTHOR]

A reconfigurable is an object or collection of objects whose transformation between various states defines its functionality or aesthetic appeal. For example, consider a mechanical assembly composed of interlocking pieces, a transforming folding bicycle, or a space-saving arrangement of apartment furniture. Unlike traditional computer-aided design of static objects, specialized tools are required to address problems unique to the computational design and revision of objects undergoing rigid transformations. Collisions and interpenetrations as objects transition from one configuration to another prevent the physical realization of a design. We present a software environment intended to support fluid interactive design of reconfigurables, featuring tools that identify, visualize, monitor and resolve infeasible configurations. We demonstrate the versatility of the environment on a number of examples spanning mechanical systems, urban dwelling, and interlocking puzzles, some of which we then realize via additive manufacturing. Spatial-temporal information about collisions between objects is presented to the designer according to a cascading order of precedence. A designer may quickly determine when, and then where, and then how objects are colliding. This precedence guides the design and implementation of our four-dimensional spacetime bounding volume hierarchy for interactive-rate collision detection. On screen, the designer experiences a suite of interactive visualization and monitoring tools during editing: timeline notifications of new collisions, picture-in-picture windows for tracking collisions and suggestive hints for contact resolution. Contacts too tedious to remove manually can be eliminated automatically via our proposed constrained numerical optimization and swept-volume carving. [ABSTRACT FROM AUTHOR]

We propose a novel surface-only technique for simulating incompressible, inviscid and uniform-density liquids with surface tension in three dimensions. The liquid surface is captured by a triangle mesh on which a Lagrangian velocity field is stored. Because advection of the velocity field may violate the incompressibility condition, we devise an orthogonal projection technique to remove the divergence while requiring the evaluation of only two boundary integrals. The forces of surface tension, gravity, and solid contact are all treated by a boundary element solve, allowing us to perform detailed simulations of a wide range of liquid phenomena, including waterbells, droplet and jet collisions, fluid chains, and crown splashes. [ABSTRACT FROM AUTHOR]

Many high-level geometry processing tasks rely on low-level constructive solid geometry operations. Though trivial for implicit representations, boolean operations are notoriously difficult to execute robustly for explicit boundary representations. Existing methods for 3D triangle meshes fall short in one way or another. Some methods are fast but fail to produce closed, self-intersection free output. Other methods are robust but place prohibitively strict assumptions on the input, e.g., no hollow cavities, non-manifold edges or self-intersections. We propose a systematic recipe for conducting a family of exact constructive solid geometry operations. The two-stage method makes no general position assumptions and does not resort to numerical perturbation. The method is variadic, operating on any number of input meshes. This generalizes unary mesh-repair operations, classic binary boolean differencing, and n-ary operations such as finding all regions inside at least k out of n inputs. We demonstrate the superior effectiveness and robustness of our method on a dataset of 10,000 "real-world" meshes from a popular online repository. To encourage development, validation, and comparison, we release both our code and dataset to the public. [ABSTRACT FROM AUTHOR]

Mosaics are widely used for surface decoration to produce appealing visual effects. We present a method for synthesizing digital surface mosaics with irregularly shaped tiles, which are a type of tiles often used for mosaics design. Our method employs both continuous optimization and combinatorial optimization to improve tile arrangement. In the continuous optimization step, we iteratively partition the base surface into approximate Voronoi regions of the tiles and optimize the positions and orientations of the tiles to achieve a tight fit. Combination optimization performs tile permutation and replacement to further increase surface coverage and diversify tile selection. The alternative applications of these two optimization steps lead to rich combination of tiles and high surface coverage. We demonstrate the effectiveness of our solution with extensive experiments and comparisons. [ABSTRACT FROM PUBLISHER]

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. [ABSTRACT FROM AUTHOR]

Simulating the delightful dynamics of soap films, bubbles, and foams has traditionally required the use of a fully three-dimensional many-phase Navier-Stokes solver, even though their visual appearance is completely dominated by the thin liquid surface. We depart from earlier work on soap bubbles and foams by noting that their dynamics are naturally described by a Lagrangian vortex sheet model in which circulation is the primary variable. This leads us to derive a novel circulation-preserving surface-only discretization of foam dynamics driven by surface tension on a non-manifold triangle mesh. We represent the surface using a mesh-based multimaterial surface tracker which supports complex bubble topology changes, and evolve the surface according to the ambient air flow induced by a scalar circulation field stored on the mesh. Surface tension forces give rise to a simple update rule for circulation, even at non-manifold Plateau borders, based on a discrete measure of signed scalar mean curvature. We further incorporate vertex constraints to enable the interaction of soap films with wires. The result is a method that is at once simple, robust, and efficient, yet able to capture an array of soap films behaviors including foam rearrangement, catenoid collapse, blowing bubbles, and double bubbles being pulled apart. [ABSTRACT FROM AUTHOR]

