Despite recent advances in single-object front-facing inpainting using NeRF and 3D Gaussian Splatting (3DGS), inpainting in complex 360° scenes remains largely underexplored. This is primarily due to three key challenges: (i) identifying target objects in the 3D field of 360° environments, (ii) dealing with severe occlusions in multi-object scenes, which makes it hard to define regions to inpaint, and (iii) maintaining consistent and high-quality appearance across views effectively.To tackle these challenges, we propose Inpaint360GS, a flexible 360° editing framework based on 3DGS that supports multi-object removal and high-fidelity inpainting in 3D space. By distilling 2D segmentation into 3D and leveraging virtual camera views for contextual guidance, our method enables accurate object-level editing and consistent scene completion. We further introduce a new dataset tailored for 360° inpainting, addressing the lack of ground truth object-free scenes. Experiments demonstrate that Inpaint360GS outperforms existing baselines and achieves state-of-the-art performance. Project page: https://dfki-av.github.io/inpaint360gs/

We introduce a single-view reconstruction technique of volumetric fields in which multiple light scattering effects are omnipresent, such as in clouds. We model the unknown distribution of volumetric fields using an unconditional diffusion model trained on a novel benchmark dataset comprising 1,000 synthetically simulated volumetric density fields. The neural diffusion model is trained on the latent codes of a novel, diffusion-friendly, monoplanar representation. The generative model is used to incorporate a tailored parametric diffusion posterior sampling technique into different reconstruction tasks. A physically-based differentiable volume renderer is employed to provide gradients with respect to light transport in the latent space. This stands in contrast to classic NeRF approaches and makes the reconstructions better aligned with observed data. Through various experiments, we demonstrate single-view reconstruction of volumetric clouds at a previously unattainable quality.

Abstract Maintaining the maximum stiffness of components with as little material as possible is an overarching objective in computational design and engineering. It is well‐established that in stiffness‐optimal designs, material is aligned with orthogonal principal stress directions. In the limit of material volume, this alignment forms micro‐structures resembling quads or hexahedra. Achieving a globally consistent layout of such orthogonal micro‐structures presents a significant challenge, particularly in three‐dimensional settings. In this paper, we propose a novel geometric algorithm for compiling stress‐aligned hexahedral lattice structures. Our method involves deforming an input mesh under load to align the resulting stress field along an orthogonal basis. The deformed object is filled with a hexahedral grid, and the deformation is reverted to recover the original shape. The resulting stress‐aligned mesh is used as basis for a final hollowing procedure, generating a volume‐reduced stiff infill composed of hexahedral micro‐structures. We perform quantitative comparisons with structural optimization and hexahedral meshing approaches and demonstrate the superior mechanical performance of our designs with finite element simulation experiments.

We introduce the Stress-Guided Lightweight Design Benchmark (SGLDBench), a comprehensive benchmark suite for applying and evaluating material layout strategies to generate stiff, lightweight designs in 3D domains. SGLDBench provides a seamlessly integrated simulation and analysis framework, including six reference strategies and a scalable multigrid elasticity solver to efficiently execute these strategies and validate the stiffness of their results. This facilitates the systematic analysis and comparison of design strategies based on the mechanical properties they achieve. SGLDBench enables the evaluation of diverse load conditions and, through the tight integration of the solver, supports high-resolution designs and stiffness analysis. Additionally, SGLDBench emphasizes visual analysis to explore the relationship between the geometric structure of a design and the distribution of stresses, offering insights into the specific properties and behaviors of different design strategies. SGLDBench's specific features are highlighted through several experiments, comparing the results of reference strategies with respect to geometric and mechanical properties.

Recently, high-fidelity scene reconstruction with an optimized 3D Gaussian splat representation has been introducedfor novel view synthesis from sparse image sets. Making such representations suitable for applications like network streaming and rendering on low-power devices requires significantly reduced memory consumption as well as improved rendering efficiency. We propose a compressed 3D Gaussian splat representation that utilizes sensitivity-aware vector clustering with quantization-aware training to compress directional colors and Gaussian parameters. The learned codebooks have low bitrates and achieve a compression rate of up to 31 × on real-world scenes with only minimal degradation of visual quality. We demonstrate that the compressed splat representation can be efficiently rendered with hardware rasterization on lightweight GPUs at up to 4 × higher framerates than reported via an optimized GPU compute pipeline. Extensive experiments across multiple datasets demonstrate the robustness and rendering speed of the proposed approach.

We introduce the Autoregressive PDE Emulator Benchmark (APEBench), a comprehensive benchmark suite to evaluate autoregressive neural emulators for solving partial differential equations. APEBench is based on JAX and provides a seamlessly integrated differentiable simulation framework employing efficient pseudo-spectral methods, enabling 46 distinct PDEs across 1D, 2D, and 3D. Facilitating systematic analysis and comparison of learned emulators, we propose a novel taxonomy for unrolled training and introduce a unique identifier for PDE dynamics that directly relates to the stability criteria of classical numerical methods. APEBench enables the evaluation of diverse neural architectures, and unlike existing benchmarks, its tight integration of the solver enables support for differentiable physics training and neural-hybrid emulators. Moreover, APEBench emphasizes rollout metrics to understand temporal generalization, providing insights into the long-term behavior of emulating PDE dynamics. In several experiments, we highlight the similarities between neural emulators and numerical simulators. The code is available at github.com/tum-pbs/apebench and APEBench can be installed via pip install apebench.

Authoring graph visualization requires advanced programming skills, expert domain knowledge, and significant workload. Existing authoring tools either support limited templates of graph visualization, or suffer from a high learning cost. We analyze the design requirements on a tool for graph visualizations, and contribute Nuwa, a user-friendly declarative authoring tool for the interactive specification of graph visualizations in terms of data, entity, change, and encoding. Our implementation empowers users to conveniently create, compare, and modulate comprehensive graph visualizations with a wide range of styles. We showcase various examples to verify the expressiveness of Nuwa. Via an expert interview and the analysis on cognitive dimensions we evaluate the usability of Nuwa.

Database systems face challenges when using mutual information (MI) for analyzing non-linear relationships between large timeseries, due to computational and memory requirements. Interactive workflows are especially hindered by long response times. To address these challenges, we present timeseries neural MI fields (TNMIFs), a compact data structure that has been trained to reconstruct MI efficiently across various time-windows and window positions in large timeseries. We demonstrate learning and reconstruction with a large timeseries dataset comprising 1420 timeseries, each storing data at 1639 timesteps. While the learned data structure consumes only 45 megabytes, it answers queries for the MI estimates between the windows in a selected timeseries and the corresponding windows in all other timeseries within 44 milliseconds. Given a measure of similarity between timeseries based on windowed MI estimates, even the matrix showing all mutual timeseries similarities can be computed in less than 32 seconds. To support measuring dependence between lagged timeseries, an extended data structure learns to reconstruct MI to positively (future) and negatively (past) lagged windows. Using a maximum lag of 64 in both directions decreases query times by about a factor of 10.

Image-based reconstruction of a three-dimensional heterogeneous density field in the presence of multiple scattering of light is intrinsically under-constrained. This leads to reconstructions that look similar to the ground truth when rendered, but the recovered field is often far off the real one. We shed light on the sources of uncertainty in the reconstruction process which are responsible for this ambiguity, and propose the following approaches to improve the reconstruction quality: Firstly, we introduce a new path sampling strategy, which yields more accurate estimates of the gradients of the extinction field. Secondly, we build upon the observation that the variance in the loss computation is one source of bias in the optimization process. To reduce this variance in the primal estimator, we propose exploiting temporal coherence by reusing previously rendered images. All this is coupled with a constraint on spatial object occupancy, which restricts the problem to a reconstructed shape prior. In a number of examples we demonstrate that compared to existing approaches the proposed reconstruction pipeline leads to improved accuracy of the reconstructed density fields.

The large-scale motions in 3D turbulent channel flows, known as Turbulent Superstructures (TSS), play an essential role in the dynamics of small-scale structures within the turbulent boundary layer. However, as of today, there is no common agreement on the spatial and temporal relationships between these multiscale structures. We propose a novel space-time visualization technique for analyzing the temporal evolution of these multiscale structures in their spatial context and, thus, to further shed light on the conceptually different explanations of their dynamics. Since the temporal dynamics of TSS are believed to influence the structures in the turbulent boundary layer, we propose a combination of a 2D space-time velocity plot with an orthogonal 2D plot of projected 3D flow structures, which can interactively span the time and the space axis. Besides flow structures indicating the fluid motion, we propose showing the variations in derived fields as an additional source of explanation. The relationships between the structures in different spatial and temporal scales can be more effectively resolved by using various filtering operations and image registration algorithms. To reduce the information loss due to the non-injective nature of projection, spatial information is encoded into transparency or color. Since the proposed visualization is heavily demanding computational resources and memory bandwidth to stream unsteady flow fields and instantly compute derived 3D flow structures, the implementation exploits data compression, parallel computation capabilities, and high memory bandwidth on recent GPUs via the CUDA compute library.

Visualizing spatial correlations in 3D ensembles is challenging due to the vast amounts of information that need to be conveyed. Memory and time constraints make it unfeasible to pre-compute and store the correlations between all pairs of domain points. We propose the embedding of adaptive correlation sampling into chord diagrams with hierarchical edge bundling to alleviate these constraints. Entities representing spatial regions are arranged along the circular chord layout via a space-filling curve, and Bayesian optimal sampling is used to efficiently estimate the maximum occurring correlation between any two points from different regions. Hierarchical edge bundling reduces visual clutter and emphasizes the major correlation structures. By selecting an edge, the user triggers a focus diagram in which only the two regions connected via this edge are refined and arranged in a specific way in a second chord layout. For visualizing correlations between two different variables, which are not symmetric anymore, we switch to showing a full correlation matrix. This avoids drawing the same edges twice with different correlation values. We introduce GPU implementations of both linear and non-linear correlation measures to further reduce the time that is required to generate the context and focus views, and to even enable the analysis of correlations in a 1000-member ensemble.

