Abstract We present a fast, robust method for continuous collision detection (CCD) directly between pairs of complex signed distance fields (SDFs). By casting CCD as an alternating spatio‐temporal optimization and driving a small set of smartly sampled surface points along SDF tangent spaces, our approach avoids dense sampling or triangle meshes entirely. The result is real‐time SDF‐SDF time‐of‐impact queries—often within 1 ms on a single CPU core—even for highly detailed, non‐convex geometry undergoing fast spinning motion. This is, to our knowledge, the first practical CCD method operating directly on SDF pairs.

Adapting motion to new contexts in digital entertainment often demands fast agile prototyping. State-of-the-art techniques use reinforcement learning policies for simulating the underlined motion in a physics engine. Unfortunately, policies typically fail on unseen tasks and it is too time-consuming to fine-tune the policy for every new morphological, environmental, or motion change. We propose a novel point of view on using policy networks as a representation of motion for physics-based character animation. Our policies are compact, tailored to individual motion tasks, and preserve similarity with nearby tasks. This allows us to view the space of all motions as a manifold of policies where sampling substitutes training. We obtain memory-efficient encoding of motion that leverages the characteristics of control policies such as being generative, and robust to small environmental changes. With this perspective, we can sample novel motions by directly manipulating weights and biases through a Diffusion Model. Our newly generated policies can adapt to previously unseen characters, potentially saving time in rapid prototyping scenarios. Our contributions include the introduction of Common Neighbor Policy regularization to constrain policy similarity during motion imitation training making them suitable for generative modeling; a Diffusion Model adaptation for diverse morphology; and an open policy dataset. The results show that we can learn non-linear transformations in the policy space from labeled examples, and conditionally generate new ones. In a matter of seconds, we sample a batch of policies for different conditions that show comparable motion fidelity metrics as their respective trained ones.

Abstract While IMU based motion capture offers a cost‐effective alternative to premium camera‐based systems, it often falls short in matching the latter's realism. Common distortions, such as self‐penetrating body parts, foot skating, and floating, limit the usability of these systems, particularly for high‐end users. To address this, we employed reinforcement learning to train an AI agent that mimics erroneous sample motion. Since our agent operates within a simulated environment, it inherently avoids generating these distortions since it must adhere to the laws of physics. Impressively, the agent manages to mimic the sample motions while preserving their distinctive characteristics. We assessed our method's efficacy across various types of input data, showcasing an ideal blend of artefact‐laden IMU‐based data with high‐grade optical motion capture data. Furthermore, we compared the configuration of observation and action spaces with other implementations, pinpointing the most suitable configuration for our purposes. All our models underwent rigorous evaluation using a spectrum of quantitative metrics complemented by a qualitative review. These evaluations were performed using a benchmark dataset of IMU‐based motion data from actors not included in the training data.

Abstract In this work, we present a novel approach for calibrating material model parameters for soft body simulations using real data. We use a fully differentiable pipeline, combining a differentiable soft body simulator and differentiable depth rendering, which permits fast gradient‐based optimizations. Our method requires no data pre‐processing, and minimal experimental set‐up, as we directly minimize the L2‐norm between raw LIDAR scans and rendered simulation states. In essence, we provide the first marker‐free approach for calibrating a soft‐body simulator to match observed real‐world deformations. Our approach is inexpensive as it solely requires a consumer‐level LIDAR sensor compared to acquiring a professional marker‐based motion capture system. We investigate the effects of different material parameterizations and evaluate convergence for parameter optimization in both single and multi‐material scenarios of varying complexity. Finally, we show that our set‐up can be extended to optimize for dynamic behaviour as well.