We present a user-guided, semi-automatic approach to completing large holes in a mesh. The reconstruction of the missing features in such holes is usually ambiguous. Thus, unsupervised methods may produce unsatisfactory results. To overcome this problem, we let the user indicate constraints by providing merely four points per important feature curve on the mesh. Our algorithm regards this input as an indication of an important broken feature curve. Our completion is formulated as a global energy minimization problem, with user-defined spatial-coherence constraints, allows for completion that adheres to the existing features. We demonstrate the method on example problems that are not handled satisfactorily by fully automatic methods. [ABSTRACT FROM AUTHOR]

We develop an algorithm for the efficient and stable simulation of large-scale elastic rod assemblies. We observe that the time-integration step is severely restricted by a strong nonlinearity in the response of stretching modes to transversal impact, the degree of this nonlinearity varying greatly with the shape of the rod. Building on these observations, we propose a collision response algorithm that adapts its degree of nonlinearity. We illustrate the advantages of the resulting algorithm by analyzing simulations involving elastic rod assemblies of varying density and scale, with up to 1.7 million individual contacts per time step. [ABSTRACT FROM AUTHOR]

We present a triangle mesh-based technique for tracking the evolution of three-dimensional multimaterial interfaces undergoing complex deformations. It is the first non-manifold triangle mesh tracking method to simultaneously maintain intersection-free meshes and support the proposed broad set of multimaterial remeshing and topological operations. We represent the interface as a non-manifold triangle mesh with material labels assigned to each half-face to distinguish volumetric regions. Starting from proposed application-dependent vertex velocities, we deform the mesh, seeking a non-intersecting, watertight solution. This goal necessitates development of various collision-safe, label-aware non-manifold mesh operations: multimaterial mesh improvement; T1 and T2 processes, topological transitions arising in foam dynamics and multiphase flows; and multimaterial merging, in which a new interface is created between colliding materials. We demonstrate the robustness and effectiveness of our approach on a range of scenarios including geometric flows and multiphase fluid animation. [ABSTRACT FROM AUTHOR]

We present a computational approach for designing wire meshes, i.e., freeform surfaces composed of woven wires arranged in a regular grid. To facilitate shape exploration, we map material properties of wire meshes to the geometric model of Chebyshev nets. This abstraction is exploited to build an efficient optimization scheme. While the theory of Chebyshev nets suggests a highly constrained design space, we show that allowing controlled deviations from the underlying surface provides a rich shape space for design exploration. Our algorithm balances globally coupled material constraints with aesthetic and geometric design objectives that can be specified by the user in an interactive design session. In addition to sculptural art, wire meshes represent an innovative medium for industrial applications including composite materials and architectural façades. We demonstrate the effectiveness of our approach using a variety of digital and physical prototypes with a level of shape complexity unobtainable using previous methods. [ABSTRACT FROM AUTHOR]

We present a design system for linkage-based characters, combining form and function in an aesthetically-pleasing manner. Linkage-based character design exhibits a mix of discrete and continuous problems, making for a highly unintuitive design space that is difficult to navigate without assistance. Our system significantly simplifies this task by allowing users to interactively browse different topology options, thus guiding the discrete set of choices that need to be made. A subsequent continuous optimization step improves motion quality and, crucially, safeguards against singularities. We demonstrate the flexibility of our method on a diverse set of character designs, and then realize our designs by physically fabricating prototypes. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

We introduce an algorithm to synthesize missing geometry for a given triangle mesh that has "holes." Similarly to previous work, the algorithm is context based in that it fills the hole by synthesizing geometry that is similar to the remainder of the input mesh. Our algorithm goes further to impose a coherence objective. A synthesis is coherent if every local neighborhood of the filled hole is similar to some local neighborhood of the input mesh. This requirement avoids undesired features such as can occur in context-based completion. We demonstrate the algorithm's ability to fill holes that were difficult or impossible to fill in a compelling manner by earlier approaches. [ABSTRACT FROM AUTHOR]