Parallel coordinates are a powerful technique to visually analyze multi-parameter data, i.e., sets of datapoints with potentially many associated parameter values per datapoint. When these sets are large, line rendering becomes a severe performance bottleneck , and since many lines fall into the same pixel the numerical precision of the color buffer is quickly reached. We propose a scalable GPU realization of parallel coordinates building upon 2D pairwise attribute bins, to significantly reduce the number of lines to be rendered. Our approach comprises a GPU compute pipeline that combines shader-based scattering with atomic increment operations to efficiently count how often a line is drawn. These counts are then used to draw all pairwise sub-plots in the parallel coordinates plot, by analytically calculating the opacity for each count and rendering a line with end points determined by the 2D coordinates of the bin. In this way, framebuffer precision issues that are paramount in classical approaches can be overcome. We demonstrate the efficiency of the proposed realization for visualizing a weather forecast ensemble comprising 2.7 billion datapoints, each carrying 7 prognostic floating-point variables like temperature, precipitation and pressure, plus spatial and simulation input variables. We compare our pipeline to a rasterization-based approach regarding performance, and demonstrate interactive brushing at 4 s per frame at full HD viewport resolution.

Abstract Despite the potential of neural scene representations to effectively compress 3D scalar fields at high reconstruction quality, the computational complexity of the training and data reconstruction step using scene representation networks limits their use in practical applications. In this paper, we analyse whether scene representation networks can be modified to reduce these limitations and whether such architectures can also be used for temporal reconstruction tasks. We propose a novel design of scene representation networks using GPU tensor cores to integrate the reconstruction seamlessly into on‐chip raytracing kernels, and compare the quality and performance of this network to alternative network‐ and non‐network‐based compression schemes. The results indicate competitive quality of our design at high compression rates, and significantly faster decoding times and lower memory consumption during data reconstruction. We investigate how density gradients can be computed using the network and show an extension where density, gradient and curvature are predicted jointly. As an alternative to spatial super‐resolution approaches for time‐varying fields, we propose a solution that builds upon latent‐space interpolation to enable random access reconstruction at arbitrary granularity. We summarize our findings in the form of an assessment of the strengths and limitations of scene representation networks for compression domain volume rendering, and outline future research directions. Source code: https://github.com/shamanDevel/fV‐SRN

For an ensemble of 3D multi-parameter fields, we present a visual analytics workflow to analyse whether and which parts of a selected multi-parameter distribution is present in all ensemble members. Supported by a parallel coordinate plot, a multi-parameter brush is applied to all ensemble members to select data points with similar multi-parameter distribution. By a combination of spatial sub-division and a covariance analysis of partitioned sub-sets of data points, a tight partition in multi-parameter space with reduced number of selected data points is obtained. To assess the representativeness of the selected multi-parameter distribution across the ensemble, we propose a novel extension of violin plots that can show multiple parameter distributions simultaneously. We investigate the visual design that effectively conveys (dis-)similarities in multi-parameter distributions, and demonstrate that users can quickly comprehend parameter-specific differences regarding distribution shape and representativeness from a side-by-side view of these plots. In a 3D spatial view, users can analyse and compare the spatial distribution of selected data points in different ensemble members via interval-based isosurface raycasting. In two real-world application cases we show how our approach is used to analyse the multi-parameter distributions across an ensemble of 3D fields.

This February 2022 issue of theIEEE Transactions on Visualization and Computer Graphics (TVCG)contains the proceedings of IEEE VIS 2021, held online on October 24-29, 2021, with General Chairs from Tulane University and Universidade de Sao Paulo. With IEEE VIS 2021, the conference series is in its 32nd year.

A central challenge in data visualization is to understand which data samples are required to generate an image of a data set in which the relevant information is encoded. In this article, we make a first step towards answering the question of whether an artificial neural network can predict where to sample the data with higher or lower density, by learning of correspondences between the data, the sampling patterns and the generated images. We introduce a novel neural rendering pipeline, which is trained end-to-end to generate a sparse adaptive sampling structure from a given low-resolution input image, and reconstructs a high-resolution image from the sparse set of samples. For the first time, to the best of our knowledge, we demonstrate that the selection of structures that are relevant for the final visual representation can be jointly learned together with the reconstruction of this representation from these structures. Therefore, we introduce differentiable sampling and reconstruction stages, which can leverage back-propagation based on supervised losses solely on the final image. We shed light on the adaptive sampling patterns generated by the network pipeline and analyze its use for volume visualization including isosurface and direct volume rendering.

We present a differentiable volume rendering solution that provides differentiability of all continuous parameters of the volume rendering process. This differentiable renderer is used to steer the parameters towards a setting with an optimal solution of a problem-specific objective function. We have tailored the approach to volume rendering by enforcing a constant memory footprint via analytic inversion of the blending functions. This makes it independent of the number of sampling steps through the volume and facilitates the consideration of small-scale changes. The approach forms the basis for automatic optimizations regarding external parameters of the rendering process and the volumetric density field itself. We demonstrate its use for automatic viewpoint selection using differentiable entropy as objective, and for optimizing a transfer function from rendered images of a given volume. Optimization of per-voxel densities is addressed in two different ways: First, we mimic inverse tomography and optimize a 3D density field from images using an absorption model. This simplification enables comparisons with algebraic reconstruction techniques and state-of-the-art differentiable path tracers. Second, we introduce a novel approach for tomographic reconstruction from images using an emission-absorption model with post-shading via an arbitrary transfer function.

Abstract Accurate subsurface scattering solutions require the integration of optical material properties along many complicated light paths. We present a method that learns a simple geometric approximation of random paths in a homogeneous volume with translucent material. The generated representation allows determining the absorption along the path as well as a direct lighting contribution, which is representative of all scatter events along the path. A sequence of conditional variational auto‐encoders (CVAEs) is trained to model the statistical distribution of the photon paths inside a spherical region in the presence of multiple scattering events. A first CVAE learns how to sample the number of scatter events, occurring on a ray path inside the sphere, which effectively determines the probability of this ray to be absorbed. Conditioned on this, a second model predicts the exit position and direction of the light particle. Finally, a third model generates a representative sample of photon position and direction along the path, which is used to approximate the contribution of direct illumination due to in‐scattering. To accelerate the tracing of the light path through the volumetric medium toward the solid boundary, we employ a sphere‐tracing strategy that considers the light absorption and can perform a statistically accurate next‐event estimation. We demonstrate efficient learning using shallow networks of only three layers and no more than 16 nodes. In combination with a GPU shader that evaluates the CVAEs’ predictions, performance gains can be demonstrated for a variety of different scenarios. We analyze the approximation error that is introduced by the data‐driven scattering simulation and shed light on the major sources of error.

Abstract Summed Volume Tables (SVTs) allow one to compute integrals over the data values in any cubical area of a three‐dimensional orthogonal grid in constant time, and they are especially interesting for building spatial search structures for sparse volumes. However, SVTs become extremely memory consuming due to the large values they need to store; for a dataset of n values an SVT requires 𝒪(n log n) bits. The 3D Fenwick tree allows recovering the integral values in 𝒪(log3 n) time, at a memory consumption of 𝒪(n) bits. We propose an algorithm that generates SVT representations that can flexibly trade speed for memory: From similar characteristics as SVTs, over equal memory consumption as 3D Fenwick trees at significantly lower computational complexity, to even further reduced memory consumption at the cost of raising computational complexity. For a 641 × 9601 × 9601 binary dataset, the algorithm can generate an SVT representation that requires 27.0GB and 46 · 8 data fetch operations to retrieve an integral value, compared to 27.5GB and 1521·8 fetches by 3D Fenwick trees, a decrease in fetches of 97%. A full SVT requires 247.6GB and 8 fetches per integral value. We present a novel hierarchical approach to compute and store intermediate prefix sums of SVTs, so that any prescribed memory consumption between 𝒪(n) bits and 𝒪(n log n) bits is achieved. We evaluate the performance of the proposed algorithm in a number of examples considering large volume data, and we perform comparisons to existing alternatives.

This February 2021 issue of the IEEE Transactions on Visualization and Computer Graphics (TVCG) contains the proceedings of IEEE VIS 2020, held online between 25-30 October 2020, hosted by General Chairs from the University of Utah. With IEEE VIS 2020, the conference series is in its 31st year. IEEE VIS consists of three conferences, held concurrently: the IEEE Visual Analytics Science and Technology Conference (VAST), the IEEE Information Visualization Conference (InfoVis), and the IEEE Scientific Visualization Conference (SciVis). These three conferences are the premier venues for the visualization community to exchange the latest ideas and developments, attracting researchers and practitioners alike.

This article presents a comprehensive study of rendering techniques for 3D line sets with transparency. The rendering of transparent lines is widely used for visualizing trajectories of tracer particles in flow fields. Transparency is then used to fade out lines deemed unimportant, based on, for instance, geometric properties or attributes defined along with them. Accurate blending of transparent lines requires rendering the lines in back-to-front or front-to-back order, yet enforcing this order for space-filling 3D line sets with extremely high-depth complexity becomes challenging. In this article, we study CPU and GPU rendering techniques for transparent 3D line sets. We compare accurate and approximate techniques using optimized implementations and several benchmark data sets. We discuss the effects of data size and transparency on quality, performance, and memory consumption. Based on our study, we propose two improvements to per-pixel fragment lists and multi-layer alpha blending. The first improves the rendering speed via an improved GPU sorting operation, and the second improves rendering quality via transparency-based bucketing.

