Position based dynamics [Müller et al. 2007] is a powerful technique for simulating a variety of materials. Its primary strength is its robustness when run with limited computational budget. Even though PBD is based on the projection of static constraints, it does not work well for quasistatic problems. This is particularly relevant since the efficient creation of large data sets of plausible, but not necessarily accurate elastic equilibria is of increasing importance with the emergence of quasistatic neural networks [Bailey et al. 2018; Chentanez et al. 2020; Jin et al. 2022; Luo et al. 2020]. Recent work [Macklin et al. 2016] has shown that PBD can be related to the Gauss-Seidel approximation of a Lagrange multiplier formulation of backward Euler time stepping, where each constraint is solved/projected independently of the others in an iterative fashion. We show that a position-based, rather than constraint-based nonlinear Gauss-Seidel approach resolves a number of issues with PBD, particularly in the quasistatic setting. Our approach retains the essential PBD feature of stable behavior with constrained computational budgets, but also allows for convergent behavior with expanded budgets. We demonstrate the efficacy of our method on a variety of representative hyperelastic problems and show that both successive over relaxation (SOR), Chebyshev and multiresolution-based acceleration can be easily applied.

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.

We propose a novel method to model and fabricate shapes using a small set of specified discrete equivalence classes of triangles. The core of our modeling technique is a fabrication-error-driven remeshing algorithm. Given a triangle and a template triangle, which are coplanar and have one-to-one corresponding vertices, we define their similarity error from a manufacturing point of view as follows: the minimizer of the maximum of the three distances between the corresponding pair of vertices concerning a rigid transformation. To compute the similarity error, we convert it into an easy-to-compute form. Then, a greedy remeshing method is developed to optimize the topology and geometry of the input mesh to minimize the fabrication error defined as the maximum similarity error of all triangles. Besides, constraints are enforced to ensure the similarity between input and output shapes and the smoothness of the resulting shapes. Since the fabrication error has been considered during the modeling process, the fabrication process is easy to proceed. To assist users in performing fabrication using common materials and tools manually, we present a straightforward manufacturing solution. The feasibility and practicability of our method are demonstrated over various examples, including seven physical manufacturing models with only nine template triangles.

Computer-generated holographic (CGH) displays show great potential and are emerging as the next-generation displays for augmented and virtual reality, and automotive heads-up displays. One of the critical problems harming the wide adoption of such displays is the presence of speckle noise inherent to holography, that compromises its quality by introducing perceptible artifacts. Although speckle noise suppression has been an active research area, the previous works have not considered the perceptual characteristics of the Human Visual System (HVS), which receives the final displayed imagery. However, it is well studied that the sensitivity of the HVS is not uniform across the visual field, which has led to gaze-contingent rendering schemes for maximizing the perceptual quality in various computer-generated imagery. Inspired by this, we present the first method that reduces the "perceived speckle noise" by integrating foveal and peripheral vision characteristics of the HVS, along with the retinal point spread function, into the phase hologram computation. Specifically, we introduce the anatomical and statistical retinal receptor distribution into our computational hologram optimization, which places a higher priority on reducing the perceived foveal speckle noise while being adaptable to any individual's optical aberration on the retina. Our method demonstrates superior perceptual quality on our emulated holographic display. Our evaluations with objective measurements and subjective studies demonstrate a significant reduction of the human perceived noise.