SIGGRAPH Asia 2023 Papers

Mechanical metamaterials enable customizing the elastic properties of physical objects by altering their fine-scale structure. A broad gamut of effective material properties can be produced even from a single fabrication material by optimizing the geometry of a periodic microstructure tiling. Past work has extensively studied the capabilities of microstructures in the small-displacement regime, where periodic homogenization of linear elasticity yields computationally efficient optimal design algorithms. However, many applications involve flexible structures undergoing large deformations for which the accuracy of linear elasticity rapidly deteriorates due to geometric nonlinearities. Design of microstructures at finite strains involves a massive increase in computation and is much less explored; no computational tool yet exists to design metamaterials emulating target hyperelastic laws over finite regions of strain space. We make an initial step in this direction, developing algorithms to accelerate homogenization and metamaterial design for nonlinear elasticity and building a complete framework for the optimal design of planar metamaterials. Our nonlinear homogenization method works by efficiently constructing an accurate interpolant of a microstructure's deformation over a finite space of macroscopic strains likely to be endured by the metamaterial. From this interpolant, the homogenized energy density, stress, and tangent elasticity tensor describing the microstructure's effective properties can be inexpensively computed at any strain. Our design tool then fits the effective material properties to a target constitutive law over a region of strain space using a parametric shape optimization approach, producing a directly manufacturable geometry. We systematically test our framework by designing a catalog of materials fitting isotropic Hooke's laws as closely as possible. We demonstrate significantly improved accuracy over traditional linear metamaterial design techniques by fabricating and testing physical prototypes.

National Key Laboratory of General Artificial Intelligence, Beijing Institute for General Artificial Intelligence (BIGAI), China Retrieving out-of-reach objects is a crucial task in virtual reality (VR). One of the most commonly used approaches for this task is the gesture-based approach, which allows for bare-hand, eyes-free, and direct retrieval. However, previous work has primarily focused on assigned gesture design, neglecting the context. This can make it challenging to accurately retrieve an object from a large number of objects due to the one-to-one mapping metaphor, limitations of finger poses, and memory burdens. There is a general consensus that objects and contexts are related, which suggests that the object expected to be retrieved is related to the context, including the scene and the objects with which users interact. As such, we propose a commonsense knowledge-driven joint reasoning approach for object retrieval, where human grasping gestures and context are modeled using an And-Or graph (AOG). This approach enables users to accurately retrieve objects from a large number of candidate objects by using natural grasping gestures based on their experience of grasping physical objects. Experimental results demonstrate that our proposed approach improves retrieval accuracy. We also propose an object retrieval system based on the proposed approach. Two user studies show that our system enables efficient object retrieval in virtual environments (VEs).

We present a set of operators to perform modifications, in particular collapses and splits, in volumetric cell complexes which are discretely embedded in a background mesh. Topological integrity and geometric embedding validity are carefully maintained. We apply these operators strategically to volumetric block decompositions, so-called T-meshes or base complexes, in the context of hexahedral mesh generation. This allows circumventing the expensive and unreliable global volumetric remapping step in the versatile meshing pipeline based on 3D integer-grid maps. In essence, we reduce this step to simpler local cube mapping problems, for which reliable solutions are available. As a consequence, the robustness of the mesh generation process is increased, especially when targeting coarse or block-structured hexahedral meshes. We furthermore extend this pipeline to support feature alignment constraints, and systematically respect these throughout, enabling the generation of meshes that align to points, curves, and surfaces of special interest, whether on the boundary or in the interior of the domain.

Neural Radiance Fields (NeRF) can be optimized to obtain high-fidelity 3D scene reconstructions of objects and large-scale scenes. However, NeRFs require accurate camera parameters as input --- inaccurate camera parameters result in blurry renderings. Extrinsic and intrinsic camera parameters are usually estimated using Structure-from-Motion (SfM) methods as a pre-processing step to NeRF, but these techniques rarely yield perfect estimates. Thus, prior works have proposed jointly optimizing camera parameters alongside a NeRF, but these methods are prone to local minima in challenging settings. In this work, we analyze how different camera parameterizations affect this joint optimization problem, and observe that standard parameterizations exhibit large differences in magnitude with respect to small perturbations, which can lead to an ill-conditioned optimization problem. We propose using a proxy problem to compute a whitening transform that eliminates the correlation between camera parameters and normalizes their effects, and we propose to use this transform as a preconditioner for the camera parameters during joint optimization. Our preconditioned camera optimization significantly improves reconstruction quality on scenes from the Mip-NeRF 360 dataset: we reduce error rates (RMSE) by 67% compared to state-of-the-art NeRF approaches that do not optimize for cameras like Zip-NeRF, and by 29% relative to state-of-the-art joint optimization approaches using the camera parameterization of SCNeRF. Our approach is easy to implement, does not significantly increase runtime, can be applied to a wide variety of camera parameterizations, and can straightforwardly be incorporated into other NeRF-like models.

We introduce a computational pipeline for simulating and designing C-shells, a new class of planar-to-spatial deployable linkage structures. A C-shell is composed of curved flexible beams connected at rotational joints that can be assembled in a stress-free planar configuration. When actuated, the elastic beams deform and the assembly deploys towards the target 3D shape. We propose two alternative computational design approaches for C-shells: (i) Forward exploration simulates the deployed shape from a planar beam layout provided by the user. Once a satisfactory overall shape is found, a subsequent design optimization adapts the beam geometry to reduce the elastic energy of the linkage while preserving the target shape. (ii) Inverse design is facilitated by a new geometric flattening method that takes a design surface as input and computes an initial layout of piecewise straight linkage beams. Our design optimization algorithm then calculates the smooth curved beams to best reproduce the target shape at minimal elastic energy. We find that C-shells offer a rich space for design and show several studies that highlight new shape topologies that cannot be achieved with existing deployable linkage structures.