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This paper presents a method for animating fluid using unstructured tetrahedral meshes that change at each time step. We show that meshes that conform well to changing boundaries and that focus computation in the visually important parts of the domain can be generated quickly and reliably using existing techniques. We also describe a new approach to two-way coupling of fluid and rigid bodies that, while general, benefits from remeshing. Overall, the method provides a flexible environment for creating complex scenes involving fluid animation. Copyright © 2006 by the Association for Computing Machinery, Inc.

We propose a hierarchical graph for learning physics and a novel way to handle obstacles. The finest level of the graph consist of the particles itself. Coarser levels consist of the cells of sparse grids with successively doubling cell sizes covering the volume occupied by the particles. The hierarchical structure allows for the information to propagate at great distance in a single message passing iteration. The novel obstacle handling allows the simulation to be obstacle aware without the need for ghost particles. We train the network to predict effective acceleration produced by multiple sub‐steps of 3D multi‐material material point method (MPM) simulation consisting of water, sand and snow with complex obstacles. Our network produces lower error, trains up to 7.0X faster and inferences up to 11.3X faster than [SGGP*20]. It is also, on average, about 3.7X faster compared to Taichi Elements simulation running on the same hardware in our tests. [ABSTRACT FROM AUTHOR]

The shape matching method is a popular approach to simulate deformable objects in interactive applications due to its stability and simplicity. An important feature is that there is no need for a mesh since the method works on arbitrary local groups within a set of particles. A major drawback of shape matching is the fact that it is geometrically motivated and not derived from physical principles which makes calibration difficult. The fact that the method does not conserve volume can yield visual artifacts, e.g. when a tire is compressed but does not bulge. In this paper we present a new meshless simulation method that is related to shape matching but derived from continuous constitutive models. Volume conservation and stiffness can be specified with physical parameters. Further, if the elements of a tetrahedral mesh are used as groups, our method perfectly reproduces FEM based simulations. [ABSTRACT FROM AUTHOR]

We introduce a triangle mesh based convolutional neural network. The proposed network structure can be used for problems where input and/or output are defined on a manifold triangle mesh with or without boundary. We demonstrate its applications in cloth upsampling, adding back details to Principal Component Analysis (PCA) compressed cloth, regressing clothing deformation from character poses, and regressing hand skin deformation from bones' joint angles. The data used for training in this work are generated from high resolution extended position based dynamics (XPBD) physics simulations with small time steps and high iteration counts and from an offline FEM simulator, but it can come from other sources. The inference time of our prototype implementation, depending on the mesh resolution and the network size, can provide between 4 to 134 times faster than a GPU based simulator. The inference also only needs to be done for meshes currently visible by the camera. [ABSTRACT FROM AUTHOR]

We present a rigid body simulation method that can resolve small temporal and spatial details by using a quasi explicit integration scheme that is unconditionally stable. Traditional rigid body simulators linearize constraints because they operate on the velocity level or solve the equations of motion implicitly thereby freezing the constraint directions for multiple iterations. Our method always works with the most recent constraint directions. This allows us to trace high speed motion of objects colliding against curved geometry, to reduce the number of constraints, to increase the robustness of the simulation, and to simplify the formulation of the solver. In this paper we provide all the details to implement a fully fledged rigid body solver that handles contacts, a variety of joint types and the interaction with soft objects. [ABSTRACT FROM AUTHOR]

Abstract: Robustly and efficiently simulating cables and ropes that are part of a larger system such as cable driven machines, cable cars or tendons in a human or robot is a challenging task. To be able to adapt to the environment, cables are typically modeled as a large number of small segments that are connected via joints. The two main difficulties with this approach are to satisfy the inextensibility constraint and to handle the typically large mass ratio between the small segments and the larger objects they connect. In this paper we present a new approach which solves these problems in a simple and effective way. Our method is based on the idea to simulate the effect of the cables instead of the cables themselves. To this end we propose a new special type of distance constraint we call cable joint that changes both its attachment points and its rest length dynamically. A cable connecting a series of objects is then modeled as a sequence of cable joints which reduces the complexity of the simulation from the order of the number of segments to just the number of connected objects. This makes simulations both faster and more robust as we will demonstrate on a variety of examples. [ABSTRACT FROM AUTHOR]

