We present XCube (abbreviated as$\mathcal{X}^{\mathrm{3}}$), a novel generative model for high-resolution sparse 3D voxel grids with arbitrary attributes. Our model can generate millions of voxels with a finest effective resolution of up to 10243in a feed-forward fashion without time-consuming test-time optimization. To achieve this, we employ a hierarchical voxel latent diffusion model which generates progressively higher resolution grids in a coarse-to-fine manner using a custom framework built on the highly efficient VDB data structure. Apart from generating high-resolution objects, we demonstrate the effectiveness of XCube on large outdoor scenes at scales of 100 m× 100 m with a voxel size as small as 10 cm. We observe clear qualitative and quantitative improvements over past approaches. In addition to unconditional generation, we show that our model can be used to solve a variety of tasks such as user-guided editing, scene completion from a single scan, and text-to-3D. More results and details can be found on our project webpage.

We introduce NeuralVDB, which improves on an existing industry standard for efficient storage of sparse volumetric data, denoted VDB [Museth 2013 ], by leveraging recent advancements in machine learning. Our novel hybrid data structure can reduce the memory footprints of VDB volumes by orders of magnitude, while maintaining its flexibility and only incurring small (user-controlled) compression errors. Specifically, NeuralVDB replaces the lower nodes of a shallow and wide VDB tree structure with multiple hierarchical neural networks that separately encode topology and value information by means of neural classifiers and regressors respectively. This approach is proven to maximize the compression ratio while maintaining the spatial adaptivity offered by the higher-level VDB data structure. For sparse signed distance fields and density volumes, we have observed compression ratios on the order of 10× to more than 100× from already compressed VDB inputs, with little to no visual artifacts. Furthermore, NeuralVDB is shown to offer more effective compression performance compared to other neural representations such as Neural Geometric Level of Detail [Takikawa et al. 2021 ], Variable Bitrate Neural Fields [Takikawa et al. 2022a ], and Instant Neural Graphics Primitives [Müller et al. 2022 ]. Finally, we demonstrate how warm-starting from previous frames can accelerate training, i.e., compression, of animated volumes as well as improve temporal coherency of model inference, i.e., decompression.

We present a neural network-based simulation super-resolution framework that can efficiently and realistically enhance a facial performance produced by a low-cost, real-time physics-based simulation to a level of detail that closely approximates that of a reference-quality off-line simulator with much higher resolution (27× element count in our examples) and accurate physical modeling. Our approach is rooted in our ability to construct a training set of paired frames, from the low- and high-resolution simulators respectively, that are in semantic correspondence with each other. We use face animation as an exemplar of such a simulation domain, where creating this semantic congruence is achieved by simply dialing in the same muscle actuation controls and skeletal pose in the two simulators. Our proposed neural network super-resolution framework generalizes from this training set to unseen expressions, compensates for modeling discrepancies between the two simulations due to limited resolution or cost-cutting approximations in the real-time variant, and does not require any semantic descriptors or parameters to be provided as input, other than the result of the real-time simulation. We evaluate the efficacy of our pipeline on a variety of expressive performances and provide comparisons and ablation experiments for plausible variations and alternatives to our proposed scheme. Our code is available at https://github.com/hjoonpark/3d-sim-super- res.git.

We present f VDB, a novel GPU-optimized framework for deep learning on large-scale 3D data. f VDB provides a complete set of differentiable primitives to build deep learning architectures for common tasks in 3D learning such as convolution, pooling, attention, ray-tracing, meshing, etc. f VDB simultaneously provides a much larger feature set (primitives and operators) than established frameworks with no loss in efficiency: our operators match or exceed the performance of other frameworks with narrower scope. Furthermore, f VDB can process datasets with much larger footprint and spatial resolution than prior works, while providing a competitive memory footprint on small inputs. To achieve this combination of versatility and performance, f VDB relies on a single novel VDB index grid acceleration structure paired with several key innovations including GPU accelerated sparse grid construction, convolution using tensorcores, fast ray tracing kernels using a Hierarchical Digital Differential Analyzer algorithm (HDDA), and jagged tensors. Our framework is fully integrated with PyTorch enabling interoperability with existing pipelines, and we demonstrate its effectiveness on a number of representative tasks such as large-scale point-cloud segmentation, high resolution 3D generative modeling, unbounded scale Neural Radiance Fields, and large-scale point cloud reconstruction.

