A CNN‐based Flow Correction Method for Fast Preview

Eulerian‐based smoke simulations are sensitive to the initial parameters and grid resolutions. Due to the numerical dissipation on different levels of the grid and the nonlinearity of the governing equations, the differences in simulation resolutions will result in different results. This makes it challenging for artists to preview the animation results based on low‐resolution simulations. In this paper, we propose a learning‐based flow correction method for fast previewing based on low‐resolution smoke simulations. The main components of our approach lie in a deep convolutional neural network, a grid‐layer feature vector and a special loss function. We provide a novel matching model to represent the relationship between low‐resolution and high‐resolution smoke simulations and correct the overall shape of a low‐resolution simulation to closely follow the shape of a high‐resolution down‐sampled version. We introduce the grid‐layer concept to effectively represent the 3D fluid shape, which can also reduce the input and output dimensions. We design a special loss function for the fluid divergence‐free constraint in the neural network training process. We have demonstrated the efficacy and the generality of our approach by simulating a diversity of animations deviating from the original training set. In addition, we have integrated our approach into an existing fluid simulation framework to showcase its wide applications.     

Compressive Image Reconstruction in Reduced Union of Subspaces

We present a new compressed sensing framework for reconstruction of incomplete and possibly noisy images and their higher dimensional variants, e.g. animations and light‐fields. The algorithm relies on a learning‐based basis representation. We train an ensemble of intrinsically two‐dimensional (2D) dictionaries that operate locally on a set of 2D patches extracted from the input data. We show that one can convert the problem of 2D sparse signal recovery to an equivalent 1D form, enabling us to utilize a large family of sparse solvers. The proposed framework represents the input signals in a reduced union of subspaces model, while allowing sparsity in each subspace. Such a model leads to a much more sparse representation than widely used methods such as K‐SVD. To evaluate our method, we apply it to three different scenarios where the signal dimensionality varies from 2D (images) to 3D (animations) and 4D (light‐fields). We show that our method outperforms state‐of‐the‐art algorithms in computer graphics and image processing literature.     

Fitting Polynomial Volumes to Surface Meshes with Voronoï Squared Distance Minimization

We propose a method for mapping polynomial volumes. Given a closed surface and an initial template volume grid, our method deforms the template grid by fitting its boundary to the input surface while minimizing a volume distortion criterion. The result is a point‐to‐point map distorting linear cells into curved ones. Our method is based on several extensions of Voronoi Squared Distance Minimization (VSDM) combined with a higher‐order finite element formulation of the deformation energy. This allows us to globally optimize the mapping without prior parameterization. The anisotropic VSDM formulation allows for sharp and semi‐sharp features to be implicitly preserved without tagging. We use a hierarchical finite element function basis that selectively adapts to the geometric details. This makes both the method more efficient and the representation more compact. We apply our method to geometric modeling applications in computer‐aided design and computer graphics, including mixed‐element meshing, mesh optimization, subdivision volume fitting, and shell meshing.     

Fast Fluid Simulations with Sparse Volumes on the GPU

We introduce efficient, large scale fluid simulation on GPU hardware using the fluid‐implicit particle (FLIP) method over a sparse hierarchy of grids represented in NVIDIA^® GVDB Voxels. Our approach handles tens of millions of particles within a virtually unbounded simulation domain. We describe novel techniques for parallel sparse grid hierarchy construction and fast incremental updates on the GPU for moving particles. In addition, our FLIP technique introduces sparse, work efficient parallel data gathering from particle to voxel, and a matrix‐free GPU‐based conjugate gradient solver optimized for sparse grids. Our results show that our method can achieve up to an order of magnitude faster simulations on the GPU as compared to FLIP simulations running on the CPU.     

Hybrid particle–grid fluid animation with enhanced details

Simulating large-scale fluid while retaining and rendering details still remains to be a difficult task in spite of rapid advancements of computer graphics during the last two decades. Grid-based methods can be easily extended to handle large-scale fluid, yet they are unable to preserve sub-grid surface details like spray and foam without multi-level grid refinement. On the other hand, the particle-based methods model details naturally, but at the expense of increasing particle densities. This paper proposes a hybrid particle–grid coupling method to simulate fluid with finer details. The interaction between particles and fluid grids occurs in the vicinity of “coupling band” where multiple particle level sets are introduced simultaneously. First, fluids free of interaction could be modeled by grids and SPH particles independently after initialization. A coupling band inside and near the interface is then identified where the grids interact with the particles. Second, the grids inside and far away from the interface are adaptively sampled for large-scale simulation. Third, the SPH particles outside the coupling band are enhanced by diffuse particles which render little computational cost to simulate spray, foam, and bubbles. A distance function is continuously updated to adaptively coarsen or refine the grids near the coupling band and provides the coupling weights for the two-way coupling between grids and particles. One characteristic of our hybrid approach is that the two-way coupling between these particles of spray and foam and the grids of fluid volume can retain details with little extra computational cost. Our rendering results realistically exhibit fluids with enhanced details like spray, foam, and bubbles. We make comprehensive comparisons with existing works to demonstrate the effectiveness of our new method.     