We present techniques for automatically parsing existing sewing patterns and converting them into 3D garment models. Our parser takes a sewing pattern in PDF format as input and starts by extracting the set of panels and styling elements (e.g. darts, pleats and hemlines) contained in the pattern. It then applies a combination of machine learning and integer programming to infer how the panels must be stitched together to form the garment. Our system includes an interactive garment simulator that takes the parsed result and generates the corresponding 3D model. Our fully automatic approach correctly parses 68% of the sewing patterns in our collection. Most of the remaining patterns contain only a few errors that can be quickly corrected within the garment simulator. Finally we present two applications that take advantage of our collection of parsed sewing patterns. Our garment hybrids application lets users smoothly interpolate multiple garments in the 2D space of patterns. Our sketch-based search application allows users to navigate the pattern collection by drawing the shape of panels. [ABSTRACT FROM AUTHOR]

We extend the Asynchronous Contact Mechanics algorithm [Harmon et al. 2009] and improve its performance by two orders of magnitude, using only optimizations that do not compromise ACM's three guarantees of safety, progress, and correctness. The key to this speedup is replacing ACM's timid, forward-looking mechanism for detecting collisions---locating and rescheduling separating plane kinetic data structures---with an optimistic speculative method inspired by Mirtich's rigid body Time Warp algorithm [2000]. Time warp allows us to perform collision detection over a window of time containing many of ACM's asynchronous trajectory changes; in this way we cull away large intervals as being collision free. Moreover, by replacing force processing intermingled with KDS rescheduling by windows of pure processing followed by collision detection, we transform an algorithm that is very difficult to parallelize into one that is embarrassingly parallel. [ABSTRACT FROM AUTHOR]

We introduce a discrete paradigm for developable surface modeling. Unlike previous attempts at interactive developable surface modeling, our system is able to enforce exact developability at every step, ensuring that users do not inadvertently suggest configurations that leave the manifold of admissible folds of a flat two-dimensional sheet. With methods for navigation of this highly nonlinear constraint space in place, we show how to formulate a discrete mean curvature bending energy measuring how far a given discrete developable surface is from being flat. This energy enables relaxation of user-generated configurations and suggests a straightforward subdivision scheme that produces admissible smoothed versions of bent regions of our discrete developable surfaces. [ABSTRACT FROM AUTHOR]

Example-based texture synthesis algorithms generate novel texture images from example data. A popular hierarchical pixel-based approach uses spatial jitter to introduce diversity, at the risk of breaking coarse structure beyond repair. We propose a multiscale descriptor that enables appearance-space jitter, which retains structure. This idea enables repurposing of existing texture synthesis implementations for a qualitatively different problem statement and class of inputs: generating hybrids of structured images. [ABSTRACT FROM AUTHOR]

We develop a method for reliable simulation of elastica in complex contact scenarios. Our focus is on firmly establishing three parameter-independent guarantees: that simulations of well-posed problems (a) have no interpenetrations, (b) obey causality, momentum- and energy-conservation laws, and (c) complete in finite time. We achieve these guarantees through a novel synthesis of asynchronous variational integrators, kinetic data structures, and a discretization of the contact barrier potential by an infinite sum of nested quadratic potentials. In a series of two- and three-dimensional examples, we illustrate that this method more easily handles challenging problems involving complex contact geometries, sharp features, and sliding during extremely tight contact. [ABSTRACT FROM AUTHOR]

We present a method for simulating highly detailed cutting and fracturing of thin shells using low-resolution simulation meshes. Instead of refining or remeshing the underlying simulation domain to resolve complex cut paths, we adapt the extended finite element method (XFEM) and enrich our approximation by custom-designed basis functions, while keeping the simulation mesh unchanged. The enrichment functions are stored in enrichment textures, which allows for fracture and cutting discontinuities at a resolution much finer than the underlying mesh, similar to image textures for increased visual resolution. Furthermore, we propose harmonic enrichment functions to handle multiple, intersecting, arbitrarily shaped, progressive cuts per element in a simple and unified framework. Our underlying shell simulation is based on discontinuous Galerkin (DG) FEM, which relaxes the restrictive requirement of C¹ continuous basis functions and thus allows for simpler, C0 continuous XFEM enrichment functions. [ABSTRACT FROM AUTHOR]