We propose a method to enhance the visual detail of a water surface simulation. Our method works as a post-processing step which takes a simulation as input and increases its apparent resolution by simulating many detailed Lagrangian water waves on top of it. We extend linear water wave theory to work in non-planar domains which deform over time, and we discretize the theory using Lagrangian wave packets attached to spline curves. The method is numerically stable and trivially parallelizable, and it produces high frequency ripples with dispersive wave-like behaviors customized to the underlying fluid simulation.

We propose a multi-body solver that extends the Material Point Method (MPM) to simulate cracks in computer animation. We define cracks as the intersection between pieces of bodies created by a pre-fracture process and held together by massless particle constraints (glue particles). These pieces are simulated using a MPM multi-body solver extended by us to efficiently handle N-body collisions. Benefits of the present work include (1) low computational overhead compared to a normal MPM algorithm; (2) good scaling in three dimensions due to our use of sparse grids for background computations; (3) allowing for an easy and controllable setup phase to simulate a desired material failure mode, which is especially useful for computer animation.

We present a multi-species model for the simulation of gravity driven landslides and debris flows with porous sand and water interactions. We use continuum mixture theory to describe individual phases where each species individually obeys conservation of mass and momentum and they are coupled through a momentum exchange term. Water is modeled as a weakly compressible fluid and sand is modeled with an elastoplastic law whose cohesion varies with water saturation. We use a two-grid Material Point Method to discretize the governing equations. The momentum exchange term in the mixture theory is relatively stiff and we use semi-implicit time stepping to avoid associated small time steps. Our semi-implicit treatment is explicit in plasticity and preserves symmetry of force linearizations. We develop a novel regularization of the elastic part of the sand constitutive model that better mimics plasticity during the implicit solve to prevent numerical cohesion artifacts that would otherwise have occurred. Lastly, we develop an improved return mapping for sand plasticity that prevents volume gain artifacts in the traditional Drucker-Prager model.

We have developed a novel hierarchical data structure for the efficient representation of sparse, time-varying volumetric data discretized on a 3D grid. Our “VDB”, so named because it is a Volumetric, Dynamic grid that shares several characteristics with B+trees, exploits spatial coherency of time-varying data to separately and compactly encode data values and grid topology. VDB models a virtually infinite 3D index space that allows for cache-coherent and fast data access into sparse volumes of high resolution. It imposes no topology restrictions on the sparsity of the volumetric data, and it supports fast (average O (1)) random access patterns when the data are inserted, retrieved, or deleted. This is in contrast to most existing sparse volumetric data structures, which assume either static or manifold topology and require specific data access patterns to compensate for slow random access. Since the VDB data structure is fundamentally hierarchical, it also facilitates adaptive grid sampling, and the inherent acceleration structure leads to fast algorithms that are well-suited for simulations. As such, VDB has proven useful for several applications that call for large, sparse, animated volumes, for example, level set dynamics and cloud modeling. In this article, we showcase some of these algorithms and compare VDB with existing, state-of-the-art data structures.

This article presents a novel nonreflective boundary condition for the free surface incompressible Euler and Navier-Stokes equations. Boundaries of this type are very useful when, for example, simulating water flow around a ship moving over a wide ocean. Normally waves generated by the ship will reflect off of the boundaries of the simulation domain and as these reflected waves return towards the ship they will cause undesired interference patterns. By employing a Perfectly Matched Layer (PML) approach we have derived a boundary condition that absorbs incoming waves and thus efficiently prevents these undesired wave reflections. To solve the resulting boundary equations we present a fast and stable algorithm based on the stable fluids approach. Through numerical experiments we then show that our boundaries are significantly more effective than simpler reflection preventing techniques. We also provide a thorough analysis of the parameters involved in our boundary formulation and show how they effect wave absorption efficiency.

We present techniques for warping and blending (or subtracting) geometric textures onto surfaces represented by high resolution level sets. The geometric texture itself can be represented either explicitly as a polygonal mesh or implicitly as a level set. Unlike previous approaches, we can produce topologically connected surfaces with smooth blending and low distortion. Specifically, we offer two different solutions to the problem of adding fine-scale geometric detail to surfaces. Both solutions assume a level set representation of the base surface which is easily achieved by means of a mesh-to-level-set scan conversion. To facilitate our mapping, we parameterize the embedding space of the base level set surface using fast particle advection. We can then warp explicit texture meshes onto this surface at nearly interactive speeds or blend level set representations of the texture to produce high-quality surfaces with smooth transitions.

