Volume rendering techniques for scientific visualization have recently shifted toward Monte Carlo (MC) methods for their flexibility and robustness, but their use in multi-channel visualization remains underexplored. Traditional multi-channel volume rendering often relies on arbitrary, non-physically based color blending functions that hinder interpretation. We introduce multi-density Woodcock tracking, a simple extension of Woodcock tracking that leverages an MC method to produce high-fidelity, physically grounded multi-channel renderings without arbitrary blending. By generalizing Woodcock's distance tracking, we provide a unified blending modality that also integrates blending functions from prior works. We further implement effects that enhance boundary and feature recognition. By accumulating frames in real-time, our approach delivers high-quality visualizations with perceptual benefits, demonstrated on diverse datasets.

Computing derivatives of path integrals under evolving scene geometry is a fundamental problem in physics-based differentiable rendering, which requires differentiating discontinuities in the visibility function. Warped-area reparameterization is a powerful technique to compute differential visibility, and key is construction of a velocity field that is continuous in the domain interior and agrees with defined velocities on boundaries. Robustly and efficiently constructing such fields remains challenging. We present a novel velocity field construction for differential visibility. Inspired by recent Monte Carlo solvers for partial differential equations (PDEs), we formulate the velocity field via Laplace's equation and solve it with a walk-on-spheres (WoS) algorithm. To improve efficiency, we introduce a fixed-step WoS that terminates random walks after a fixed step count, resulting in a continuous but non-harmonic velocity field still valid for warped-area reparameterization. Furthermore, to practically apply our method to complex 3D scenes, we propose an efficient cone query to find the closest silhouettes on a boundary. Our cone query finds the closest point under the geodesic distance on a unit sphere, and is analogous to the closest point query by WoS to compute Euclidean distance. As a result, our method generalizes WoS to perform random walks on spherical caps over the unit sphere. We demonstrate that this enables a more robust and efficient unbiased estimator for differential visibility.

Interactively visualizing large finite element simulation data on High-Performance Computing (HPC) systems poses several difficulties. Some of these relate to unstructured data, which, even on a single node, is much more expensive to render compared to structured volume data. Worse yet, in the data parallel rendering context, such data with highly non-convex spatial domain boundaries will cause rays along its silhouette to enter and leave a given rank's domains at different distances. This straddling, in turn, poses challenges for both ray marching, which usually assumes successive elements to share a face, and compositing, which usually assumes a single fragment per pixel per rank. We holistically address these issues using a combination of three inter-operating techniques: first, we use a highly optimized GPU ray marching technique that, given an entry point, can march a ray to its exit point with high-performance by exploiting an exclusive-or (XOR) based compaction scheme. Second, we use hardware-accelerated ray tracing to efficiently find the proper entry points for these marching operations. Third, we use a "deep" compositing scheme to properly handle cases where different ranks' ray segments interleave in depth. We use GPU-to-GPU remote direct memory access (RDMA) to achieve interactive frame rates of 10-15 frames per second and higher for our motivating use case, the Fun3D NASA Mars Lander.

Smoothed-particle hydrodynamics (SPH) is a mesh-free method used to simulate volumetric media in fluids, astrophysics, and solid mechanics. Visualizing these simulations is problematic because these datasets often contain millions, if not billions of particles carrying physical attributes and moving over time. Radial basis functions (RBFs) are used to model particles, and overlapping particles are interpolated to reconstruct a high-quality volumetric field; however, this interpolation process is expensive and makes interactive visualization difficult. Existing RBF interpolation schemes do not account for color-mapped attributes and are instead constrained to visualizing just the density field. To address these challenges, we exploit ray tracing cores in modern GPU architectures to accelerate scalar field reconstruction. We use a novel RBF interpolation scheme to integrate per-particle colors and densities, and leverage GPU-parallel tree construction and refitting to quickly update the tree as the simulation animates over time or when the user manipulates particle radii. We also propose a Hilbert reordering scheme to cluster particles together at the leaves of the tree to reduce tree memory consumption. Finally, we reduce the noise of volumetric shadows by adopting a spatially temporal blue noise sampling scheme. Our method can provide a more detailed and interactive view of these large, volumetric, time-series particle datasets than traditional methods, leading to new insights into these physics simulations.