The visual inspection of a hexahedral mesh with respect to element quality is difficult due to clutter and occlusions that are produced when rendering all element faces or their edges simultaneously. Current approaches overcome this problem by using focus on specific elements that are then rendered opaque, and carving away all elements occluding their view. In this work, we make use of advanced GPU shader functionality to generate a focus+context rendering that highlights the elements in a selected region and simultaneously conveys the global mesh structure and deformation field. To achieve this, we propose a gradual transition from edge-based focus rendering to volumetric context rendering, by combining fragment shader-based edge and face rendering with per-pixel fragment lists. A fragment shader smoothly transitions between wireframe and face-based rendering, including focus-dependent rendering style and depth-dependent edge thickness and halos, and per-pixel fragment lists are used to blend fragments in correct visibility order. To maintain the global mesh structure in the context regions, we propose a new method to construct a sheet-based level-of-detail hierarchy and smoothly blend it with volumetric information. The user guides the exploration process by moving a lens-like hotspot. Since all operations are performed on the GPU, interactive frame rates are achieved even for large meshes.

Rendering an accurate image of an isosurface in a volumetric field typically requires large numbers of data samples. Reducing this number lies at the core of research in volume rendering. With the advent of deep learning networks, a number of architectures have been proposed recently to infer missing samples in multidimensional fields, for applications such as image super-resolution. In this article, we investigate the use of such architectures for learning the upscaling of a low resolution sampling of an isosurface to a higher resolution, with reconstruction of spatial detail and shading. We introduce a fully convolutional neural network, to learn a latent representation generating smooth, edge-aware depth and normal fields as well as ambient occlusions from a low resolution depth and normal field. By adding a frame-to-frame motion loss into the learning stage, upscaling can consider temporal variations and achieves improved frame-to-frame coherence. We assess the quality of inferred results and compare it to bi-linear and cubic upscaling. We do this for isosurfaces which were never seen during training, and investigate the improvements when the network can train on the same or similar isosurfaces. We discuss remote visualization and foveated rendering as potential applications.

We present a method to infer physical material parameters, and even external boundaries, from the scanned motion of a homogeneous deformable object via the solution of an inverse problem. Parameters are estimated from real-world data sources such as sparse observations from a Kinect sensor without correspondences. We introduce a novel Lagrangian-Eulerian optimization formulation, including a cost function that penalizes differences to observations during an optimization run. This formulation matches correspondence-free, sparse observations from a single-view depth image with a finite element simulation of deformable bodies. In a number of tests using synthetic datasets and real-world measurements, we analyse the robustness of our approach and the convergence behavior of the numerical optimization scheme.

Abstract We usek‐order Voronoi diagrams to assess the stability ofk‐neighbourhoods in ensembles of 2D point sets, and apply it to analyse the robustness of a dimensionality reduction technique to variations in its input configurations. To measure the stability ofk‐neighbourhoods over the ensemble, we use cells in thek‐order Voronoi diagrams, and consider the smallest coverings of corresponding points in all point sets to identify coherent point subsets with similar neighbourhood relations. We further introduce a pairwise similarity measure for point sets, which is used to select a subset of representative ensemble members via the PageRank algorithm as an indicator of an individual member's value. The stability information is embedded into thek‐order Voronoi diagrams of the representative ensemble members to emphasize coherent point subsets and simultaneously indicate how stable they lie together in all point sets. We use the proposed technique for visualizing the robustness of t‐distributed stochastic neighbour embedding and multi‐dimensional scaling applied to high‐dimensional data in neural network layers and multi‐parameter cloud simulations.

Abstract We present a visualization technique for 2D stress tensor fields based on the construction of a globally conforming lattice. Conformity ensures that the lattice edges follow the principal stress directions and the aspect ratio of lattice elements represents the stress anisotropy. Since such a lattice structure cannot be space‐filling in general, it is constructed from multiple intersecting lattice beams. Conformity at beam intersections is ensured via a constrained optimization problem, by computing the aspect ratio of elements at intersections so that their edges meet when continued along the principal stress lines. In combination with a coloring scheme that encodes relative stress magnitudes, a global visualization is achieved. By introducing additional constraints on the positional variation of the beam intersections, coherent visualizations are achieved when external loads or material parameters are changed. In a number of experiments using non‐trivial scenarios, we demonstrate the capability of the proposed visualization technique to show the global and local structure of a given stress field.

We present techniques to improve the understanding of pattern forming processes in Rayleigh-Bénard-type convective heat transport, through visually guided exploration of convection features in time-averaged turbulent flows. To enable the exploration of roll-like heat transfer pathways and pattern-forming anomalies, we combine feature extraction with interactive visualization of particle trajectories. To robustly determine boundaries between circulation rolls, we propose ridge extraction in a z-averaged temperature field, and in the extracted ridge network we automatically classify topological point defects hinting at pattern forming instabilities. An importance measure based on the circular movement of particles is employed to automatically control the density of 3D trajectories and, thus, enable insights into the heat flow in the interior of rolls. A quantitative analysis of the heat transport within and across cell boundaries, as well as investigations of pattern instabilities in the vicinity of defects, is supported by interactive particle visualization including instant computations of particle density maps. We demonstrate the use of the proposed techniques to explore direct numerical simulations of the 3D Boussinesq equations of convection, giving novel insights into Rayleigh-Bénard-type convective heat transport.

We present a voxel-based rendering pipeline for large 3D line sets that employs GPU ray-casting to achieve scalable rendering including transparency and global illumination effects. Even for opaque lines we demonstrate superior rendering performance compared to GPU rasterization of lines, and when transparency is used we can interactively render amounts of lines that are infeasible to be rendered via rasterization. We propose a direction-preserving encoding of lines into a regular voxel grid, along with the quantization of directions using face-to-face connectivity in this grid. On the regular grid structure, parallel GPU ray-casting is used to determine visible fragments in correct visibility order. To enable interactive rendering of global illumination effects like low-frequency shadows and ambient occlusions, illumination simulation is performed during ray-casting on a level-of-detail (LoD) line representation that considers the number of lines and their lengths per voxel. In this way we can render effects which are very difficult to render via GPU rasterization. A detailed performance and quality evaluation compares our approach to rasterization-based rendering of lines.

Atmospheric fronts play a central role in meteorology, as the boundaries between different air masses and as fundamental features of extra-tropical cyclones. They appear in numerous conceptual model depictions of extra-tropical weather systems. Conceptually, fronts are three-dimensional surfaces in space possessing an innate structural complexity, yet in meteorology, both manual and objective identification and depiction have historically focused on the structure in two dimensions. In this work, we -a team of visualization scientists and meteorologists- propose a novel visualization approach to analyze the three-dimensional structure of atmospheric fronts and related physical and dynamical processes. We build upon existing approaches to objectively identify fronts as lines in two dimensions and extend these to obtain frontal surfaces in three dimensions, using the magnitude of temperature change along the gradient of a moist potential temperature field as the primary identifying factor. We introduce the use of normal curves in the temperature gradient field to visualize a frontal zone (i.e., the transitional zone between the air masses) and the distribution of atmospheric variables in such zones. To enable for the first time a statistical analysis of frontal zones, we present a new approach to obtain the volume enclosed by a zone, by classifying grid boxes that intersect with normal curves emanating from a selected front. We introduce our method by means of an idealized numerical simulation and demonstrate its use with two real-world cases using numerical weather prediction data.

Ensemble sensitivity analysis (ESA) has been established in the atmospheric sciences as a correlation-based approach to determine the sensitivity of a scalar forecast quantity computed by a numerical weather prediction model to changes in another model variable at a different model state. Its applications include determining the origin of forecast errors and placing targeted observations to improve future forecasts. We-a team of visualization scientists and meteorologists-present a visual analysis framework to improve upon current practice of ESA. We support the user in selecting regions to compute a meaningful target forecast quantity by embedding correlation-based grid-point clustering to obtain statistically coherent regions. The evolution of sensitivity features computed via ESA are then traced through time, by integrating a quantitative measure of feature matching into optical-flow-based feature assignment, and displayed by means of a swipe-path showing the geo-spatial evolution of the sensitivities. Visualization of the internal correlation structure of computed features guides the user towards those features robustly predicting a certain weather event. We demonstrate the use of our method by application to real-world 2D and 3D cases that occurred during the 2016 NAWDEX field campaign, showing the interactive generation of hypothesis chains to explore how atmospheric processes sensitive to each other are interrelated.

The papers in this special issue were presented at the 2019 IEEE Pacific Visualization Symposium (IEEE PacificVis 2019), which was held in Bangkok, Thailand from April 23 to 26, 2019 hosted by Chulalongkorn University. The IEEE Pacific Visualization Symposium, sponsored by the IEEE Visualization and Graphics Technical Committee (VGTC), aims to foster greater exchange between visualization researchers and practitioners especially in the Asia-Pacific region.

Jet-streams, their core lines and their role in atmospheric dynamics have been subject to considerable meteorological research since the first half of the twentieth century. Yet, until today no consistent automated feature detection approach has been proposed to identify jet-stream core lines from 3D wind fields. Such 3D core lines can facilitate meteorological analyses previously not possible. Although jet-stream cores can be manually analyzed by meteorologists in 2D as height ridges in the wind speed field, to the best of our knowledge no automated ridge detection approach has been applied to jet-stream core detection. In this work, we -a team of visualization scientists and meteorologists-propose a method that exploits directional information in the wind field to extract core lines in a robust and numerically less involved manner than traditional 3D ridge detection. For the first time, we apply the extracted 3D core lines to meteorological analysis, considering real-world case studies and demonstrating our method's benefits for weather forecasting and meteorological research.