Using interpolation to improve path planning: The Field D* algorithm

We present an interpolation‐based planning and replanning algorithm for generating low‐cost paths through uniform and nonuniform resolution grids. Most grid‐based path planners use discrete state transitions that artificially constrain an agent's motion to a small set of possible headings (e.g., 0, π/4, π/2, etc.). As a result, even “optimal” grid‐based planners produce unnatural, suboptimal paths. Our approach uses linear interpolation during planning to calculate accurate path cost estimates for arbitrary positions within each grid cell and produce paths with a range of continuous headings. Consequently, it is particularly well suited to planning low‐cost trajectories for mobile robots. In this paper, we introduce a version of the algorithm for uniform resolution grids and a version for nonuniform resolution grids. Together, these approaches address two of the most significant shortcomings of grid‐based path planning: the quality of the paths produced and the memory and computational requirements of planning over grids. We demonstrate our approaches on a number of example planning problems, compare them to related algorithms, and present several implementations on real robotic systems.     

A Hybrid Lagrangian/Eulerian Collocated Velocity Advection and Projection Method for Fluid Simulation

We present a hybrid particle/grid approach for simulating incompressible fluids on collocated velocity grids. Our approach supports both particle-based Lagrangian advection in very detailed regions of the flow and efficient Eulerian grid-based advection in other regions of the flow. A novel Backward Semi-Lagrangian method is derived to improve accuracy of grid based advection. Our approach utilizes the implicit formula associated with solutions of the inviscid Burgers’ equation. We solve this equation using Newton's method enabled by C¹ continuous grid interpolation. We enforce incompressibility over collocated, rather than staggered grids. Our projection technique is variational and designed for B-spline interpolation over regular grids where multiquadratic interpolation is used for velocity and multilinear interpolation for pressure. Despite our use of regular grids, we extend the variational technique to allow for cut-cell definition of irregular flow domains for both Dirichlet and free surface boundary conditions.     

A generic and scalable pipeline for GPU tetrahedral grid rendering

Recent advances in algorithms and graphics hardware have opened the possibility to render tetrahedral grids at interactive rates on commodity PCs. This paper extends on this work in that it presents a direct volume rendering method for such grids which supports both current and upcoming graphics hardware architectures, large and deformable grids, as well as different rendering options. At the core of our method is the idea to perform the sampling of tetrahedral elements along the view rays entirely in local barycentric coordinates. Then, sampling requires minimum GPU memory and texture access operations, and it maps efficiently onto a feed-forward pipeline of multiple stages performing computation and geometry construction. We propose to spawn rendered elements from one single vertex. This makes the method amenable to upcoming Direct3D 10 graphics hardware which allows to create geometry on the GPU. By only modifying the algorithm slightly it can be used to render per-pixel iso-surfaces and to perform tetrahedral cell projection. As our method neither requires any pre-processing nor an intermediate grid representation it can efficiently deal with dynamic and large 3D meshes.     

Back-to-Front Ordering of Triangles in Digital Terrain Models over Regular Grids

Visiting triangles that conform a digital terrain model is a core operation in a number of fields like animation and video games or generating profiles, cross-sections, and contours in civil engineering. Performing the visit in an efficient manner is an issue specially when the output of the traversal depends in some way on additional parameters or information changing over time, for example, a moving point of view. In this work we report a set of rules that, given a digital terrain model defined over a regular grid and an arbitrary point of view outside the terrain, define a total back-to-front order in the set of digital terrain model triangles with respect to the point. The set of rules is minimal, complete and correct. To assess how the rules perform, we have implemented a CPU-based algorithm for realistically rendering height fields defined over regular grids. The algorithm does not make use of the z-buffer or shaders featured by our graphics card. We show how our algorithm is implemented and show visual results obtained from synthetic and real data. We further discuss the algorithm performance with respect to two algorithms: a naive algorithm that visits triangles according to grid indices and does not solve the hidden line problem, and the z-buffer provided by the graphics card featured by our computer. Our algorithm allows real-time interaction when the point of view arbitrarily moves in 3D space and we show that its performance is as good as that of the z-buffer graphics card.     

