Bending-active structures are composed of elastic elements that deform to achieve a desired target shape. To support effective design, inverse algorithms have been proposed that optimize the geometry of each element specifically for each design. This makes it difficult to reuse elements across designs or gain efficiency in fabrication through mass production. We address this issue and propose a computational framework to rationalize bending-active structures into a sparse kit of parts. Our method solves for the optimal part geometry such that multiple input designs can be faithfully realized with the same kit of parts. Assigning parts to different assemblies leads to a combinatorial explosion that makes exhaustive search intractable. Instead, we propose a relaxed continuous optimization incorporating a physics-based simulation in its inner loop to model the elastic deformation of the bending-active structure accurately. Our algorithm allows analyzing different design trade-offs of a kit of parts to tune the balance between fabrication complexity and fidelity to the original designs. We demonstrate our method on three different classes of bending-active structures, showcasing the effectiveness of our approach for part reuse and sustainable practices in fabrication-driven design.

Surface-based inflatables are composed of two thin layers of nearly inextensible sheet material joined together along carefully selected fusing curves. During inflation, pressure forces separate the two sheets to maximize the enclosed volume. The fusing curves restrict this expansion, leading to a spatially varying in-plane contraction and hence metric frustration. The inflated structure settles into a 3D equilibrium that balances pressure forces with the internal elastic forces of the sheets. We present a computational framework for analyzing and designing surface-based inflatable structures with arbitrary fusing patterns. Our approach employs numerical homogenization to characterize the behavior of parametric families of periodic inflatable patch geometries, which can then be combined to tessellate the sheet with smoothly varying patterns. We propose a novel parametrization of the underlying deformation space that allows accurate, efficient, and systematical analysis of the stretching and bending behavior of inflated patches with potentially open boundaries. We apply our homogenization algorithm to create a database of geometrically diverse fusing patterns spanning a wide range of material properties and deformation characteristics. This database is employed in an inverse design algorithm that solves for fusing curves to best approximate a given input target surface. Local patches are selected and blended to form a global network of curves based on a geometric flattening algorithm. These fusing curves are then further optimized to minimize the distance of the deployed structure to target surface. We show that this approach offers greater flexibility to approximate given target geometries compared to previous work while significantly improving structural performance.

We present a computational inverse design framework for a new class of volumetric deployable structures that have compact rest states and deploy into bending-active 3D target surfaces. Umbrella meshes consist of elastic beams, rigid plates, and hinge joints that can be directly printed or assembled in a zero-energy fabrication state. During deployment, as the elastic beams of varying heights rotate from vertical to horizontal configurations, the entire structure transforms from a compact block into a target curved surface. Umbrella Meshes encode both intrinsic and extrinsic curvature of the target surface and in principle are free from the area expansion ratio bounds of past auxetic material systems. We build a reduced physics-based simulation framework to accurately and efficiently model the complex interaction between the elastically deforming components. To determine the mesh topology and optimal shape parameters for approximating a given target surface, we propose an inverse design optimization algorithm initialized with conformal flattening. Our algorithm minimizes the structure's strain energy in its deployed state and optimizes actuation forces so that the final deployed structure is in stable equilibrium close to the desired surface with few or no external constraints. We validate our approach by fabricating a series of physical models at various scales using different manufacturing techniques.

Accurate stereo depth estimation plays a critical role in various 3D tasks in both indoor and outdoor environments. Recently, learning-based multi-view stereo methods have demonstrated competitive performance with limited number of views. However, in challenging scenarios, especially when building cross-view correspondences is hard, these methods still cannot produce satisfying results. In this paper, we study how to enforce the consistency between surface normal and depth at training time to improve the performance. We couple the learning of a multi-view normal estimation module and a multi-view depth estimation module. In addition, we propose a novel consistency loss to train an independent consistency module that refines the depths from depth/normal pairs. We find that the joint learning can improve both the prediction of normal and depth, and the accuracy and smoothness can be further improved by enforcing the consistency. Experiments on MVS, SUN3D, RGBD and Scenes11 demonstrate the effectiveness of our method and state-of-the-art performance.