Coronavirus disease 2019 (COVID-19) has become a severe global pandemic. Accurate pneumonia infection segmentation is important for assisting doctors in diagnosing COVID-19. Deep learning-based methods can be developed for automatic segmentation, but the lack of large-scale well-annotated COVID-19 training datasets may hinder their performance. Semi-supervised segmentation is a promising solution which explores large amounts of unlabelled data, while most existing methods focus on pseudo-label refinement. In this paper, we propose a new perspective on semi-supervised learning for COVID-19 pneumonia infection segmentation, namely pseudo-label guided image synthesis. The main idea is to keep the pseudo-labels and synthesize new images to match them. The synthetic image has the same COVID-19 infected regions as indicated in the pseudo-label, and the reference style extracted from the style code pool is added to make it more realistic. We introduce two representative methods by incorporating the synthetic images into model training, including single-stage Synthesis-Assisted Cross Pseudo Supervision (SA-CPS) and multi-stage Synthesis-Assisted Self-Training (SA-ST), which can work individually as well as cooperatively. Synthesis-assisted methods expand the training data with high-quality synthetic data, thus improving the segmentation performance. Extensive experiments on two COVID-19 CT datasets for segmenting the infections demonstrate our method is superior to existing schemes for semi-supervised segmentation, and achieves the state-of-the-art performance on both datasets. Code is available at: https://github.com/FeiLyu/SASSL.

High fidelity interactions between game characters and gaseous effects like smoke, fire and explosions are often neglected in realtime applications due to the high computational cost of simulating fluids. In addition, the pose of game characters is only known at runtime as it depends on input from the user. Thus simulation-suitable representations of surface geometry must be generated on the fly. Common approaches like conversion into signed distance fields are not feasible for high-resolution geometry due to the computational cost and the amount of memory required on the GPU to store these fields. We present a purely vortex particle based fluid model for games which is capable of resolving the collision between fluids and complex objects such as moving game characters in real time. To handle collisions, we use a collocation method which only require a set of disassociated particles stuck to collision surfaces. Contrary to most other vorticity based methods, we use a simple inversion free approach to obtain the collision velocity field on surfaces while at the same time avoiding the expensive pressure projection step associated with pressure based fluid solvers.

The simulation of incompressible materials suffers from locking when using the standard finite element method (FEM) and coarse linear tetrahedral meshes. Locking increases as the Poisson ratio ν gets close to 0.5 and often lower Poisson ratio values are used to reduce locking, affecting volume preservation. We propose a novel mixed FEM approach to simulating incompressible solids that alleviates the locking problem for tetrahedra. Our method uses linear shape functions for both displacements and pressure, and adds one scalar per node. It can accommodate nonlinear isotropic materials described by a Young’s modulus and any Poisson ratio value by enforcing a volumetric constitutive law. The most realistic such material is Neo-Hookean, and we focus on adapting it to our method. For ν = 0.5, we can obtain full volume preservation up to any desired numerical accuracy. We show that standard Neo-Hookean simulations using tetrahedra are often locking, which, in turn, affects accuracy. We show that our method gives better results and that our Newton solver is more robust. As an alternative, we propose a dual ascent solver that is simple and has a good convergence rate. We validate these results using numerical experiments and quantitative analysis.

Abstract Inspired by frictional behaviour that is observed when sliding matchsticks against one another at different angles, we propose a phenomenological anisotropic friction model for structured surfaces. Our model interpolates isotropic and anisotropic elliptical Coulomb friction parameters for a pair of surfaces with perpendicular and parallel structure directions (e.g. the wood grain direction). We view our model as a special case of an abstract friction model that produces a cone based on state information, specifically the relationship between structure directions. We show how our model can be integrated into LCP and NCP‐based simulators using different solvers with both explicit and fully implicit time‐integration. The focus of our work is on symmetric friction cones, and we therefore demonstrate a variety of simulation scenarios where the friction structure directions play an important part in the resulting motions. Consequently, authoring of friction using our model is intuitive and we demonstrate that our model is compatible with standard authoring practices, such as texture mapping.

Abstract We examine the relationship between primal, or force‐based, and dual, or constraint‐based formulations of dynamics. Variational frameworks such as Projective Dynamics have proved popular for deformable simulation, however they have not been adopted for contact‐rich scenarios such as rigid body simulation. We propose a new preconditioned frictional contact solver that is compatible with existing primal optimization methods, and competitive with complementarity‐based approaches. Our relaxed primal model generates improved contact force distributions when compared to dual methods, and has the advantage of being differentiable, making it well‐suited for trajectory optimization. We derive both primal and dual methods from a common variational point of view, and present a comprehensive numerical analysis of both methods with respect to conditioning. We demonstrate our method on scenarios including rigid body contact, deformable simulation, and robotic manipulation.