The three papers in this special section are extended versions of three papers from the Ninth Eurographics/IEEE VGTC Symposium on Visualization (EuroVis '07), held in Norrkoping, Sweden, May 23-25, 2007. The papers are summarized here.

One of the most common visualization tasks is the extraction of significant boundaries, often performed with isosurfaces or level set segmentation. Isosurface extraction is simple and can be guided by geometric and topological analysis, yet frequently does not extract the desired boundary. Level set segmentation is better at boundary extraction, but either leads to global segmentation without edges, [CV01], that scales unfavorably in 3D or requires an initial estimate of the boundary from which to locally solve segmentation with edges. We propose a hybrid system in which topological analysis is used for semi-automatic initialization of a level set segmentation, and geometric information bounded topologically is used to guide and accelerate an iterative segmentation algorithm that combines several state-of-the-art level set terms. We thus combine and improve both the flexible isosurface interface and level set segmentation without edges.

This article presents a generic framework for the representation and deformation of level set surfaces at extreme resolutions. The framework is composed of two modules that each utilize optimized and application specific algorithms: 1) A fastout-of-coredata management scheme that allows for resolutions of the deforming geometry limited only by the available disk space as opposed to memory, and 2) compact and fastcompressionstrategies that reduce both offline storage requirements and online memory footprints during simulation. Out-of-core and compression techniques have been applied to a wide range of computer graphics problems in recent years, but this article is the first to apply it in the context of level set and fluidsimulations. Our framework is generic and flexible in the sense that the two modules can transparently be integrated, separately or in any combination, into existing level set and fluid simulation software based on recently proposed narrow band data structures like the DT-Grid of Nielsen and Museth [2006] and the H-RLE of Houston et al [2006]. The framework can be applied to narrow band signed distances, fluid velocities, scalar fields, particle properties as well as standard graphics attributes like colors, texture coordinates, normals, displacements etc. In fact, our framework is applicable to a large body of computer graphics problems that involve sequential or random access to very large co-dimension one (level set) and zero (e.g. fluid) data sets. We demonstrate this with several applications, including fluid simulations interacting with large boundaries (≈ 15003), surface deformations (≈ 20483), the solution of partial differential equations on large surfaces (≈ 40963) and mesh-to-level set scan conversions of resolutions up to ≈ 350003(7 billion voxels in the narrow band). Our out-of-core framework is shown to be several times faster than current state-of-the-art level set data structures relying on OS paging. In particular we show sustained throughput (grid points/sec) for gigabyte sized level sets as high as 65% of state-of-the-art throughput for in-core simulations. We also demonstrate that our compression techniques out-perform state-of-the-art compression algorithms for narrow bands.

This article introduces the Hierarchical Run-Length Encoded (H-RLE) Level Set data structure. This novel data structure combines the best features of the DT-Grid (of Nielsen and Museth [2004]) and the RLE Sparse Level Set (of Houston et al. [2004]) to provide both optimal efficiency and extreme versatility. In brief, the H-RLE level set employs an RLE in a dimensionally recursive fashion. The RLE scheme allows the compact storage of sequential nonnarrowband regions while the dimensionally recursive encoding along each axis efficiently compacts nonnarrowband planes and volumes. Consequently, this new structure can store and process level sets with effective voxel resolutions exceeding 5000 × 3000 × 3000 (45 billion voxels) on commodity PCs with only 1 GB of memory. This article, besides introducing the H-RLE level set data structure and its efficient core algorithms, also describes numerous applications that have benefited from our use of this structure: our unified implicit object representation, efficient and robust mesh to level set conversion, rapid ray tracing, level set metamorphosis, collision detection, and fully sparse fluid simulation (including RLE vector and matrix representations.) Our comparisons of the popular octree level set and Peng level set structures to the H-RLE level set indicate that the latter is superior in both narrowband sequential access speed and overall memory usage.

