While thin shells have ubiquitous applications and have been studied inside and outside computer graphics for decades, there is little consensus on how to best discretize them. We systematically study models for simulating bending of Kirchhoff-Love shells, with the goal of making practical recommendations, backed by careful numerical experiments, of when and how these models should be used. We analyze ten of the most popular discrete bending models in computer graphics for thin-shell simulation, along with new variants that we propose ourselves. We first verify all models on an analytic test benchmark to probe convergence under refinement and mesh-dependence, and then stress-test with a second benchmark that considers behavior at sharp bends. Finally, we test benchmark leaders on a practical suite of challenging large-scale equilibrium and dynamic shell modeling problems, analyzing both full solution behavior and comparative compute costs. We identify leading existing models and their tradeoffs in terms of accuracy and performance. During this analysis we also identify some issues and modeling gaps in the best-performing discrete bending models. We construct new energy model variants to address some of these gaps, as well as formulas and algorithmic tools for their practical simulation, and finally recommend best practices for modeling thin-shell bending.

In this paper, we introduce a method for reconstructing 3D humans from a single image using a biomechanically accurate skeleton model. To achieve this, we train a transformer that takes an image as input and estimates the parameters of the model. Due to the lack of training data for this task, we build a pipeline to produce pseudo ground truth model parameters for single images and implement a training procedure that iteratively refines these pseudo labels. Compared to state-of-the-art methods for 3D human mesh recovery, our model achieves competitive performance on standard benchmarks, while it significantly outperforms them in settings with extreme 3D poses and viewpoints. Additionally, we show that previous reconstruction methods frequently violate joint angle limits, leading to unnatural rotations. In contrast, our approach leverages the biomechanically plausible degrees of freedom making more realistic joint rotation estimates. We validate our approach across multiple human pose estimation benchmarks. We make the code, models and data available at: https://isshikihugh.github.io/HSMR/

Abstract This paper studies the problem of unconstrained (e.g. not orthogonal or unit) symmetric frame field design in volumes. Our principal contribution is a novel (and theoretically well‐founded) local integrability condition for frame fields represented as a triplet of symmetric tensors of second, fourth, and sixth order. We also formulate a novel smoothness energy for this representation. To validate our discritization, we study the problem of seamless parameterization of volumetric objects. We compare against baseline approaches by formulating a smooth, integrable, and approximately octahedral frame objective in our discritization. Our method is the first to solve these problems with automatic placement of singularities while also enforcing a symmetric proxy for local integrability as a hard constraint, achieving significantly higher quality parameterizations, in expectation, relative to other frame field design based approaches.

There are many applications for which we want to learn a latent scale for subjective properties, such as the excitement of a photo or the legibility of a font; however, obtaining human-labeled data is costly and time-consuming. One oft-used method for acquiring these labels, despite the cost being quadratic in the number of items, is the method of pairwise comparisons since this method minimizes the effect of biases and generally can be used effectively outside of a controlled environment.

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 propose a robust re-meshing approach that can automatically generate visual-preserving low-poly meshes for any high-poly models found in the wild. Our method can be seamlessly integrated into current mesh-based 3D asset production pipelines. Given an input high-poly, our method proceeds in two stages: 1) Robustly extracting an offset surface mesh that is feature-preserving, and guaranteed to be watertight, manifold, and self-intersection free; 2) Progressively simplifying and flowing the offset mesh to bring it close to the input. The simplicity and the visual-preservation of the generated low-poly is controlled by a user-required target screen size of the input: decreasing the screen size reduces the element count of the low-poly but enlarges its visual difference from the input. We have evaluated our method on a subset of the Thingi10K dataset that contains models created by practitioners in different domains, with varying topological and geometric complexities. Compared to state-of-the-art approaches and widely used software, our method demonstrates its superiority in terms of the element count, visual preservation, geometry, and topology guarantees of the generated low-polys.

We present Virtual Elastic Objects (VEOs): virtual objects that not only look like their real-world counterparts but also behave like them, even when subject to novel interactions. Achieving this presents multiple challenges: not only do objects have to be captured including the physical forces acting on them, then faithfully reconstructed and rendered, but also plausible material parameters found and simulated. To create VEOs, we built a multi-view capture system that captures objects under the influence of a compressed air stream. Building on recent advances in model-free, dynamic Neural Radiance Fields, we reconstruct the objects and corresponding deformation fields. We propose to use a differentiable, particle-based simulator to use these deformation fields to find representative material parameters, which enable us to run new simulations. To render simulated objects, we devise a method for integrating the simulation results with Neural Radiance Fields. The resulting method is applicable to a wide range of scenarios: it can handle objects composed of inhomogeneous material, with very different shapes, and it can simulate interactions with other virtual objects. We present our results using a newly collected dataset of 12 objects under a variety of force fields, which will be made available upon publication.

