Abstract Texture‐space shading (TSS) methods decouple shading and rasterization, allowing shading to be performed at a different framerate and spatial resolution than rasterization. TSS has many potential applications, including streaming shading across networks, and reducing rendering cost via shading reuse across consecutive frames and/or shading at reduced resolutions relative to display resolution. Real‐time TSS shading requires texture atlases small enough to be easily stored in GPU memory. Using static atlases leads to significant space wastage, motivating real‐time per‐frame atlassing strategies that pack only the content visible in each frame. We propose FastAtlas, a novel atlasing method that runs entirely on the GPU and is fast enough to be performed at interactive rates per‐frame. Our method combines new per‐frame chart computation and parametrization strategies and an efficient general chart packing algorithm. Our chartification strategy removes visible seams in output renders, and our parameterization ensures a constant texel‐to‐pixel ratio, avoiding undesirable undersampling artifacts. Our packing method is more general, and produces more tightly packed atlases, than previous work. Jointly, these innovations enable us to produce shading outputs of significantly higher visual quality than those produced using alternative atlasing strategies. We validate FastAtlas by shading and rendering challenging scenes using different atlasing settings, reflecting the needs of different TSS applications (temporal reuse, streaming, reduced or elevated shading rates). We extensively compare FastAtlas to prior alternatives and demonstrate that it achieves better shading quality and reduces texture stretch compared to prior approaches using the same settings.

We construct a subspace simulator that adaptively balances solution improvement against system size. The core components of our simulator are an adaptive subspace oracle, model, and parallel time-step solver algorithm. Our in-time-step adaptivity oracle continually assesses subspace solution quality and candidate update proposals while accounting for temporal variations in deformation and spatial variations in material. In turn our adaptivity model is subspace agnostic. It allows application across subspace representations and expresses unrestricted deformations independent of subspace choice. We couple our oracle and model with a custom-constructed parallel time-step solver for our enriched systems that exposes a pair of user tolerances which provide controllable simulation quality. As tolerances are tightened our model converges to full-space solutions (with expected cost increases). On the other hand, as tolerances are relaxed we obtain output-bound simulation costs. We demonstrate the efficacy of our approach across a wide range of challenging nonlinear materials models, material stiffnesses, heterogeneities, dynamic behaviors, and frictionally contacting conditions, obtaining scalable and efficient simulations of complex elastodynamic scenarios.

Real-time elastodynamic solvers are well-suited for the rapid simulation of homogeneous elastic materials, with high-rates generally enabled by aggressive early termination of timestep solves. Unfortunately, the introduction of strong domain heterogeneities can make these solvers slow to converge. Stopping the solve short creates visible damping artifacts and rotational errors. To address these challenges we develop a reduced mixed finite element solver that preserves rich rotational motion, even at low-iteration regimes. Specifically, this solver augments time-step solve optimizations with auxillary stretch degrees of freedom at mesh elements, and maintains consistency with the primary positional degrees of freedoms at mesh nodes via explicit constraints. We make use of a Skinning Eigenmode subspace for our positional degrees of freedom. We accelerate integration of non-linear elastic energies with a cubature approximation, placing stretch degrees of freedom at cubature points. Across a wide range of examples we demonstrate that this subspace is particularly well suited for heterogeneous material simulation. Our resulting method is a subspace mixed finite element method completely decoupled from the resolution of the mesh that is well-suited for real-time simulation of heterogeneous domains.

We propose and explore a new method for the implicit time integration of elastica. Key to our approach is the use of a mixed variational principle. In turn, its finite element discretization leads to an efficient and accurate sequential quadratic programming solver with a superset of the desirable properties of many previous integration strategies. This framework fits a range of elastic constitutive models and remains stable across a wide span of time step sizes and material parameters (including problems that are approximately rigid). Our method exhibits convergence on par with full Newton type solvers and also generates visually plausible results in just a few iterations comparable to recent fast simulation methods that do not converge. These properties make it suitable for both offline accurate simulation and performant applications with expressive physics. We demonstrate the efficacy of our approach on a number of simulated examples.

We introduce a new method for direct physics-based animation of volumetric curved models, represented using NURBS surfaces. Our technical contribution is the Shape Matching Element Method (SEM). SEM is a completely meshless algorithm, the first to simultaneously be robust to gaps and overlaps in geometry, be compatible with standard constitutive models and time integration schemes, support contact and frictional interactions and to preserve feature correspondence during simulation which enables editable simulated output. We demonstrate the efficacy of our algorithm by producing compelling physics-based animations from a variety of curved input models.