In this work we present a framework that is capable of accurately representing soft robotic actuators in a multiphysics environment in real-time. We propose a constraint-based dynamics model of a 1-dimensional pneumatic soft actuator that accounts for internal pressure forces, as well as the effect of actuator latency and damping under inflation and deflation and demonstrate its accuracy a full soft robotic snake with the composition of multiple 1D actuators. We verify our model's accuracy in static deformation and dynamic locomotion open-loop control experiments. To achieve real-time performance we leverage the parallel computation power of GPUs to allow interactive control and feedback.

Soft robots are advantageous in terms of flexibility, safety and adaptability. It is challenging to find efficient computational approaches for planning and controlling their motion. This work takes a direct data-driven approach to learn the kinematics of the three-dimensional shape of a soft robot, by using visual markers. No prior information about the robot at hand is required. The model is oblivious to the design of the robot and type of actuation system. This allows adaptation to erroneous manufacturing. We present a highly versatile and inexpensive learning cube environment for collecting and analysing data. We prove that using multiple, lower order models of data opposed to one global, higher order model, will reduce the required data quantity, time complexity and memory complexity significantly without compromising accuracy. Further, our approach allows for embarrassingly parallelism. Yielding an overall much more simple and efficient approach.

We present a novel method of simulating incompressible materials undergoing large deformation without locking artifacts. We apply it for simulating silicone soft robots with a Poisson ratio close to 0.5. The new approach is based on the mixed finite element method (FEM) using a pressure-displacement formulation; the deviatoric deformation is still handled in a traditional fashion. We support large deformations without volume increase using the corotational formulation of linear elasticity. Stability is ensured by an implicit integration scheme which always reduces to a sparse linear system. For even more deformation accuracy we support higher order simulation through the use of Bernstein-Bézier polynomials.

We present a framework for the simulation of rigid and deformable bodies in the presence of contact and friction. Our method is based on a non-smooth Newton iteration that solves the underlying nonlinear complementarity problems (NCPs) directly. This approach allows us to support nonlinear dynamics models, including hyperelastic deformable bodies and articulated rigid mechanisms, coupled through a smooth isotropic friction model. The fixed-point nature of our method means it requires only the solution of a symmetric linear system as a building block. We propose a new complementarity preconditioner for NCP functions that improves convergence, and we develop an efficient GPU-based solver based on the conjugate residual (CR) method that is suitable for interactive simulations. We show how to improve robustness using a new geometric stiffness approximation and evaluate our method’s performance on a number of robotics simulation scenarios, including dexterous manipulation and training using reinforcement learning.

Computation of contact points is a critical sub-component of physics-based animation. The success and correctness of simulation results are very sensitive to the quality of the contact points. Hence, quality plays a critical role when comparing methods, and this is highly relevant for simulating objects with sharp edges. The importance of contact point quality is largely overlooked and lacks rigor and as such may become a bottleneck in moving the research field forward. We establish a taxonomy of contact point generation methods and lay down an analysis of what normal contact quality implies. The analysis enables us to establish a novel methodology for assessing and studying quality for mesh-based shapes. The core idea is based on a test suite of three complex cases and a small portfolio of simple cases. We apply our methodology to eight local contact point generation methods and conclude that the selected local methods are unable to provide correct information in all cases. The immediate benefit of the proposed methodology is a foundation for others to evaluate and select the best local method for their specific application. In the longer perspective, the presented work suggests future research focusing on semi-local methods.