A Fast Simulation Method Using Overlapping Grids for Interactions between Smoke and Rigid Objects

Recently, many techniques using computational fluid dynamics have been proposed for the simulation of natural phenomena such as smoke and fire. Traditionally, a single grid is used for computing the motion of fluids. When an object interacts with a fluid, the resolution of the grid must be sufficiently high because the shape of the object is represented by a shape sampled at the grid points. This increases the number of grid points that are required, and hence the computational cost is increased. To address this problem, we propose a method using multiple grids that overlap with each other. In addition to a large single grid (a global grid) that covers the whole of the simulation space, separate grids (local grids) are generated that surround each object. The resolution of a local grid is higher than that of the global grid. The local grids move according to the motion of the objects. Therefore, the process of resampling the shape of the object is unnecessary when the object moves. To accelerate the computation, appropriate resolutions are adaptively‐determined for the local grids according to their distance from the viewpoint. Furthermore, since we use regular (orthogonal) lattices for the grids, the method is suitable for GPU implementation. This realizes the real‐time simulation of interactions between objects and smoke.     

基于物理模型的烟雾模拟

在分析研究流体物理特性算法基础上,提出一种新的烟雾模拟实现方法。该方法基于物理模型的求解简化方程模拟烟雾的动态变化过程。模型中采用了非粘性欧拉方程,通常它比其他用粘性Navier-Stoke方程建模的更适合用来对气体进行建模并且减少计算量。实验验证该模型还可以正确处理烟雾与移动的物体之间的相互作用。     

Vector graphics depicting marbling flow

We present an efficient framework for generating marbled textures that can be exported into a vector graphics format based on an explicit surface tracking method. The proposed method enables artists to create complex and realistic marbling textures that can be used for design purposes. Our algorithm is unique in that the marbling paint on the surface of water is represented as an enclosed contour and is advected by fluid flow to deform the marbling silhouette. In contrast to previous methods, in which the shape is tracked with a concentration density field in Eulerian grids, our approach facilitates greater complexity that is free from grid resolution and per-pixel computation while retaining real-time performance. To forestall the propagation of large vertices, we adaptively resample the contours, exploiting the curvature and the turbulence of the fluid as criteria. At the convection phase, we parallelly advect contour particles on a Graphics Processing Unit (GPU) in addition to applying volume corrections. Finally, we quickly remove extremely thin lines in shapes to remove dozens of vertices. We performed our method with an interactive prototype to demonstrate the robustness of the proposed method in several scenarios.     

真实感固流交互动画的统一物质点法模拟

固流交互模拟是基于物理的流体模拟技术的重要研究内容,其中如何解决非穿透 和滑移接触是难点。为此,提出一种真实感固流交互动画的统一物质点法模拟方法。首先,给 出一种基于物质点法的快速微可压缩流体模拟方法,并在统一背景欧拉网格上对固体和流体动 量方程进行求解;其次,检测固流接触区域并在其上构建局部多重背景网格,给出一种动量守 恒保持的速度修正方法对固体和流体各自网格结点进行速度修正,从而实现固流交互的非穿透 和滑移接触效果模拟。实验结果表明,该方法可以模拟稳定、真实的固流交互动画,适用于计 算机图形学和虚拟现实领域中的真实感模拟应用。     

Interactive Graphics for Computer Adaptive Testing

Interactive graphics are commonly used in games and have been shown to be successful in attracting the general audience. Instead of computer games, animations, cartoons, and videos being used only for entertainment, there is now an interest in using interactive graphics for ‘innovative testing’. Rather than traditional pen‐and‐paper tests, audio, video and graphics are being conceived as alternative means for more effective testing in the future. In this paper, we review some examples of graphics item types for testing. As well, we outline how games can be used to interactively test concepts; discuss designing chemistry item types with interactive 3D graphics; suggest approaches for automatically adjusting difficulty level in interactive graphics based questions; and propose strategies for giving partial marks for incorrect answers. We study how to test different cognitive skills, such as music, using multimedia interfaces; and also evaluate the effectiveness of our model. Methods for estimating difficulty level of a mathematical item type using Item Response Theory (IRT) and a molecule construction item type using Graph Edit Distance are discussed. Evaluation of the graphics item types through extensive testing on some students is described. We also outline the application of using interactive graphics over cell phones. All of the graphics item types used in this paper are developed by members of our research group.     