We present a robust method for 3D reconstruction of closed surfaces from sparsely sampled parallel contours. A solution to this problem is especially important for medical segmentation, where manual contouring of 2D imaging scans is still extensively used. Our proposed method is based on a morphing process applied to neighboring contours that sweeps out a 3D surface. Our method is guaranteed to produce closed surfaces that exactly pass through the input contours, regardless of the topology of the reconstruction. Our general approach consecutively morphs between sets of input contours using an Eulerian formulation (i.e. fixed grid) augmented with Lagrangian particles (i.e. interface tracking). This is numerically accomplished by propagating the input contours as 2D level sets with carefully constructed continuous speed functions. Specifically this involves particle advection to estimate distances between the contours, monotonicity constrained spline interpolation to compute continuous speed functions without overshooting, and state-of-the-art numerical techniques for solving the level set equations. We demonstrate the robustness of our method on a variety of medical, topographic and synthetic data sets.

Abstract Level set models combine a low‐level volumetric representation, the mathematics of deformable implicit surfaces and powerful, robust numerical techniques to produce a novel approach to shape design. While these models offer many benefits, their large‐scale representation and numerical requirements create significant challenges when developing an interactive system. This paper describes the collection of techniques and algorithms (some new, some pre‐existing) needed to overcome these challenges and to create an interactive editing system for this new type of geometric model. We summarize the algorithms for producing level set input models and, more importantly, for localizing/minimizing computation during the editing process. These algorithms include distance calculations, scan conversion, closest point determination, fast marching methods, bounding box creation, fast and incremental mesh extraction, numerical integration and narrow band techniques. Together these algorithms provide the capabilities required for interactive editing of level set models.

We present a novel approach to interactive visualization and exploration of large unstructured tetrahedral meshes. These massive 3D meshes are used in mission-critical CFD and structural mechanics simulations, and typically sample multiple field values on several millions of unstructured grid points. Our method relies on the preprocessing of the tetrahedral mesh to partition it into nonconvex boundaries and internal fragments that are subsequently encoded into compressed multiresolution data representations. These compact hierarchical data structures are then adaptively rendered and probed in real-time on a commodity PC. Our point-based rendering algorithm, which is inspired by QSplat, employs a simple but highly efficient splatting technique that guarantees interactive frame-rates regardless of the size of the input mesh and the available rendering hardware. It furthermore allows for real-time probing of the volumetric data-set through constructive solid geometry operations as well as interactive editing of color transfer functions for an arbitrary number of field values. Thus, the presented visualization technique allows end-users for the first time to interactively render and explore very large unstructured tetrahedral meshes on relatively inexpensive hardware.

We present a level set framework for implementing editing operators for surfaces. Level set models are deformable implicit surfaces where the deformation of the surface is controlled by a speed function in the level set partial differential equation. In this paper we define a collection of speed functions that produce a set of surface editing operators. The speed functions describe the velocity at each point on the evolving surface in the direction of the surface normal. All of the information needed to deform a surface is encapsulated in the speed function, providing a simple, unified computational framework. The user combines pre-defined building blocks to create the desired speed function. The surface editing operators are quickly computed and may be applied both regionally and globally. The level set framework offers several advantages. 1) By construction, self-intersection cannot occur, which guarantees the generation of physically-realizable, simple, closed surfaces. 2) Level set models easily change topological genus, and 3) are free of the edge connectivity and mesh quality problems associated with mesh models. We present five examples of surface editing operators: blending, smoothing, sharpening, openings/closings and embossing. We demonstrate their effectiveness on several scanned objects and scan-converted models.

The paper addresses visualization issues of the Terrestrial Planet Finder Mission (C.A. Beichman et al., 1999). The goal of this mission is to search for chemical signatures of life in distant solar systems using five satellites flying in formation to simulate a large telescope. To design and visually verify such a delicate mission, one has to analyze and interact with many different 3D spacecraft trajectories, which is often difficult in 2D. We employ a novel trajectory design approach using invariant manifold theory, which is best understood and utilized in an immersive setting. The visualization also addresses multi-scale issues related to the vast differences in distance, velocity, and time at different phases of the mission. Additionally, the parameterization and coordinate frames used for numerical simulations may not be suitable for direct visualization. Relative motion presents a more serious problem where the patterns of the trajectories can only be viewed in particular rotating frames. Some of these problems are greatly relieved by using interactive, animated stereo 3D visualization in a semi-immersive environment such as a Responsive Workbench. Others were solved using standard techniques such as a stratify approach with multiple windows to address the multiscale issues, re-parameterizations of trajectories and associated 2D manifolds and relative motion of the camera to "evoke" the desired patterns.