The current state of the art in real-time two-dimensional water wave simulation requires developers to choose between efficient Fourier-based methods, which lack interactions with moving obstacles, and finite-difference or finite element methods, which handle environmental interactions but are significantly more expensive. This paper attempts to bridge this long-standing gap between complexity and performance, by proposing a new wave simulation method that can faithfully simulate wave interactions with moving obstacles in real time while simultaneously preserving minute details and accommodating very large simulation domains. Previous methods for simulating 2D water waves directly compute the change in height of the water surface, a strategy which imposes limitations based on the CFL condition (fast moving waves require small time steps) and Nyquist's limit (small wave details require closely-spaced simulation variables). This paper proposes a novel wavelet transformation that discretizes the liquid motion in terms of amplitude-like functions that vary over space, frequency, and direction, effectively generalizing Fourier-based methods to handle local interactions. Because these new variables change much more slowly over space than the original water height function, our change of variables drastically reduces the limitations of the CFL condition and Nyquist limit, allowing us to simulate highly detailed water waves at very large visual resolutions. Our discretization is amenable to fast summation and easy to parallelize. We also present basic extensions like pre-computed wave paths and two-way solid fluid coupling. Finally, we argue that our discretization provides a convenient set of variables for artistic manipulation, which we illustrate with a novel wave-painting interface. [ABSTRACT FROM AUTHOR]

We propose a new method to simulate large scale water phenomena by combining particle, 3D grid and height field methods. In contrast to most hybrid approaches that use particles to simulate foam and spray only, we also represent the bulk of water near the surface with both particles and a grid depending on the regions of interest and switch between those two representations during the course of the simulation. For the coupling we leverage the recent idea of tracking the water surface with a density field in grid based methods. Combining particles and a grid simulation then amounts to adding the density field of the particles and the one stored on the grid. For open scenes, we simulate the water outside of the 3D grid domain by solving the Shallow Water Equations on a height field. We propose new methods to couple these two domains such that waves travel naturally across the border. We demonstrate the effectiveness of our approach in various scenarios including a whale breaching simulation, all running in real-time or at interactive rates. [ABSTRACT FROM PUBLISHER]

We present a novel explicit surface tracking method. Its main advantage over existing approaches is the fact that it is both completely grid- free and fast which makes it ideal for the use in large unbounded domains. A further advantage is that its running time is less sensitive to temporal variations of the input mesh than existing approaches. In terms of performance, the method provides a good trade-off point between speed and quality. The main idea behind our approach to handle topological changes is to delete all overlapping triangles and to fill or join the resulting holes in a robust and efficient way while guaranteeing that the output mesh is both manifold and without boundary. We demonstrate the flexibility, speed and quality of our method in various applications such as Eulerian and Lagrangian liquid simulations and the simulation of solids under large plastic deformations. [ABSTRACT FROM AUTHOR]

We propose a new method for both collision detection and collision response geared towards handling complex deformable objects in close contact. Our method does not miss collision events between time steps and solves the challenging problem of untangling automatically and robustly. It is conceptually simple and straight forward to parallelize due to the regularity of the algorithm. The main idea is to tessellate the air between objects once before the simulation and by considering one unilateral constraint per element that prevents its inversion during the simulation. If large relative rotations and translations are present in the simulation, an additional dynamic mesh optimization step is needed to prevent mesh locking. This step is fast in 2D and allows the simulation of arbitrary scenes. Because mesh optimization is expensive in 3D, however, the method is best suited for the subclass of 3D scenarios in which relative motions are limited. This subclass contains two important problems, namely the simulation of multi-layered clothing and tissue on animated characters. [ABSTRACT FROM AUTHOR]

We present a unified dynamics framework for real-time visual effects. Using particles connected by constraints as our fundamental building block allows us to treat contact and collisions in a unified manner, and we show how this representation is flexible enough to model gases, liquids, deformable solids, rigid bodies and cloth with two-way interactions. We address some common problems with traditional particle-based methods and describe a parallel constraint solver based on position-based dynamics that is efficient enough for real-time applications. [ABSTRACT FROM AUTHOR]

We present a GPU friendly, Eulerian, free surface fluid simulation method that conserves mass locally and globally without the use of Lagrangian components. Local mass conservation prevents small-scale details of the free surface from disappearing, a problem that plagues many previous approaches, while global mass conservation ensures that the total volume of the liquid does not decrease over time. Our method handles moving solid boundaries as well as cells that are partially filled with solids. Due to its stability, it allows the use of large time steps that makes it suitable for both offline and real-time applications. We achieve this by using density-based surface tracking with a novel, unconditionally stable, conservative advection scheme. We also propose mass conserving methods to sharpen the interface and to reveal subgrid features of the liquid. While our approach conserves mass, volume loss is still possible but only temporarily. With constant mass, local volume loss causes a local increase of the density used for surface tracking which we detect and correct over time. We show the effectiveness of the proposed methods in several practical examples all running either at interactive rates or in real time. [ABSTRACT FROM AUTHOR]