A novel, integrated smoke simulation design method supporting local projection and guiding control over adaptive grids

High-fidelity smoke simulation in a large-scale complex environment is extremely time-consuming due to the expensive computational cost of using highly dense regular grids. There have been quite a few improved algorithms/techniques aiming to enhance the simulation’s visual effects and reduce the time consumption during the last two decades. However, most of the state-of-the-art methods will encounter difficulties of not being able to model fine turbulent details during simulation or losing high-frequency shape details at the fine scale when simulated smoke interacting with nearby obstacles. One straightforward solution is to continue to refine spatial resolution at the expense of increased time complexity. This paper, however, advocates an improved strategy for smoke simulation design over adaptive grids, while simultaneously enabling the functionalities of local projection and guiding control. First, our new integrated method supports adaptive grid projection that can significantly reduce the computational cost during the velocity projection phase. During smoke simulation design, the use of adaptive grids flexibly accommodates finer cells near obstacles with fine details, and coarser cells anywhere else, as a result, fine-scale object features can be faithfully retained without the need of global grid refinement. Second, our integrated solution over adaptive grids can tightly couple guiding control with local projection, which is capable of handling tiny obstacles that are impossible to model with global coarse grids alone during simulation preview. Comprehensive experiments have shown that our integrated method has the advantage of generating turbulent phenomena when interacting with small-scale features of obstacles, and at the same time offering the preview mechanism for efficient large-scale smoke simulation design.     

Procedural Synthesis using Vortex Particle Method for Fluid Simulation

We propose a fast and effective technique to improve sub‐grid visual details of the grid based fluid simulation. Our method procedurally synthesizes the flow fields coming from the incompressible Navier‐Stokes solver and the vorticity fields generated by vortex particle method for sub‐grid turbulence. We are able to efficiently animate smoke which is highly turbulent and swirling with small scale details. Since this technique does not solve the linear system in high‐resolution grids, it can perform fluid simulation more rapidly. We can easily estimate the influence of turbulent and swirling effect to the fluid flow.     

A model for real-time on-surface flows

Simulating fluid flows for visualization purposes is known to be one of the most challenging fields of the computer graphics domain. While rendering vast liquid areas has been widely addressed this last decade, few papers have tackled the problematic of on-surface flows, even though real-time applications such as drive simulators or video games could greatly benefit from such methods. We present a novel empirical method for the animation of liquid droplets lying on a flat surface, the core of our technique being a simulation operating on a 2D grid which is implementable on GPU. The wetted surface can freely be oriented in space and is not limited to translucent materials, the liquid flow being governed by external forces, the viscosity parameter and the presence of obstacles. Furthermore, we show how to simply incorporate in our simulation scheme two enriching visual effects, namely absorption and ink transport. Rendering can be achieved from an arbitrary view point using a GPU image based raycasting approach and takes into account the refraction and reflection of light. Even though our method doesn’t benefit from the literature of fluid mechanics, we show that convincing animations in terms of realism can be achieved in real-time.     

Distributed multi-join query processing in data grids

Query processing in data grids is a difficult issue due to the heterogeneous, unpredictable and volatile behaviors of the grid resources. Applying join operations on remote relations in data grids is a unique and interesting problem. However, to the best of our knowledge, little is done to date on multi-join query processing in data grids. An approach for processing multi-join queries is proposed in this paper. Firstly, a relation-reduction algorithm for reducing the sizes of operand relations is presented in order to minimize data transmission cost among grid nodes. Then, a method for scheduling computer nodes in data grids is devised to parallel process multi-join queries. Thirdly, an innovative method is developed to efficiently execute join operations in a pipeline fashion. Finally, a complete algorithm for processing multi-join queries is given. Analytical and experimental results show the effectiveness and efficiency of the proposed approach.     

Two‐Level Grids for Ray Tracing on GPUs

We investigate the use of two‐level nested grids as acceleration structure for ray tracing of dynamic scenes. We propose a massively parallel, sort‐based construction algorithm and show that the two‐level grid is one of the structures that is fastest to construct on modern graphics processors. The structure handles non‐uniform primitive distributions more robustly than the uniform grid and its traversal performance is comparable to those of other high quality acceleration structures used for dynamic scenes. We propose a cost model to determine the grid resolution and improve SIMD utilization during ray‐triangle intersection by employing a hybrid packetization strategy. The build times and ray traversal acceleration provide overall rendering performance superior to previous approaches for real time rendering of animated scenes on GPUs.     

Physically‐based forehead animation including wrinkles

Physically‐based animation techniques enable more realistic and accurate animation to be created. We present a fully physically‐based approach for efficiently producing realistic‐looking animations of facial movement, including animation of expressive wrinkles. This involves simulation of detailed voxel‐based models using a graphics processing unit‐based total Lagrangian explicit dynamic finite element solver with an anatomical muscle contraction model, and advanced boundary conditions that can model the sliding of soft tissue over the skull. The flexibility of our approach enables detailed animations of gross and fine‐scale soft‐tissue movement to be easily produced with different muscle structures and material parameters, for example, to animate different aged skins. Although we focus on the forehead, our approach can be used to animate any multi‐layered soft body. © 2014 The Authors. Computer Animation and Virtual Worlds published by John Wiley & Sons, Ltd.