In meteorology, cluster analysis is frequently used to determine representative trends in ensemble weather predictions in a selected spatio-temporal region, e.g., to reduce a set of ensemble members to simplify and improve their analysis. Identified clusters (i.e., groups of similar members), however, can be very sensitive to small changes of the selected region, so that clustering results can be misleading and bias subsequent analyses. In this article, we - a team of visualization scientists and meteorologists-deliver visual analytics solutions to analyze the sensitivity of clustering results with respect to changes of a selected region. We propose an interactive visual interface that enables simultaneous visualization of a) the variation in composition of identified clusters (i.e., their robustness), b) the variability in cluster membership for individual ensemble members, and c) the uncertainty in the spatial locations of identified trends. We demonstrate that our solution shows meteorologists how representative a clustering result is, and with respect to which changes in the selected region it becomes unstable. Furthermore, our solution helps to identify those ensemble members which stably belong to a given cluster and can thus be considered similar. In a real-world application case we show how our approach is used to analyze the clustering behavior of different regions in a forecast of "Tropical Cyclone Karl", guiding the user towards the cluster robustness information required for subsequent ensemble analysis.

This article surveys the history and current state of the art of visualization in meteorology, focusing on visualization techniques and tools used for meteorological data analysis. We examine characteristics of meteorological data and analysis tasks, describe the development of computer graphics methods for visualization in meteorology from the 1960s to today, and visit the state of the art of visualization techniques and tools in operational weather forecasting and atmospheric research. We approach the topic from both the visualization and the meteorological side, showing visualization techniques commonly used in meteorological practice, and surveying recent studies in visualization research aimed at meteorological applications. Our overview covers visualization techniques from the fields of display design, 3D visualization, flow dynamics, feature-based visualization, comparative visualization and data fusion, uncertainty and ensemble visualization, interactive visual analysis, efficient rendering, and scalability and reproducibility. We discuss demands and challenges for visualization research targeting meteorological data analysis, highlighting aspects in demonstration of benefit, interactive visual analysis, seamless visualization, ensemble visualization, 3D visualization, and technical issues.

Porous structures such as trabecular bone are widely seen in nature. These structures are lightweight and exhibit strong mechanical properties. In this paper, we present a method to generate bone-like porous structures as lightweight infill for additive manufacturing. Our method builds upon and extends voxel-wise topology optimization. In particular, for the purpose of generating sparse yet stable structures distributed in the interior of a given shape, we propose upper bounds on the localized material volume in the proximity of each voxel in the design domain. We then aggregate the local per-voxel constraints by their p-norm into an equivalent global constraint, in order to facilitate an efficient optimization process. Implemented on a high-resolution topology optimization framework, our results demonstrate mechanically optimized, detailed porous structures which mimic those found in nature. We further show variants of the optimized structures subject to different design specifications, and we analyze the optimality and robustness of the obtained structures.

We propose a new approach for analyzing the temporal growth of the uncertainty in ensembles of weather forecasts which are started from perturbed but similar initial conditions. As an alternative to traditional approaches in meteorology, which use juxtaposition and animation of spaghetti plots of iso-contours, we make use of contour clustering and provide means to encode forecast dynamics and spread in one single visualization. Based on a given ensemble clustering in a specified time window, we merge clusters in time-reversed order to indicate when and where forecast trajectories start to diverge. We present and compare different visualizations of the resulting time-hierarchical grouping, including space-time surfaces built by connecting cluster representatives over time, and stacked contour variability plots. We demonstrate the effectiveness of our visual encodings with forecast examples of the European Centre for Medium-Range Weather Forecasts, which convey the evolution of specific features in the data as well as the temporally increasing spatial variability.

Visualizing sets of isosurfaces from 3D scalar ensemble fields is a difficult task due to inherent occlusion effects, yet it is often required to analyze the uncertainty represented by such an ensemble. In this paper, we present a novel visualization technique for ensembles of isosurfaces based on screen-space silhouettes. By using silhouettes, the displayed information is reduced to avoid occlusions, yet the major shape of the surfaces can be maintained. Our approach preserves spatial coherence and does not make any assumption about the underlying surface distribution. By providing additional mechanisms, i.e., picking, clustering, cutting and animation, we enable the user to explore an ensemble of surfaces interactively.

Abstract The Fluid Implicit Particle method (FLIP) for liquid simulations uses particles to reduce numerical dissipation and provide important visual cues for events like complex splashes and small‐scale features near the liquid surface. Unfortunately, FLIP simulations can be computationally expensive, because they require a dense sampling of particles to fill the entire liquid volume. Furthermore, the vast majority of these FLIP particles contribute nothing to the fluid's visual appearance, especially for larger volumes of liquid. We present a method that only uses FLIP particles within a narrow band of the liquid surface, while efficiently representing the remaining inner volume on a regular grid. We show that a naïve realization of this idea introduces unstable and uncontrollable energy fluctuations, and we propose a novel coupling scheme between FLIP particles and regular grid which overcomes this problem. Our method drastically reduces the particle count and simulation times while yielding results that are nearly indistinguishable from regular FLIP simulations. Our approach is easy to integrate into any existing FLIP implementation.

Abstract For an ensemble of iso‐contours in multi‐dimensional scalar fields, we present new methods to a) visualize their dominant spatial patterns of variability, and b) to compute the conditional probability of the occurrence of a contour at one location given the occurrence at some other location. We first show how to derive a statistical model describing the contour variability, by representing the contours implicitly via signed distance functions and clustering similar functions in a reduced order space. We show that the spatial patterns of the ensemble can then be derived by analytically transforming the boundaries of a confidence interval computed from each cluster into the spatial domain. Furthermore, we introduce a mathematical basis for computing correlations between the occurrences of iso‐contours at different locations. We show that the computation of these correlations can be posed in the reduced order space as an integration problem over a region bounded by four hyper‐planes. To visualize the derived statistical properties we employ a variant of variability plots for streamlines, now including the color coding of probabilities of joint contour occurrences. We demonstrate the use of the proposed techniques for ensemble exploration in a number of 2D and 3D examples, using artificial and meteorological data sets.

Abstract We describe how the pipeline for 3D online reconstruction using commodity depth and image scanning hardware can be made scalable for large spatial extents and high scanning resolutions. Our modified pipeline requires less than 10% of the memory that is required by previous approaches at similar speed and resolution. To achieve this, we avoid storing a 3D distance field and weight map during online scene reconstruction. Instead, surface samples are binned into a high‐resolution binary voxel grid. This grid is used in combination with caching and deferred processing of depth images to reconstruct the scene geometry. For pose estimation, GPU ray‐casting is performed on the binary voxel grid. A one‐to‐one comparison to level‐set ray‐casting in a distance volume indicates slightly lower pose accuracy. To enable unlimited spatial extents and store acquired samples at the appropriate level of detail, we combine a hash map with a hierarchical tree representation.

In many numerical simulations of fluids governed by the incompressible Navier-Stokes equations, the pressure Poisson equation needs to be solved to enforce mass conservation. Multigrid solvers show excellent convergence in simple scenarios, yet they can converge slowly in domains where physically separated regions are combined at coarser scales. Moreover, existing multigrid solvers are tailored to specific discretizations of the pressure Poisson equation, and they cannot easily be adapted to other discretizations. In this paper we analyze the convergence properties of existing multigrid solvers for the pressure Poisson equation in different simulation domains, and we show how to further improve the multigrid convergence rate by using a graph-based extension to determine the coarse grid hierarchy. The proposed multigrid solver is generic in that it can be applied to different kinds of discretizations of the pressure Poisson equation, by using solely the specification of the simulation domain and pre-assembled computational stencils. We analyze the proposed solver in combination with finite difference and finite volume discretizations of the pressure Poisson equation. Our evaluations show that, despite the common assumption, multigrid schemes can exploit their potential even in the most complicated simulation scenarios, yet this behavior is obtained at the price of higher memory consumption.

We present a new method to visualize from an ensemble of flow fields the statistical properties of streamlines passing through a selected location. We use principal component analysis to transform the set of streamlines into a low-dimensional Euclidean space. In this space the streamlines are clustered into major trends, and each cluster is in turn approximated by a multivariate Gaussian distribution. This yields a probabilistic mixture model for the streamline distribution, from which confidence regions can be derived in which the streamlines are most likely to reside. This is achieved by transforming the Gaussian random distributions from the low-dimensional Euclidean space into a streamline distribution that follows the statistical model, and by visualizing confidence regions in this distribution via iso-contours. We further make use of the principal component representation to introduce a new concept of streamline-median, based on existing median concepts in multidimensional Euclidean spaces. We demonstrate the potential of our method in a number of real-world examples, and we compare our results to alternative clustering approaches for particle trajectories as well as curve boxplots.

A key requirement in 3D fabrication is to generate objects with individual exterior shapes and their interior being optimized to application-specific force constraints and low material consumption. Accomplishing this task is challenging on desktop computers, due to the extreme model resolutions that are required to accurately predict the physical shape properties, requiring memory and computational capacities going beyond what is currently available. Moreover, fabrication-specific constraints need to be considered to enable printability. To address these challenges, we present a scalable system for generating 3D objects using topology optimization, which allows to efficiently evolve the topology of high-resolution solids towards printable and light-weight-high-resistance structures. To achieve this, the system is equipped with a high-performance GPU solver which can efficiently handle models comprising several millions of elements. A minimum thickness constraint is built into the optimization process to automatically enforce printability of the resulting shapes. We further shed light on the question how to incorporate geometric shape constraints, such as symmetry and pattern repetition, in the optimization process. We analyze the performance of the system and demonstrate its potential by a variety of different shapes such as interior structures within closed surfaces, exposed support structures, and surface models.