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.

This paper introduces HPNet, a novel deep-learning approach for segmenting a 3D shape represented as a point cloud into primitive patches. The key to deep primitive segmentation is learning a feature representation that can separate points of different primitives. Unlike utilizing a single feature representation, HPNet leverages hybrid representations that combine one learned semantic descriptor, two spectral descriptors derived from predicted geometric parameters, as well as an adjacency matrix that encodes sharp edges. Moreover, instead of merely concatenating the descriptors, HPNet optimally combines hybrid representations by learning combination weights. This weighting module builds on the entropy of input features. The output primitive segmentation is obtained from a meanshift clustering module. Experimental results on benchmark datasets ANSI and ABCParts show that HPNet leads to significant performance gains from baseline approaches.

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 introduce an approach for establishing dense correspondences between partial scans of human models and a complete template model. Our approach's key novelty lies in formulating dense correspondence computation as initializing and synchronizing local transformations between the scan and the template model. We introduce an optimization formulation for synchronizing transformations among a graph of the input scan, which automatically enforces smoothness of correspondences and recovers the underlying articulated deformations. We then show how to convert the iterative optimization procedure among a graph of the input scan into an end-to-end trainable network. The network design utilizes additional trainable parameters to break the barrier of the original optimization formulation's exact and robust recovery conditions. Experimental results on benchmark datasets demonstrate that our approach considerably outperforms baseline approaches in accuracy and robustness.

Rigid body disentanglement puzzles are challenging for both humans and motion planning algorithms because their solutions involve tricky twisting and sliding moves that correspond to navigating through narrow tunnels in the puzzle's configuration space (C-space). We propose a tunnel-discovery and planning strategy for solving these puzzles. First, we locate important features on the pieces using geometric heuristics and machine learning, and then match pairs of these features to discover collision free states in the puzzle's C-space that lie within the narrow tunnels. Second, we propose a Rapidly-exploring Dense Tree (RDT) motion planner variant that builds tunnel escape roadmaps and then connects these roadmaps into a solution path connecting start and goal states. We evaluate our approach on a variety of challenging disentanglement puzzles and provide extensive baseline comparisons with other motion planning techniques.

We present a method for designing smooth cross fields on surfaces that automatically align to sharp features of an underlying geometry. Our approach introduces a novel class of energies based on a representation of cross fields in the spherical harmonic basis. We provide theoretical analysis of these energies in the smooth setting, showing that they penalize deviations from surface creases while otherwise promoting intrinsically smooth fields. We demonstrate the applicability of our method to quad meshing and include an extensive benchmark comparing our fields to other automatic approaches for generating feature-aligned cross fields on triangle meshes.

We present a deep generative scene modeling technique for indoor environments. Our goal is to train a generative model using a feed-forward neural network that maps a prior distribution (e.g., a normal distribution) to the distribution of primary objects in indoor scenes. We introduce a 3D object arrangement representation that models the locations and orientations of objects, based on their size and shape attributes. Moreover, our scene representation is applicable for 3D objects with different multiplicities (repetition counts), selected from a database. We show a principled way to train this model by combining discriminative losses for both a 3D object arrangement representation and a 2D image-based representation. We demonstrate the effectiveness of our scene representation and the network training method on benchmark datasets. We also show the applications of this generative model in scene interpolation and scene completion.

We study discrete geodesic foliations of surfaces---foliations whose leaves are all approximately geodesic curves---and develop several new variational algorithms for computing such foliations. Our key insight is a relaxation of vector field integrability in the discrete setting, which allows us to optimize for curl-free unit vector fields that remain well-defined near singularities and robustly recover a scalar function whose gradient is well aligned to these fields. We then connect the physics governing surfaces woven out of thin ribbons to the geometry of geodesic foliations, and present a design and fabrication pipeline for approximating surfaces of arbitrary geometry and topology by triaxially-woven structures, where the ribbon layout is determined by a geodesic foliation on a sixfold branched cover of the input surface. We validate the effectiveness of our pipeline on a variety of simulated and fabricated woven designs, including an example for readers to try at home.

Consumer-grade printers are widely available, but their ability to print complex objects is limited. Therefore, new designs need to be discovered that serve the same function, but are printable. A representative such problem is to produce a working, reliable mechanical spring. The proposed methodology for discovering solutions to this problem consists of three components: First, an effective search space is learned through a variational autoencoder (VAE); second, a surrogate model for functional designs is built; and third, a genetic algorithm is used to simultaneously update the hyperparameters of the surrogate and to optimize the designs using the updated surrogate. Using a car-launcher mechanism as a test domain, spring designs were 3D-printed and evaluated to update the surrogate model. Two experiments were then performed: First, the initial set of designs for the surrogate-based optimizer was selected randomly from the training set that was used for training the VAE model, which resulted in an exploitative search behavior. On the other hand, in the second experiment, the initial set was composed of more uniformly selected designs from the same training set and a more explorative search behavior was observed. Both of the experiments showed that the methodology generates interesting, successful, and reliable spring geometries robust to the noise inherent in the 3D printing process. The methodology can be generalized to other functional design problems, thus making consumer-grade 3D printing more versatile.