We propose a new fast, robust and controllable method to simulate the dynamic destruction of large and complex objects in real time. The common method for fracture simulation in computer games is to pre-fracture models and replace objects by their pre-computed parts at run-time. This popular method is computationally cheap but has the disadvantages that the fracture pattern does not align with the impact location and that the number of hierarchical fracture levels is fixed. Our method allows dynamic fracturing of large objects into an unlimited number of pieces fast enough to be used in computer games. We represent visual meshes by volumetric approximate convex decompositions (VACD) and apply user-defined fracture patterns dependent on the impact location. The method supports partial fracturing meaning that fracture patterns can be applied locally at multiple locations of an object. We propose new methods for computing a VACD, for approximate convex hull construction and for detecting islands in the convex decomposition after partial destruction in order to determine support structures. [ABSTRACT FROM AUTHOR]

We present a system for creating a hair model that matches a user's hairstyle from images. The model consists of guide hair strands and can be used in a real‐time hair simulator. Our goal differs from most previous works that aim to create realistic high‐resolution hair for off‐line applications or create a mesh of the exterior of the hair volume for image manipulation. Our primary aim is for a user to be able to put his/her hairstyle into game or other real‐time applications. By taking photos in eight views of the user's head using a smartphone camera and segmenting the images with some easy‐to‐use tools, the player will obtain his/her own hair model in NVIDIA's HairWorks, which is a hair simulator used in many games. We show a number of results demonstrating the capabilities of our system in this paper. We present a system for creating a hair model that matches a user's hairstyle from images. The model consists of guide hair strands and can be used in a real‐time hair simulator.We show a number of results demonstrating the capabilities of our system in this paper. [ABSTRACT FROM AUTHOR]

We present a multigrid method for solving the linear complementarity problem (LCP) resulting from discretizing the Poisson equation subject to separating solid boundary conditions in an Eulerian liquid simulation's pressure projection step. The method requires only a few small changes to a multigrid solver for linear systems. Our generalized solver is fast enough to handle 3D liquid simulations with separating boundary conditions in practical domain sizes. Previous methods could only handle relatively small 2D domains in reasonable time, because they used expensive quadratic programming (QP) solvers. We demonstrate our technique in several practical scenarios, including nonaxis-aligned containers and moving solids in which the omission of separating boundary conditions results in disturbing artifacts of liquid sticking to solids. Our measurements show, that the convergence rate of our LCP solver is close to that of a standard multigrid solver. [ABSTRACT FROM PUBLISHER]

Robotic surgical assistants (RSAs) have the potential to facilitate surgeries and reduce human fatigue. In this paper we focus on surgical retraction , the common surgical primitive of grasping and lifting a thin layer of tissue to expose an underlying area. Given a 2D cross-sectional model of heterogeneous tissue with embedded structures (such as veins) and a desired underlying exposure region, we present an algorithm that computes a set of stable and secure grasp-and-retract trajectories, and runs a 3D finite element (FEM) simulation to certify the quality of each trajectory. To choose secure candidate grasp locations, we introduce the continuous spring method and combine it with the Deformation Space (D-Space) approach to grasping deformable objects with a linearized potential energy model based on the locations of embedded bodies. Experiments show that this method produces many of the same grasps as an exhaustive computation with an FEM mesh, but is orders of magnitude cheaper: our method runs in O ( υ log υ ) time, when υ is the number of veins, while the FEM computation takes O ( pn 3 ) time, where n is the number of nodes in the FEM mesh and p is the number of nodes on its perimeter. Furthermore, we present a constant tissue curvature (CTC) retraction trajectory that distributes strain uniformly around the medial axis of the tissue, by moving the gripper such that the tissue follows a constant-curvature, constant-length arc. 3D FEM simulations show that the CTC achieves retractions with lower tissue strain than circular and linear trajectories. Overall, our algorithm computes and certifies a high-quality retraction in about one minute on a PC.

Bevel-tip steerable needles are a promising new technology for improving accuracy and accessibility in minimally invasive medical procedures. As yet, 3D needle steering has not been demonstrated in the presence of tissue deformation and uncertainty, despite the application of progressively more sophisticated planning algorithms. This paper presents a feedback controller that steers a needle along 3D helical paths, and varies the helix radius to correct for perturbations. It achieves high accuracy for targets sufficiently far from the needle insertion point; this is counterintuitive because the system is highly under-actuated and not locally controllable. The controller uses a model predictive control framework that chooses a needle twist rate such that the predicted helical trajectory minimizes the distance to the target. Fast branch and bound techniques enable execution at kilohertz rates on a 2GHz PC. We evaluate the controller under a variety of simulated perturbations, including imaging noise, needle deflections, and curvature estimation errors. We also test the controller in a 3D finite element simulator that incorporates deformation in the tissue as well as the needle. In deformable tissue examples, the controller reduced targeting error by up to 88% compared to open-loop execution.