Abstract Virtual cutting of deformable bodies has been an important and active research topic in physically based modelling and simulation for more than a decade. A particular challenge in virtual cutting is the robust and efficient incorporation of cuts into an accurate computational model that is used for the simulation of the deformable body. This report presents a coherent summary of the state of the art in virtual cutting of deformable bodies, focusing on the distinct geometrical and topological representations of the deformable body, as well as the specific numerical discretizations of the governing equations of motion. In particular, we discuss virtual cutting based on tetrahedral, hexahedral and polyhedral meshes, in combination with standard, polyhedral, composite and extended finite element discretizations. A separate section is devoted to meshfree methods. Furthermore, we discuss cutting‐related research problems such as collision detection and haptic rendering in the context of interactive cutting scenarios. The report is complemented with an application study to assess the performance of virtual cutting simulators.

Breast augmentation was the most commonly performed cosmetic surgery procedure in 2011 in the United States. Although aesthetically pleasing surgical results can only be achieved if the correct breast implant is selected from a large variety of different prosthesis sizes and shapes available on the market, surgeons still rely on visual assessment and other subjective approaches for operative planning because of lacking objective evaluation tools. In this paper, we present the development of a software prototype for augmentation mammaplasty simulation solely based on 3-D surface scans, from which patient-specific finite-element models are generated in a semiautomatic process. The finite-element model is used to preoperatively simulate the expected breast shapes using physical soft-tissue mechanics. Our approach uses a novel mechanism based on so-called displacement templates, which, for a specific implant shape and position, describe the respective internal body forces. Due to a highly efficient numerical solver we can provide immediate visual feedback of the simulation results, and thus, the software prototype can be integrated smoothly into the medical workflow. The clinical value of the developed 3-D computational tool for aesthetic breast augmentation surgery planning is demonstrated in patient-specific use cases.

A comparative visualization of multiple volume data sets is challenging due to the inherent occlusion effects, yet it is important to effectively reveal uncertainties, correlations and reliable trends in 3D ensemble fields. In this paper we present bidirectional linking of multi-charts and volume visualization as a means to analyze visually 3D scalar ensemble fields at the data level. Multi-charts are an extension of conventional bar and line charts: They linearize the 3D data points along a space-filling curve and draw them as multiple charts in the same plot area. The bar charts encode statistical information on ensemble members, such as histograms and probability densities, and line charts are overlayed to allow comparing members against the ensemble. Alternative linearizations based on histogram similarities or ensemble variation allow clustering of spatial locations depending on data distribution. Multi-charts organize the data at multiple scales to quickly provide overviews and enable users to select regions exhibiting interesting behavior interactively. They are further put into a spatial context by allowing the user to brush or query value intervals and specific distributions, and to simultaneously visualize the corresponding spatial points via volume rendering. By providing a picking mechanism in 3D and instantly highlighting the corresponding data points in the chart, the user can go back and forth between the abstract and the 3D view to focus the analysis.

Regular grids are attractive for numerical fluid simulations because they give rise to efficient computational kernels. However, for simulating high resolution effects in complicated domains they are only of limited suitability due to memory constraints. In this paper we present a method for liquid simulation on an adaptive octree grid using a hexahedral finite element discretization, which reduces memory requirements by coarsening the elements in the interior of the liquid body. To impose free surface boundary conditions with second order accuracy, we incorporate a particular class of Nitsche methods enforcing the Dirichlet boundary conditions for the pressure in a variational sense. We then show how to construct a multigrid hierarchy from the adaptive octree grid, so that a time efficient geometric multigrid solver can be used. To improve solver convergence, we propose a special treatment of liquid boundaries via composite finite elements at coarser scales. We demonstrate the effectiveness of our method for liquid simulations that would require hundreds of millions of simulation elements in a non-adaptive regime.

Interactive and high-quality visualization of spatially continuous 3D fields represented by scattered distributions of billions of particles is challenging. One common approach is to resample the quantities carried by the particles to a regular grid and to render the grid via volume ray-casting. In large-scale applications such as astrophysics, however, the required grid resolution can easily exceed 10K samples per spatial dimension, letting resampling approaches appear unfeasible. In this paper we demonstrate that even in these extreme cases such approaches perform surprisingly well, both in terms of memory requirement and rendering performance. We resample the particle data to a multiresolution multiblock grid, where the resolution of the blocks is dictated by the particle distribution. From this structure we build an octree grid, and we then compress each block in the hierarchy at no visual loss using wavelet-based compression. Since decompression can be performed on the GPU, it can be integrated effectively into GPU-based out-of-core volume ray-casting. We compare our approach to the perspective grid approach which resamples at run-time into a view-aligned grid. We demonstrate considerably faster rendering times at high quality, at only a moderate memory increase compared to the raw particle set.

Abstract We present an Eulerian method for the real‐time simulation of intrinsic fluid dynamics effects on deforming surfaces. Our method is based on a novel semi‐Lagrangian closest point method for the solution of partial differential equations on animated triangle meshes. We describe this method and demonstrate its use to compute and visualize flow and wave propagation along such meshes at high resolution and speed. Underlying our technique is the efficient conversion of an animated triangle mesh into a time‐dependent implicit representation based on closest surface points. The proposed technique is unconditionally stable with respect to the surface deformation and, in contrast to comparable Lagrangian techniques, its precision does not depend on the level of detail of the surface triangulation.

Abstract In this paper we present a technique which allows us to perform high quality and progressive response surface prediction from multidimensional input samples in an efficient manner. We utilize kriging interpolation to estimate a response surface which minimizes the expectation value and variance of the prediction error. High computational efficiency is achieved by employing parallel matrix and vector operations on the GPU. Our approach differs from previous kriging approaches in that it uses a novel progressive updating scheme for new samples based on blockwise matrix inversion. In this way we can handle very large sample sets to which new samples are continually added. Furthermore, we can monitor the incremental evolution of the surface, providing a means to early terminate the computation when no significant changes have occurred. When the generation of input samples is fast enough, our technique enables steering this generation process interactively to find relevant dependency relations.

Abstract Surface models derived from medical image data often exhibit artefacts, such as noise and staircases, which can be reduced by applying mesh smoothing filters. Usually, an iterative adaption of smoothing parameters to the specific data and continuous re‐evaluation of accuracy and curvature is required. Depending on the number of vertices and the filter algorithm, computation time may vary strongly and interfere with an interactive mesh generation procedure. In this paper, we present an approach to improve the handling of mesh smoothing filters. Based on a GPU mesh smoothing implementation of uniform and anisotropic filters, model quality is evaluated in real‐time and provided to the user to support the mental optimization of input parameters. This is achieved by means of quality graphs and quality bars. Moreover, this framework is used to find appropriate smoothing parameters automatically and to provide data‐specific parameter suggestions. These suggestions are employed to generate a preview gallery with different smoothing suggestions. The preview functionality is additionally used for the inspection of specific artefacts and their possible reduction with different parameter sets.

In uncertain scalar fields where data values vary with a certain probability, the strength of this variability indicates the confidence in the data. It does not, however, allow inferring on the effect of uncertainty on differential quantities such as the gradient, which depend on the variability of the rate of change of the data. Analyzing the variability of gradients is nonetheless more complicated, since, unlike scalars, gradients vary in both strength and direction. This requires initially the mathematical derivation of their respective value ranges, and then the development of effective analysis techniques for these ranges. This paper takes a first step into this direction: Based on the stochastic modeling of uncertainty via multivariate random variables, we start by deriving uncertainty parameters, such as the mean and the covariance matrix, for gradients in uncertain discrete scalar fields. We do not make any assumption about the distribution of the random variables. Then, for the first time to our best knowledge, we develop a mathematical framework for computing confidence intervals for both the gradient orientation and the strength of the derivative in any prescribed direction, for instance, the mean gradient direction. While this framework generalizes to 3D uncertain scalar fields, we concentrate on the visualization of the resulting intervals in 2D fields. We propose a novel color diffusion scheme to visualize both the absolute variability of the derivative strength and its magnitude relative to the mean values. A special family of circular glyphs is introduced to convey the uncertainty in gradient orientation. For a number of synthetic and real-world data sets, we demonstrate the use of our approach for analyzing the stability of certain features in uncertain 2D scalar fields, with respect to both local derivatives and feature orientation.

Abstract The Closest Point Method (CPM) is a method for numerically solving partial differential equations (PDEs) on arbitrary surfaces, independent of the existence of a surface parametrization. The CPM uses a closest point representation of the surface, to solve the unmodified Cartesian version of a surface PDE in a 3D volume embedding, using simple and well‐understood techniques. In this paper, we present the numerical solution of the wave equation and the incompressible Navier‐Stokes equations on surfaces via the CPM, and we demonstrate surface appearance and shape variations in real‐time using this method. To fully exploit the potential of the CPM, we present a novel GPU realization of the entire CPM pipeline. We propose a surface‐embedding adaptive 3D spatial grid for efficient representation of the surface, and present a high‐performance approach using CUDA for converting surfaces given by triangulations into this representation. For real‐time performance, CUDA is also used for the numerical procedures of the CPM. For rendering the surface (and the PDE solution) directly from the closest point representation without the need to reconstruct a triangulated surface, we present a GPU ray‐casting method that works on the adaptive 3D grid.