We present a physically accurate low-order elastic shell model that incorporates active material response to dynamically changing stimuli such as heat, moisture, and growth. Our continuous formulation of the geometrically non-linear elastic energy derives from the principles of differential geometry, and as such naturally incorporates shell thickness, non-zero rest curvature, and physical material properties. By modeling the environmental stimulus as local, dynamic changes in the rest metric of the material, we are able to solve for the corresponding shape changes by integrating the equations of motions given this non-Euclidean rest state. We present models for differential growth and shrinking due to moisture and temperature gradients along and across the surface, and incorporate anisotropic growth by defining an intrinsic machine direction within the material. Comparisons with experiments and volumetric finite elements show that our simulations achieve excellent qualitative and quantitative agreement. By combining the reduced-order shell theory with appropriate physical models, our approach accurately captures all the physical phenomena while avoiding expensive volumetric discretization of the shell volume.

Capabilities of extrusion-based 3D-printers have progressed significantly, but complex forms are still challenging to print. One major problem is overhanging surfaces. These surfaces require extra support structure to be printed, wasting material and time. Furthermore, delicate parts of the object can be damaged when these structures are removed. One potential solution is to print the object in parts, but decomposition is difficult. This paper proposes an evolutionary approach for determining optimal object decompositions for 3D printing. Two alternative methods, with different complementary strengths, are tested: Multi-objective Genetic Algorithm (MOGA) and Covariance Matrix Adaptation Evolution Strategy (CMA-ES). MOGA is able to evolve a set of decompositions at variable complexity, i.e. number of pieces, whereas CMA-ES is able to find a limited number of comparable decompositions with significantly less computational time.

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.

We propose a deep learning approach for finding dense correspondences between 3D scans of people. Our method requires only partial geometric information in the form of two depth maps or partial reconstructed surfaces, works for humans in arbitrary poses and wearing any clothing, does not require the two people to be scanned from similar view-points, and runs in real time. We use a deep convolutional neural network to train a feature descriptor on depth map pixels, but crucially, rather than training the network to solve the shape correspondence problem directly, we train it to solve a body region classification problem, modified to increase the smoothness of the learned descriptors near region boundaries. This approach ensures that nearby points on the human body are nearby in feature space, and vice versa, rendering the feature descriptor suitable for computing dense correspondences between the scans. We validate our method on real and synthetic data for both clothed and unclothed humans, and show that our correspondences are more robust than is possible with state-of-the-art unsupervised methods, and more accurate than those found using methods that require full watertight 3D geometry.

With existing programming tools, writing high-performance simulation code is labor intensive and requires sacrificing readability and portability. The alternative is to prototype simulations in a high-level language like Matlab, thereby sacrificing performance. The Matlab programming model naturally describes the behavior of an entire physical system using the language of linear algebra. However, simulations also manipulate individual geometric elements, which are best represented using linked data structures like meshes. Translating between the linked data structures and linear algebra comes at significant cost, both to the programmer and to the machine. High-performance implementations avoid the cost by rephrasing the computation in terms of linked or index data structures, leaving the code complicated and monolithic, often increasing its size by an order of magnitude. In this article, we present Simit, a new language for physical simulations that lets the programmer view the system both as a linked data structure in the form of a hypergraph and as a set of global vectors, matrices, and tensors depending on what is convenient at any given time. Simit provides a novel assembly construct that makes it conceptually easy and computationally efficient to move between the two abstractions. Using the information provided by the assembly construct, the compiler generates efficient in-place computation on the graph. We demonstrate that Simit is easy to use: a Simit program is typically shorter than a Matlab program; that it is high performance: a Simit program running sequentially on a CPU performs comparably to hand-optimized simulations; and that it is portable: Simit programs can be compiled for GPUs with no change to the program, delivering 4 to 20× speedups over our optimized CPU code.

We examine two widely used classes of methods for static analysis of masonry buildings: linear elasticity analysis using finite elements and equilibrium methods. It is often claimed in the literature that finite element analysis is less accurate than equilibrium analysis when it comes to masonry analysis; we examine and qualify this claimed inaccuracy, provide a systematic explanation for the discrepancy observed between their results, and present a unified formulation of the two approaches to stability analysis. We prove that both approaches can be viewed as equivalent, dual methods for getting the same answer to the same problem. We validate our observations with simulations and physical tilt experiments of structures.