We propose a simple yet effective method for clustering finite elements to improve preprocessing times and rendering performance of unstructured volumetric grids without requiring auxiliary connectivity data. Rather than building bounding volume hierarchies (BVHs) over individual elements, we sort elements along with a Hilbert curve and aggregate neighboring elements together, improving BVH memory consumption by over an order of magnitude. Then to further reduce memory consumption, we cluster the mesh on the fly into sub-meshes with smaller indices using a series of efficient parallel mesh re-indexing operations. These clusters are then passed to a highly optimized ray tracing API for point containment queries and ray-cluster intersection testing. Each cluster is assigned a maximum extinction value for adaptive sampling, which we rasterize into non-overlapping view-aligned bins allocated along the ray. These maximum extinction bins are then used to guide the placement of samples along the ray during visualization, reducing the number of samples required by multiple orders of magnitude (depending on the dataset), thereby improving overall visualization interactivity. Using our approach, we improve rendering performance over a competitive baseline on the NASA Mars Lander dataset from 6× (1 frame per second (fps) and 1.0 M rays per second (rps) up to now 6 fps and 12.4 M rps, now including volumetric shadows) while simultaneously reducing memory consumption by 3×(33 GB down to 11 GB) and avoiding any offline preprocessing steps, enabling high-quality interactive visualization on consumer graphics cards. Then by utilizing the full 48 GB of an RTX 8000, we improve the performance of Lander by 17 × (1 fps up to 17 fps, 1.0 M rps up to 35.6 M rps).

Blue noise error patterns are well suited to human perception, and when applied to stochastic rendering techniques, blue noise masks (blue noise textures) minimize unwanted low-frequency noise in the final image. Current methods of applying blue noise masks at each frame independently produce white noise frequency spectra temporally. This white noise results in slower integration convergence over time and unstable results when filtered temporally. Unfortunately, achieving temporally stable blue noise distributions is non-trivial since 3D blue noise does not exhibit the desired 2D blue noise properties, and alternative approaches degrade the spatial blue noise qualities. We propose novel blue noise patterns that, when animated, produce values at a pixel that are well distributed over time, converge rapidly for Monte Carlo integration, and are more stable under TAA, while still retaining spatial blue noise properties. To do so, we propose an extension to the well-known void and cluster algorithm that reformulates the underlying energy function to produce spatiotemporal blue noise masks. These masks exhibit blue noise frequency spectra in both the spatial and temporal domains, resulting in visually pleasing error patterns, rapid convergence speeds, and increased stability when filtered temporally. We demonstrate these improvements on a variety of applications, including dithering, stochastic transparency, ambient occlusion, and volumetric rendering. By extending spatial blue noise to spatiotemporal blue noise, we overcome the convergence limitations of prior blue noise works, enabling new applications for blue noise distributions.

Adaptive representations are increasingly indispensable for reducing the in-memory and on-disk footprints of large-scale data. Usual solutions are designed broadly along two themes: reducing data precision, e.g., through compression, or adapting data resolution, e.g., using spatial hierarchies. Recent research suggests that combining the two approaches, i.e., adapting both resolution and precision simultaneously, can offer significant gains over using them individually. However, there currently exist no practical solutions to creating and evaluating such representations at scale. In this work, we present a new resolution-precision-adaptive representation to support hybrid data reduction schemes and offer an interface to existing tools and algorithms. Through novelties in spatial hierarchy, our representation, Adaptive Multilinear Meshes (AMM), provides considerable reduction in the mesh size. AMM creates a piecewise multilinear representation of uniformly sampled scalar data and can selectively relax or enforce constraints on conformity, continuity, and coverage, delivering a flexible adaptive representation. AMM also supports representing the function using mixed-precision values to further the achievable gains in data reduction. We describe a practical approach to creating AMM incrementally using arbitrary orderings of data and demonstrate AMM on six types of resolution and precision datastreams. By interfacing with state-of-the-art rendering tools through VTK, we demonstrate the practical and computational advantages of our representation for visualization techniques. With an open-source release of our tool to create AMM, we make such evaluation of data reduction accessible to the community, which we hope will foster new opportunities and future data reduction schemes.