Abstract Visualizing correlations, i.e., the tendency of uncertain data values at different spatial positions to change contrarily or according to each other, allows inferring on the possible variations of structures in the data. Visualizing global correlation structures, however, is extremely challenging, since it is not clear how the visualization of complicated long‐range dependencies can be integrated into standard visualizations of spatial data. Furthermore, storing correlation information imposes a memory requirement that is quadratic in the number of spatial sample positions. This paper presents a novel approach for visualizing both positive and inverse global correlation structures in uncertain 2D scalar fields, where the uncertainty is modeled via a multivariate Gaussian distribution. We introduce a new measure for the degree of dependency of a random variable on its local and global surroundings, and we propose a spatial clustering approach based on this measure to classify regions of a particular correlation strength. The clustering performs a correlation filtering, which results in a representation that is only linear in the number of spatial sample points. Via cluster coloring the correlation information can be embedded into visualizations of other statistical quantities, such as the mean and the standard deviation. We finally propose a hierarchical cluster subdivision scheme to further allow for the simultaneous visualization of local and global correlations.

Abstract Previous terrain rendering approaches have addressed the aspect of data compression and fast decoding for rendering, but applications where the terrain is repeatedly modified and needs to be buffered on disk have not been considered so far. Such applications require both decoding and encoding to be faster than disk transfer. We present a novel approach for editing gigasample terrain fields at interactive rates and high quality. To achieve high decoding and encoding throughput, we employ a compression scheme for height and pixel maps based on a sparse wavelet representation. On recent GPUs it can encode and decode up to 270 and 730 MPix/s of color data, respectively, at compression rates and quality superior to JPEG, and it achieves more than twice these rates for lossless height field compression. The construction and rendering of a height field triangulation is avoided by using GPU ray‐casting directly on the regular grid underlying the compression scheme. We show the efficiency of our method for interactive editing and continuous level‐of‐detail rendering of terrain fields comprised of several hundreds of gigasamples.

Despite the ongoing efforts in turbulence research, the universal properties of the turbulence small-scale structure and the relationships between small- and large-scale turbulent motions are not yet fully understood. The visually guided exploration of turbulence features, including the interactive selection and simultaneous visualization of multiple features, can further progress our understanding of turbulence. Accomplishing this task for flow fields in which the full turbulence spectrum is well resolved is challenging on desktop computers. This is due to the extreme resolution of such fields, requiring memory and bandwidth capacities going beyond what is currently available. To overcome these limitations, we present a GPU system for feature-based turbulence visualization that works on a compressed flow field representation. We use a wavelet-based compression scheme including run-length and entropy encoding, which can be decoded on the GPU and embedded into brick-based volume ray-casting. This enables a drastic reduction of the data to be streamed from disk to GPU memory. Our system derives turbulence properties directly from the velocity gradient tensor, and it either renders these properties in turn or generates and renders scalar feature volumes. The quality and efficiency of the system is demonstrated in the visualization of two unsteady turbulence simulations, each comprising a spatio-temporal resolution of 10244. On a desktop computer, the system can visualize each time step in 5 seconds, and it achieves about three times this rate for the visualization of a scalar feature volume.

Abstract We present a novel approach for visualizing the positional and geometrical variability of isosurfaces in uncertain 3D scalar fields. Our approach extends recent work by Pöthkow and Hege [ PH10 ] in that it accounts for correlations in the data to determine more reliable isosurface crossing probabilities. We introduce an incremental update‐scheme that allows integrating the probability computation into front‐to‐back volume ray‐casting efficiently. Our method accounts for homogeneous and anisotropic correlations, and it determines for each sampling interval along a ray the probability of crossing an isosurface for the first time. To visualize the positional and geometrical uncertainty even under viewing directions parallel to the surface normal, we propose a new color mapping scheme based on the approximate spatial deviation of possible surface points from the mean surface. The additional use of saturation enables to distinguish between areas of high and low statistical dependence. Experimental results confirm the effectiveness of our approach for the visualization of uncertainty related to position and shape of convex and concave isosurface structures.

An instant and quantitative assessment of spatial distances between two objects plays an important role in interactive applications such as virtual model assembly, medical operation planning, or computational steering. While some research has been done on the development of distance-based measures between two objects, only very few attempts have been reported to visualize such measures in interactive scenarios. In this paper we present two different approaches for this purpose, and we investigate the effectiveness of these approaches for intuitive 3D implant positioning in a medical operation planning system. The first approach uses cylindrical glyphs to depict distances, which smoothly adapt their shape and color to changing distances when the objects are moved. This approach computes distances directly on the polygonal object representations by means of ray/triangle mesh intersection. The second approach introduces a set of slices as additional geometric structures, and uses color coding on surfaces to indicate distances. This approach obtains distances from a precomputed distance field of each object. The major findings of the performed user study indicate that a visualization that can facilitate an instant and quantitative analysis of distances between two objects in interactive 3D scenarios is demanding, yet can be achieved by including additional monocular cues into the visualization.

We present a hexahedral finite element method for simulating cuts in deformable bodies using the corotational formulation of strain at high computational efficiency. Key to our approach is a novel embedding of adaptive element refinements and topological changes of the simulation grid into a geometric multigrid solver. Starting with a coarse hexahedral simulation grid, this grid is adaptively refined at the surface of a cutting tool until a finest resolution level, and the cut is modeled by separating elements along the cell faces at this level. To represent the induced discontinuities on successive multigrid levels, the affected coarse grid cells are duplicated and the resulting connectivity components are distributed to either side of the cut. Drawing upon recent work on octree and multigrid schemes for the numerical solution of partial differential equations, we develop efficient algorithms for updating the systems of equations of the adaptive finite element discretization and the multigrid hierarchy. To construct a surface that accurately aligns with the cuts, we adapt the splitting cubes algorithm to the specific linked voxel representation of the simulation domain we use. The paper is completed by a convergence analysis of the finite element solver and a performance comparison to alternative numerical solution methods. These investigations show that our approach offers high computational efficiency and physical accuracy, and that it enables cutting of deformable bodies at very high resolutions.

In this paper, we present a sample-based approach for surface coloring, which is independent of the original surface resolution and representation. To achieve this, we introduce the Orthogonal Fragment Buffer (OFB)-an extension of the Layered Depth Cube-as a high-resolution view-independent surface representation. The OFB is a data structure that stores surface samples at a nearly uniform distribution over the surface, and it is specifically designed to support efficient random read/write access to these samples. The data access operations have a complexity that is logarithmic in the depth complexity of the surface. Thus, compared to data access operations in tree data structures like octrees, data-dependent memory access patterns are greatly reduced. Due to the particular sampling strategy that is employed to generate an OFB, it also maintains sample coherence, and thus, exhibits very good spatial access locality. Therefore, OFB-based surface coloring performs significantly faster than sample-based approaches using tree structures. In addition, since in an OFB, the surface samples are internally stored in uniform 2D grids, OFB-based surface coloring can efficiently be realized on the GPU to enable interactive coloring of high-resolution surfaces. On the OFB, we introduce novel algorithms for color painting using volumetric and surface-aligned brushes, and we present new approaches for particle-based color advection along surfaces in real time. Due to the intermediate surface representation we choose, our method can be used to color polygonal surfaces as well as any other type of surface that can be sampled.

Streak surfaces are among the most important features to support 3D unsteady flow exploration, but they are also among the computationally most demanding. Furthermore, to enable a feature driven analysis of the flow, one is mainly interested in streak surfaces that show separation profiles and thus detect unstable manifolds in the flow. The computation of such separation surfaces requires to place seeding structures at the separation locations and to let the structures move correspondingly to these locations in the unsteady flow. Since only little knowledge exists about the time evolution of separating streak surfaces, at this time, an automated exploration of 3D unsteady flows using such surfaces is not feasible. Therefore, in this paper we present an interactive approach for the visual analysis of separating streak surfaces. Our method draws upon recent work on the extraction of Lagrangian coherent structures (LCS) and the real-time visualization of streak surfaces on the GPU. We propose an interactive technique for computing ridges in the finite time Lyapunov exponent (FTLE) field at each time step, and we use these ridges as seeding structures to track streak surfaces in the time-varying flow. By showing separation surfaces in combination with particle trajectories, and by letting the user interactively change seeding parameters such as particle density and position, visually guided exploration of separation profiles in 3D is provided. To the best of our knowledge, this is the first time that the reconstruction and display of semantic separable surfaces in 3D unsteady flows can be performed interactively, giving rise to new possibilities for gaining insight into complex flow phenomena.

High quality volume rendering of SPH data requires a complex order-dependent resampling of particle quantities along the view rays. In this paper we present an efficient approach to perform this task using a novel view-space discretization of the simulation domain. Our method draws upon recent work on GPU-based particle voxelization for the efficient resampling of particles into uniform grids. We propose a new technique that leverages a perspective grid to adaptively discretize the view-volume, giving rise to a continuous level-of-detail sampling structure and reducing memory requirements compared to a uniform grid. In combination with a level-of-detail representation of the particle set, the perspective grid allows effectively reducing the amount of primitives to be processed at run-time. We demonstrate the quality and performance of our method for the rendering of fluid and gas dynamics SPH simulations consisting of many millions of particles.

Histology is the study of the structure of biological tissue using microscopy techniques. As digital imaging technology advances, high resolution microscopy of large tissue volumes is becoming feasible; however, new interactive tools are needed to explore and analyze the enormous datasets. In this paper we present a visualization framework that specifically targets interactive examination of arbitrarily large image stacks. Our framework is built upon two core techniques: display-aware processing and GPU-accelerated texture compression. With display-aware processing, only the currently visible image tiles are fetched and aligned on-the-fly, reducing memory bandwidth and minimizing the need for time-consuming global pre-processing. Our novel texture compression scheme for GPUs is tailored for quick browsing of image stacks. We evaluate the usability of our viewer for two histology applications: digital pathology and visualization of neural structure at nanoscale-resolution in serial electron micrographs.