Many tasks in geometry processing and physical simulation benefit from multiresolution hierarchies. One important characteristic across a variety of applications is that coarser layers strictly encage finer layers, nesting one another. Existing techniques such as surface mesh decimation, voxelization, or contouring distance level sets do not provide sufficient control over the quality of the output surfaces while maintaining strict nesting. We propose a solution that enables use of application-specific decimation and quality metrics. The method constructs each next-coarsest level of the hierarchy, using a sequence of decimation, flow, and contact-aware optimization steps. From coarse to fine, each layer then fully encages the next while retaining a snug fit. The method is applicable to a wide variety of shapes of complex geometry and topology. We demonstrate the effectiveness of our nested cages not only for multigrid solvers, but also for conservative collision detection, domain discretization for elastic simulation, and cage-based geometric modeling.

We develop an automatic pipeline that allows ordinary users to capture complete and fully textured 3D models of themselves in minutes, using only a single Kinect sensor, in the uncontrolled lighting environment of their own home. Our method requires neither a turntable nor a second operator, and is robust to the small deformations and changes of pose that inevitably arise during scanning. After the users rotate themselves with the same pose for a few scans from different views, our system stitches together the captured scans using multi-view non-rigid registration, and produces watertight final models. To ensure consistent texturing, we recover the underlying albedo from each scanned texture and generate seamless global textures using Poisson blending. Despite the minimal requirements we place on the hardware and users, our method is suitable for full body capture of challenging scenes that cannot be handled well using previous methods, such as those involving loose clothing, complex poses, and props.

We present a framework for generating street networks and parcel layouts. Our goal is the generation of high-quality layouts that can be used for urban planning and virtual environments. We propose a solution based on hierarchical domain splitting using two splitting types: streamline-based splitting, which splits a region along one or multiple streamlines of a cross field, and template-based splitting, which warps pre-designed templates to a region and uses the interior geometry of the template as the splitting lines. We combine these two splitting approaches into a hierarchical framework, providing automatic and interactive tools to explore the design space.

Abstract 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.

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.

Resolving simultaneous impacts is an open and significant problem in collision response modeling. Existing algorithms in this domain fail to fulfill at least one of five physical desiderata. To address this we present a simple generalized impact model motivated by both the successes and pitfalls of two popular approaches: pair-wise propagation and linear complementarity models. Our algorithm is the first to satisfy all identified desiderata, including simultaneously guaranteeing symmetry preservation, kinetic energy conservation, and allowing break-away. Furthermore, we address the associated problem of inelastic collapse, proposing a complementary generalized restitution model that eliminates this source of nontermination. We then consider the application of our models to the synchronous time-integration of large-scale assemblies of impacting rigid bodies. To enable such simulations we formulate a consistent frictional impact model that continues to satisfy the desiderata. Finally, we validate our proposed algorithm by correctly capturing the observed characteristics of physical experiments including the phenomenon of extended patterns in vertically oscillated granular materials.

Self-supporting masonry is one of the most ancient and elegant techniques for building curved shapes. Because of the very geometric nature of their failure, analyzing and modeling such strutures is more a geometry processing problem than one of classical continuum mechanics. This paper uses the thrust network method of analysis and presents an iterative nonlinear optimization algorithm for efficiently approximating freeform shapes by self-supporting ones. The rich geometry of thrust networks leads us to close connections between diverse topics in discrete differential geometry, such as a finite-element discretization of the Airy stress potential, perfect graph Laplacians, and computing admissible loads via curvatures of polyhedral surfaces. This geometric viewpoint allows us, in particular, to remesh self-supporting shapes by self-supporting quad meshes with planar faces, and leads to another application of the theory: steel/glass constructions with low moments in nodes.

We present a continuum-based discrete model for thin threads of viscous fluid by drawing upon the Rayleigh analogy to elastic rods, demonstrating canonical coiling, folding, and breakup in dynamic simulations. Our derivation emphasizes space-time symmetry, which sheds light on the role of time-parallel transport in eliminating---without approximation---all but an O ( n ) band of entries of the physical system's energy Hessian. The result is a fast, unified, implicit treatment of viscous threads and elastic rods that closely reproduces a variety of fascinating physical phenomena, including hysteretic transitions between coiling regimes, competition between surface tension and gravity, and the first numerical fluid-mechanical sewing machine. The novel implicit treatment also yields an order of magnitude speedup in our elastic rod dynamics.

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.

Robust treatment of complex collisions is a challenging problem in cloth simulation. Some state of the art methods resolve collisions iteratively, invoking a fail-safe when a bound on iteration count is exceeded. The best-known fail-safe rigidifies the contact region, causing simulation artifacts. We present a fail-safe that cancels impact but not sliding motion, considerably reducing artificial dissipation. We equip the proposed fail-safe with an approximation of Coulomb friction, allowing finer control of sliding dissipation.