We present a technique that leverages ray tracing hardware available in recent Nvidia RTX GPUs to solve a problem other than classical ray tracing. Specifically, we demonstrate how to use these units to accelerate the point location of general unstructured elements consisting of both planar and bilinear faces. This unstructured mesh point location problem has previously been challenging to accelerate on GPU architectures; yet, the performance of these queries is crucial to many unstructured volume rendering and compute applications. Starting with a CUDA reference method, we describe and evaluate three approaches that reformulate these point queries to incrementally map algorithmic complexity to these new hardware ray tracing units. Each variant replaces the simpler problem of point queries with a more complex one of ray queries. Initial variants exploit ray tracing cores for accelerated BVH traversal, and subsequent variants use ray-triangle intersections and per-face metadata to detect point-in-element intersections. Although these later variants are more algorithmically complex, they are significantly faster than the reference method thanks to hardware acceleration. Using our approach, we improve the performance of an unstructured volume renderer by up to 4× for tetrahedral meshes and up to 15× for general bilinear element meshes, matching, or out-performing state-of-the-art solutions while simultaneously improving on robustness and ease-of-implementation.

In theory, efficient and high-quality rendering of unstructured data should greatly benefit from modern GPUs, but in practice, GPUs are often limited by the large amount of memory that large meshes require for element representation and for sample reconstruction acceleration structures. We describe a memory-optimized encoding for large unstructured meshes that efficiently encodes both the unstructured mesh and corresponding sample reconstruction acceleration structure, while still allowing for fast random-access sampling as required for rendering. We demonstrate that for large data our encoding allows for rendering even the 2.9 billion element Mars Lander on a single off-the-shelf GPU-and the largest 6.3 billion version on a pair of such GPUs.

Researchers in the field of connectomics are working to reconstruct a map of neural connections in the brain in order to understand at a fundamental level how the brain processes information. Constructing this wiring diagram is done by tracing neurons through high-resolution image stacks acquired with fluorescence microscopy imaging techniques. While a large number of automatic tracing algorithms have been proposed, these frequently rely on local features in the data and fail on noisy data or ambiguous cases, requiring time-consuming manual correction. As a result, manual and semi-automatic tracing methods remain the state-of-the-art for creating accurate neuron reconstructions. We propose a new semi-automatic method that uses topological features to guide users in tracing neurons and integrate this method within a virtual reality (VR) framework previously used for manual tracing. Our approach augments both visualization and interaction with topological elements, allowing rapid understanding and tracing of complex morphologies. In our pilot study, neuroscientists demonstrated a strong preference for using our tool over prior approaches, reported less fatigue during tracing, and commended the ability to better understand possible paths and alternatives. Quantitative evaluation of the traces reveals that users' tracing speed increased, while retaining similar accuracy compared to a fully manual approach.

Structured Adaptive Mesh Refinement (Structured AMR) enables simulations to adapt the domain resolution to save computation and storage, and has become one of the dominant data representations used by scientific simulations; however, efficiently rendering such data remains a challenge. We present an efficient approach for volume- and iso-surface ray tracing of Structured AMR data on GPU-equipped workstations, using a combination of two different data structures. Together, these data structures allow a ray tracing based renderer to quickly determine which segments along the ray need to be integrated and at what frequency, while also providing quick access to all data values required for a smooth sample reconstruction kernel. Our method makes use of the RTX ray tracing hardware for surface rendering, ray marching, space skipping, and adaptive sampling; and allows for interactive changes to the transfer function and implicit iso-surfacing thresholds. We demonstrate that our method achieves high performance with little memory overhead, enabling interactive high quality rendering of complex AMR data sets on individual GPU workstations.