Abstract We present a geometry compression scheme for restricted quadtree meshes and use this scheme for the compression of adaptively triangulated digital elevation models (DEMs). A compression factor of 8–9 is achieved by employing a generalized strip representation of quadtree meshes to incrementally encode vertex positions. In combination with adaptive error‐controlled triangulation, this allows us to significantly reduce bandwidth requirements in the rendering of large DEMs that have to be paged from disk. The compression scheme is specifically tailored for GPU‐based decoding, since it minimizes dependent memory access operations. We can thus trade CPU operations and CPU–GPU data transfer for GPU processing, resulting in twice faster streaming of DEMs from main memory into GPU memory. A novel storage format for decoded DEMs on the GPU facilitates a sustained rendering throughput of about 300 million triangles per second. Due to these properties, the proposed scheme enables scalable rendering with respect to the display resolution independent of the data size. For a maximum screen‐space error below 1 pixel it achieves frame rates of over 100 fps, even on high‐resolution displays. We validate the efficiency of the proposed method by presenting experimental results on scanned elevation models of several hundred gigabytes.

In this paper we present techniques for the visualization of unsteady flows using streak surfaces, which allow for the first time an adaptive integration and rendering of such surfaces in real-time. The techniques consist of two main components, which are both realized on the GPU to exploit computational and bandwidth capacities for numerical particle integration and to minimize bandwidth requirements in the rendering of the surface. In the construction stage, an adaptive surface representation is generated. Surface refinement and coarsening strategies are based on local surface properties like distortion and curvature. We compare two different methods to generate a streak surface: a) by computing a patch-based surface representation that avoids any interdependence between patches, and b) by computing a particle-based surface representation including particle connectivity, and by updating this connectivity during particle refinement and coarsening. In the rendering stage, the surface is either rendered as a set of quadrilateral surface patches using high-quality point-based approaches, or a surface triangulation is built in turn from the given particle connectivity and the resulting triangle mesh is rendered. We perform a comparative study of the proposed techniques with respect to surface quality, visual quality and performance by visualizing streak surfaces in real flows using different rendering options.

We demonstrate the application of advanced 3D visualization techniques to determine the optimal implant design and position in hip joint replacement planning. Our methods take as input the physiological stress distribution inside a patient's bone under load and the stress distribution inside this bone under the same load after a simulated replacement surgery. The visualization aims at showing principal stress directions and magnitudes, as well as differences in both distributions. By visualizing changes of normal and shear stresses with respect to the principal stress directions of the physiological state, a comparative analysis of the physiological stress distribution and the stress distribution with implant is provided, and the implant parameters that most closely replicate the physiological stress state in order to avoid stress shielding can be determined. Our method combines volume rendering for the visualization of stress magnitudes with the tracing of short line segments for the visualization of stress directions. To improve depth perception, transparent, shaded, and antialiased lines are rendered in correct visibility order, and they are attenuated by the volume rendering. We use a focus+context approach to visually guide the user to relevant regions in the data, and to support a detailed stress analysis in these regions while preserving spatial context information. Since all of our techniques have been realized on the GPU, they can immediately react to changes in the simulated stress tensor field and thus provide an effective means for optimal implant selection and positioning in a computational steering environment.

In this paper we investigate scalability limitations in the visualization of large-scale particle-based cosmological simulations, and we present methods to reduce these limitations on current PC architectures. To minimize the amount of data to be streamed from disk to the graphics subsystem, we propose a visually continuous level-of-detail (LOD) particle representation based on a hierarchical quantization scheme for particle coordinates and rules for generating coarse particle distributions. Given the maximal world space error per level, our LOD selection technique guarantees a sub-pixel screen space error during rendering. A brick-based page-tree allows to further reduce the number of disk seek operations to be performed. Additional particle quantities like density, velocity dispersion, and radius are compressed at no visible loss using vector quantization of logarithmically encoded floating point values. By fine-grain view-frustum culling and presence acceleration in a geometry shader the required geometry throughput on the GPU can be significantly reduced. We validate the quality and scalability of our method by presenting visualizations of a particle-based cosmological dark-matter simulation exceeding 10 billion elements.

Particle tracing has been established as a powerful visualization technique to show the dynamics of 3D flows. Particle tracing in 3D, however, quickly overextends the viewer due to the massive amount of visual information that is typically produced by this technique. In this paper, we present strategies to reduce this amount at the same time revealing important structures in the flow. As an importance measure, we introduce a simple, yet effective clustering approach for vector fields, and we use scalar flow quantities at different scales in combination with user-defined regions of interest. These measures are used to control the shape, the appearance, and the density of particles in such a way that the user can focus on the dynamics in important regions at the same time preserving context information. We also introduce a new focus for particle tracing, so called anchor lines. Anchor lines are used to analyze local flow features by visualizing how much particles separate over time and how long it takes until they have separated to a fixed distance. It is of particular interest if the finite time Lyapunov exponent - a scalar quantity that measures the rate of separation of infinitesimally close particles in the flow - is used to guide the placement of anchor lines. The effectiveness of our approaches for the visualization of 3D flow fields is validated using synthetic fields as well as real simulation data.

In this work we present basic methodology for interactive volume editing on GPUs, and we demonstrate the use of these methods to achieve a number of different effects. We present fast techniques to modify the appearance and structure of volumetric scalar fields given on Cartesian grids. Similar to 2D circular brushes as used in surface painting we present 3D spherical brushes for intuitive coloring of particular structures in such fields. This paint metaphor is extended to allow the user to change the data itself, and the use of this functionality for interactive structure isolation, hole filling, and artefact removal is demonstrated. Building on previous work in the field we introduce high-resolution selection volumes, which can be seen as a resolution-based focus+context metaphor. By utilizing such volumes we present a novel approach to interactive volume editing at sub-voxel accuracy. Finally, we introduce a fast technique to paste textures onto iso-surfaces in a 3D scalar field. Since the texture resolution is independent of the volume resolution, this technique allows structure-aligned textures containing appearance properties or textual information to be used for volume augmentation and annotation.

In this paper we present a technique for image deformation in which the user is given flexible control over what kind of deformation to perform. Freeform image extends available image deformation techniques in that it provides a palette of intuitive tools including interactive object segmentation, stiffness editing and force-based controls to achieve both a natural look and realistic animations of deforming parts. The model underlying our approach is physics-based and it is amenable to a variety of different kinds of image manipulations ranging from as-rigid- as-possible to fully elastic deformations. We have developed a multigrid solver for quadrangular finite elements, which achieves real-time performance for high resolution pixel grids. On recent CPUs this solver can handle about 16K co-rotated finite elements at roughly 60 ms.

In this paper we present GPU-based techniques for the interactive visualization of large unsteady 3D flow fields on uniform grids. We propose a novel dual-core approach to asynchronously stream such fields from the CPU, thus enabling the efficient exploration of large time-resolved sequences. This approach decouples visualization from data handling, resulting in interactive frame rates. Built upon a previously published GPU particle engine for flow visualization we have developed new strategies to compute and to visualize path lines and streak lines on the GPU. To provide additional visual cues, focus+context techniques for polygonal meshes have been integrated. The proposed techniques are used in the visual analysis of the Terashake 2.1 earthquake simulation data, and they have been shown to be very effective in revealing the relevant information in this data.

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.

Volume rendered imagery often includes a barrage of 3D information like shape, appearance and topology of complex structures, and it thus quickly overwhelms the user. In particular, when focusing on a specific region a user cannot observe the relationship between various structures unless he has a mental picture of the entire data. In this paper we present ClearView, a GPU-based, interactive framework for texture-based volume ray-casting that allows users which do not have the visualization skills for this mental exercise to quickly obtain a picture of the data in a very intuitive and user-friendly way. ClearView is designed to enable the user to focus on particular areas in the data while preserving context information without visual clutter. ClearView does not require additional feature volumes as it derives any features in the data from image information only. A simple point-and-click interface enables the user to interactively highlight structures in the data. ClearView provides an easy to use interface to complex volumetric data as it only uses transparency in combination with a few specific shaders to convey focus and context information.

In this paper we introduce GPU particle tracing for the visualization of 3D diffusion tensor fields. For about half a million particles, reconstruction of diffusion directions from the tensor field, time integration and rendering can be done at interactive rates. Different visualization options like oriented particles of diffusion-dependent shape, stream lines or stream tubes facilitate the use of particle tracing for diffusion tensor visualization. The proposed methods provide efficient and intuitive means to show the dynamics in diffusion tensor fields, and they accommodate the exploration of the diffusion properties of biological tissue.

As simulation and rendering capabilities continue to increase, volumetric effects like smoke, fire or explosions will be frequently encountered in computer games and virtual environments. In this paper, we present techniques for the visual simulation and rendering of such effects that keep up with the demands for frame rates imposed by such environments. This is achieved by leveraging functionality on recent graphics programming units (GPUs) in combination with a novel approach to model non physics-based, yet realistic variations in flow fields. We show how to use this mechanism for simulating effects as demonstrated in Figure 1. Physics-based simulation is performed on 2D proxy geometries, and simulation results are extruded to 3D using particle or texture based approaches. Our method allows the animator to model and to flexibly control the dynamic behavior of volumetric effects, and it can be used to create plausible animations of a variety of natural phenomena.

We present a particle system for interactive visualization of steady 3D flow fields on uniform grids. For the amount of particles we target, particle integration needs to be accelerated and the transfer of these sets for rendering must be avoided. To fulfill these requirements, we exploit features of recent graphics accelerators to advect particles in the graphics processing unit (GPU), saving particle positions in graphics memory, and then sending these positions through the GPU again to obtain images in the frame buffer. This approach allows for interactive streaming and rendering of millions of particles and it enables virtual exploration of high resolution fields in a way similar to real-world experiments. The ability to display the dynamics of large particle sets using visualization options like shaded points or oriented texture splats provides an effective means for visual flow analysis that is far beyond existing solutions. For each particle, flow quantities like vorticity magnitude and wavelength2 are computed and displayed. Built upon a previously published GPU implementation of a sorting network, visibility sorting of transparent particles is implemented. To provide additional visual cues, the GPU constructs and displays visualization geometry like particle lines and stream ribbons.

