We propose a novel method to automatically approximate a free-form surface using a set of near developable patches that form a tensile-like structure when anchored at a sparse set of points. These structures are appealing for their ability to span large areas with low material cost and structural weight, while also offering strong aesthetic potential. Our algorithm strikes a balance between approximation accuracy, patch simplicity, and visual quality, while ensuring manufacturability and structural feasibility. The layout is guided by a curvature field and refined through a combinatorial process that incrementally adds patches until performance and fabrication constraints are met. Redundant elements are then removed to improve clarity and elegance.

Abstract Playing the guitar is a dexterous human skill that poses significant challenges in computer graphics and robotics due to the precision required in finger positioning and coordination between hands. Current methods often rely on motion capture data to replicate specific guitar playing segments, which restricts the range of performances and demands intricate post‐processing. In this paper, we introduce a novel reinforcement learning model that can play the guitar using robotic hands, without the need for motion capture datasets, from input tablatures. To achieve this, we divide the simulation task for playing guitar into three stages. (a): for an input tablature, we first generate corresponding fingerings that align with human habits. (b): based on the generated fingerings as the guidance, we train a neural network for controlling the fingers of the left hand using deep reinforcement learning, and (c): we generate plucking movements for the right hand based on inverse kinematics according to the tablature. We evaluate our method by employing precision, recall, and F1 scores as quantitative metrics to thoroughly assess its performance in playing musical notes. In addition, we conduct qualitative analysis through user studies to evaluate the visual and auditory effects of guitar performance. The results demonstrate that our model excels in playing most moderately difficult and easier musical pieces, accurately playing nearly all notes.

We present a method for computational modeling, mechanical characterization, and macro-scale simulation of discrete interlocking materials (DIM)---3D-printed chainmail fabrics made of quasi-rigid interlocking elements. Unlike conventional elastic materials for which deformation and restoring force are directly coupled, the mechanics of DIM are governed by contacts between individual elements that give rise to anisotropic deformation constraints. To model the mechanical behavior of these materials, we propose a computational approach that builds on three key components. ( a ): we explore the space of feasible deformations using native-scale simulations at the per-element level. ( b ): based on this simulation data, we introduce the concept of strain-space boundaries to represent deformation limits for in- and out-of-plane deformations, and ( c ): we use the strain-space boundaries to drive an efficient macro-scale simulation model based on homogenized deformation constraints. We evaluate our method on a set of representative discrete interlocking materials and validate our findings against measurements on physical prototypes.

Abstract Strain limiting is a widely used approach for simulating biphasic materials such as woven textiles and biological tissue that exhibit a soft elastic regime followed by a hard deformation limit. However, existing methods are either based on slowly converging local iterations, or offer no guarantees on convergence. In this work, we propose a new approach to strain limiting based on second order cone programming (SOCP). Our work is based on the key insight that upper bounds on per‐triangle deformations lead to convex quadratic inequality constraints. Though nonlinear, these constraints can be reformulated as inclusion conditions on convex sets, leading to a second order cone programming problem—a convex optimization problem that a) is guaranteed to have a unique solution and b) allows us to leverage efficient conic programming solvers. We first cast strain limiting with anisotropic bounds on stretching as a quadratically constrained quadratic program (QCQP), then show how this QCQP can be mapped to a second order cone programming problem. We further propose a constraint reflection scheme and empirically show that it exhibits superior energy‐preservation properties compared to conventional end‐of‐step projection methods. Finally, we demonstrate our prototype implementation on a set of examples and illustrate how different deformation limits can be used to model a wide range of material behaviors.

We present a computational method for designing compliant mechanical systems that exhibit large-amplitude oscillations. The technical core of our approach is an optimization-driven design tool that combines sensitivity analysis for optimization with the Harmonic Balance Method for simulation. By establishing dynamic force equilibrium in the frequency domain, our formulation avoids the major limitations of existing alternatives: it handles nonlinear forces, side-steps any transient process, and automatically produces periodic solutions. We introduce design objectives for amplitude optimization and trajectory matching that enable intuitive high-level authoring of large-amplitude motions. Our method can be applied to many types of mechanical systems, which we demonstrate through a set of examples involving compliant mechanisms, flexible rod networks, elastic thin shell models, and multi-material solids. We further validate our approach by manufacturing and evaluating several physical prototypes.