We present a novel approach to using Bounding Volume Hierarchies (BVHs) for collision detection of volumetric meshes for digital prototyping based on accurate simulation. In general, volumetric meshes contain more primitives than surface meshes, which in turn means larger BVHs. To manage these larger BVHs, we propose an algorithm for splitting meshes into smaller chunks with a limited-size BVH each. Limited-height BVHs make guided, all-pairs testing of two chunked meshes well-suited for GPU implementation. This is because the dynamically generated work during BVH traversal becomes bounded. Chunking is simple to implement compared to dynamic load balancing methods and can result in an overall two orders of magnitude speedup on GPUs. This indicates that dynamic load balancing may not be a well suited scheme for the GPU. The overall application timings showed that data transfers were not the bottleneck. Instead, the conversion to and from OpenCL friendly data structures was causing serious performance impediments. Still, a simple OpenMP acceleration of the conversion allowed the GPU solution to beat the CPU solution by 20 percent. We demonstrate our results using rigid and deformable body scenes of varying complexities on a variety of GPUs.

Inverse kinematics (IK) is a central component of systems for motion capture, character animation, motion planning, and robotics control. The field of computer graphics has developed fast stationary point solvers methods, such as the Jacobian transpose method and cyclic coordinate descent. Much work with Newton methods focus on avoiding directly computing the Hessian, and instead approximations are sought, such as in the BFGS class of solvers. This paper presents a numerical method for computing the exact Hessian of an IK system with spherical joints. It is applicable to human skeletons in computer animation applications and some, but not all, robots. Our results show that using exact Hessians can give performance advantages and higher accuracy compared to standard numerical methods used for solving IK problems. Furthermore, we provide code and supplementary details that allows researchers to plug-in exact Hessians in their own work with little effort.

Abstract Interactive rigid body simulation is an important part of many modern computer tools, which no authoring tool nor game engine can do without. Such high‐performance computer tools open up new possibilities for changing how designers, engineers, modelers and animators work with their design problems. This paper is a self contained state‐of‐the‐art report on the physics, the models, the numerical methods and the algorithms used in interactive rigid body simulation all of which have evolved and matured over the past 20 years. Furthermore, the paper communicates the mathematical and theoretical details in a pedagogical manner. This paper is not only a stake in the sand on what has been done, it also seeks to give the reader deeper insights to help guide their future research .

Abstract We present a photon splatting technique which reduces noise and blur in the rendering of caustics. Blurring of illumination edges is an inherent problem in photon splatting, as each photon is unaware of its neighbours when being splatted. This means that the splat size is usually based on heuristics rather than knowledge of the local flux density. We use photon differentials to determine the size and shape of the splats such that we achieve adaptive anisotropic flux density estimation in photon splatting. As compared to previous work that uses photon differentials, we present the first method where no photons or beams or differentials need to be stored in a map. We also present improvements in the theory of photon differentials, which give more accurate results and a faster implementation. Our technique has good potential for GPU acceleration, and we limit the number of parameters requiring user adjustment to an overall smoothing parameter and the number of photons to be traced.

In this paper, we present a method for animating multiphase flow of immiscible fluids using unstructured moving meshes. Our underlying discretization is an unstructured tetrahedral mesh, the deformable simplicial complex (DSC), that moves with the flow in a Lagrangian manner. Mesh optimization operations improve element quality and avoid element inversion. In the context of multiphase flow, we guarantee that every element is occupied by a single fluid and, consequently, the interface between fluids is represented by a set of faces in the simplicial complex. This approach ensures that the underlying discretization matches the physics and avoids the additional book-keeping required in grid-based methods where multiple fluids may occupy the same cell. Our Lagrangian approach naturally leads us to adopt a finite element approach to simulation, in contrast to the finite volume approaches adopted by a majority of fluid simulation techniques that use tetrahedral meshes. We characterize fluid simulation as an optimization problem allowing for full coupling of the pressure and velocity fields and the incorporation of a second-order surface energy. We introduce a preconditioner based on the diagonal Schur complement and solve our optimization on the GPU. We provide the results of parameter studies as well as a performance analysis of our method, together with suggestions for performance optimization.

Multibody dynamics are used in interactive and real-time applications, ranging from computer games to virtual prototyping, and engineering. All these areas strive towards faster and larger scale simulations. Particularly challenging are large-scale simulations with highly organized and structured stacking. We present a stable, robust, and versatile method for multibody dynamics simulation. Novel contributions include a new, explicit, fixed time-stepping scheme for velocity-based complementarity formulations using shock propagation with a simple reliable implementation strategy for an iterative complementarity problem solver specifically optimized for multibody dynamics.