Nowadays, direct volume rendering via 3D textures has positioned itself as an efficient tool for the display and visual analysis of volumetric scalar fields. It is commonly accepted, that for reasonably sized data sets appropriate quality at interactive rates can be achieved by means of this technique. However, despite these benefits one important issue has received little attention throughout the ongoing discussion of texture based volume rendering: the integration of acceleration techniques to reduce per-fragment operations. In this paper, we address the integration of early ray termination and empty-space skipping into texture based volume rendering on graphical processing units (GPU). Therefore, we describe volume ray-casting on programmable graphics hardware as an alternative to object-order approaches. We exploit the early z-test to terminate fragment processing once sufficient opacity has been accumulated, and to skip empty space along the rays of sight. We demonstrate performance gains up to a factor of 3 for typical renditions of volumetric data sets on the ATI 9700 graphics card.

A survey of graphics developers on the issue of texture mapping hardware for volume rendering would most likely find that the vast majority of them view limited texture memory as one of the most serious drawbacks of an otherwise fine technology. In this paper, we propose a compression scheme for static and time-varying volumetric data sets based on vector quantization that allows us to circumvent this limitation. We describe a hierarchical quantization scheme that is based on a multiresolution covariance analysis of the original field. This allows for the efficient encoding of large-scale data sets, yet providing a mechanism to exploit temporal coherence in non-stationary fields. We show, that decoding and rendering the compressed data stream can be done on the graphics chip using programmable hardware. In this way, data transfer between the CPU and the graphics processing unit (GPU) can be minimized thus enabling flexible and memory efficient real-time rendering options. We demonstrate the effectiveness of our approach by demonstrating interactive renditions of Gigabyte data sets at reasonable fidelity on commodity graphics hardware.

In this work, the emphasis is on the development of strategies to realize techniques of numerical computing on the graphics chip. In particular, the focus is on the acceleration of techniques for solving sets of algebraic equations as they occur in numerical simulation. We introduce a framework for the implementation of linear algebra operators on programmable graphics processors (GPUs), thus providing the building blocks for the design of more complex numerical algorithms. In particular, we propose a stream model for arithmetic operations on vectors and matrices that exploits the intrinsic parallelism and efficient communication on modern GPUs. Besides performance gains due to improved numerical computations, graphics algorithms benefit from this model in that the transfer of computation results to the graphics processor for display is avoided. We demonstrate the effectiveness of our approach by implementing direct solvers for sparse matrices, and by applying these solvers to multi-dimensional finite difference equations, i.e. the 2D wave equation and the incompressible Navier-Stokes equations.

Acceleration techniques for volume ray-casting are primarily based on pre-computed data structures that allow one to efficiently traverse empty or homogeneous regions. In order to display volume data that successively undergoes color lookups, however, the data structures have to be re-built continuously. In this paper we propose a technique that circumvents this drawback using hardware accelerated texture mapping. In a first rendering pass we employ graphics hardware to interactively determine for each ray where the material is hit. In a second pass ray-casting is performed, but ray traversal starts right in front of the previously determined regions. The algorithm enables interactive classification and it considerably accelerates the view dependent display of selected materials and surfaces from volume data. In contrast to other techniques that are solely based on texture mapping our approach requires less memory and accurately performs the composition of material contributions along the ray.

Real-time free-form deformation tools are primarily based on surface or particle representations to allow for interactive modification and fast rendering of complex models. The efficient handling of volumetric representations, however, is still a challenge and has not yet been addressed sufficiently. Volumetric models, on the other hand, form an important class of representation in many applications. In this paper we present a novel approach to the real-time deformation of scalar volume data sets taking advantage of hardware supported 3D texture mapping. In a prototype implementation a modeling environment has been designed that allows for interactive manipulation of arbitrary parts of volumetric objects. In this way, any desired shape can be modeled and used subsequently in various applications. The underlying algorithms have wide applicability and can be exploited effectively for volume morphing and medical data processing.

Proposes a technique for topology-preserving smoothing of sampled vector fields. The vector field data is first converted into a scalar representation in which time surfaces implicitly exist as level sets. We then locally analyze the dynamic behavior of the level sets by placing geometric primitives in the scalar field and by subsequently distorting these primitives with respect to local variations in this field. From the distorted primitives, we calculate the curvature normal and we use the normal magnitude and its direction to separate distinct flow features. Geometrical and topological considerations are then combined to successively smooth dense flow fields, at the same time retaining their topological structure.

We propose a technique for visualizing steady flow. Using this technique, we first convert the vector field data into a scalar level-set representation. We then analyze the dynamic behavior and subsequent distortion of level-sets and interactively monitor the evolving structures by means of texture-based surface rendering. Next, we combine geometrical and topological considerations to derive a multiscale representation and to implement a method for the automatic placement of a sparse set of graphical primitives depicting homogeneous streams in the fields. Using the resulting algorithms, we have built a visualization system that enables us to effectively display the flow direction and its dynamics even for dense 3D fields.

With fast 3D graphics becoming more and more available even on low end platforms, the focus in developing new graphics hardware is beginning to shift towards higher quality rendering and additional functionality instead of simply higher performance implementations of the traditional graphics pipeline.On this search for improved quality it is important to identify a powerful set of orthogonal features to'be implemented in hardware, which can then be flexibly combined to form new algorithms.Pixel textures are an OpenGL extension by Silicon Graphics that fits into this category.In this paper, we demonstrate the benefits of this extension by presenting several different algorithms exploiting its functionality to achieve high quality, high performance solutions for a variety of different applications from scientific visualization and realistic image synthesis.We conclude that pixel textures are a valuable, powerful feature that should become a standard in future graphics systems.

The reconstruction of isosurfaces from scalar volume data has positioned itself as a fundamental visualization technique in many different applications. But the dramatically increasing size of volumetric data sets often prohibits the handling of these models on affordable low-end single processor architectures. Distributed client-server systems integrating high-bandwidth transmission channels and Web based visualization tools are one alternative to attack this particular problem, but therefore new approaches to reduce the load of numerical processing and the number of generated primitives are required. We outline different scenarios for distributed isosurface reconstruction from large scale volumetric data sets. We demonstrate how to directly generate stripped surface representations and we introduce adaptive and hierarchical concepts to minimize the number of vertices that have to be reconstructed, transmitted and rendered. Furthermore, we propose a novel computation scheme, which allows the user to flexibly exploit locally available resources. The proposed algorithms have been merged together in order to build a platform-independent Web based application. Extensive use of VRML and Java OpenGL bindings allows for the exploration of large scale volume data quite efficiently.

OpenGL and its extensions provide access to advanced per-pixel operations available in the rasterization stage and in the frame buffer hardware of modern graphics workstations.With these mechanisms, completely new rendering algorithms can be designed and implemented in a very particular way.In this paper we extend the idea of extensively using graphics hardware for the rendering of volumetric data sets in various ways.First, we introduce the concept of clipping geometries by means of stencil buffer operations, and we exploit pixel textures for the mapping of volume data to spherical domains.We show ways to use 3D textures for the rendering of lighted and shaded iso-surfaces in real-time without extracting any polygonal representation.Second, we demonstrate that even for volume data on unstructured grids, where only software solutions exist up to now, both methods, iso-surface extraction and direct volume rendering, can be accelerated to new rates of interactivity by simple polygon drawing and frame buffer operations.

A number of techniques have been proposed for rendering volumetric scalar data sets. Techniques have also been proposed for analyzing the three dimensional information contents of the underlying domain, but traditionally the data analysis part is left as a post‐processing step which only involves the rendered two dimensional images. In this paper, we describe a visualization method for scalar volume data which integrates explicit knowledge of the underlying domain into the rendering process. The key of this approach lies in a hierarchical description of the discrete signal, which is decomposed into a sequence of multiscale representations. We describe a technique for the analysis of structures within the data. This allows for the segmentation and classification of the relevant features and can be used to improve their visual sensation. We also address the problem of accelerating the final rendering pass by integrating the extracted object space information into the ray traversal process.

An important challenge in the visualization of three-dimensional volume data is the efficient processing and rendering of time-resolved sequences. Only the use of compression techniques, which allow the reconstruction of the original domain from the compressed one locally, makes it possible to evaluate these sequences in their entirety. In this paper, a new approach for the extraction and visualization of so-called time features from within time-resolved volume data is presented. Based on the asymptotic decay of multiscale representations of spatially localized time evolutions of the data, singular points can be discriminated. Also, the corresponding Lipschitz exponents, which describe the signals' local regularity, can be determined, and can be taken as a measure of the variation in time. The compression ratio and the comprehension of the underlying signal is improved if we first restore the extracted regions which contain the most important information.

Abstract: This paper presents a functional method for the visual simulation of 2‐D or 3‐D turbulent gaseous motion by using time‐varying fractals. The used function incorporates results from the “spectral theory of turbulence”, thereby providing a physics‐based approach adapted to the needs of computer graphics. The involved turbulence function is band‐limited, continuous, differentiable, anisotrop, and smooth, provides different fractal dimensions along each axis, may be evaluated locally with different parameters, and requires only minimal storage space, thus supporting an implementation on large parallel processing networks with small nodes. Inhomogeneity in the form of local disturbances of the turbulence field may also be easily considered. The parameters used to describe turbulent motion are rather intuitive, so that they may be utilized easily by users. Examples for modeling different types of clouds and fire are given.