Abstract Hydrothermal plumes are turbulent structures of intense heat and mineral smoke that rise and disperse into the deep ocean. Existing models generally characterize these systems as a single axisymmetric plume originating from a point source. However, this assumption breaks down in weakly venting, spatially distributed systems, where low‐flux discharge and strong background currents produce faint and distorted plumes that traditional centerline‐based diagnostics fail to characterize. We present a topology‐based visual analysis framework that treats plumes as time‐varying three‐dimensional scalar fields and captures their full structural variability. Using merge trees, we cluster plume snapshots into representative morphologies and uncover a clear coupling between plume structure and phases of the tidal cycle. To support exploration, we introduce a radial merge tree visualization that arranges plume similarity on a tidal clock, revealing periodic behaviors not discernible with existing techniques. We further develop an extremum graph based workflow that identifies discrete surface venting regions within a reconstructed porous rock, and use streamline visualizations to link subsurface transport pathways to the overlying plume.

Abstract Scalar fields derived from 3D X‐ray CT scans of samples undergoing ex situ processes, such as thermal aging, chemical etching, or mechanical stress, pose unique challenges for characterizing similarities and differences across acquisitions. Typically, a sample A (source) is imaged, removed, and subjected to experimental conditions that alter its microstructure, and then re‐imaged as sample B (target) to study the resulting changes. Direct comparison between A and B is rendered impractical if not impossible for current techniques because the challenges of physical and morphological changes are compounded by the effects of geometric misalignment, differences in reconstruction parameters, discretization artifacts, and changes in acquisition settings such as position, beam intensity, or exposure time (the acquisition for sample B often happens at a much later time and the device may have been upgraded or changed). To overcome these challenges, we introduce a geometry‐rich topological representation that uses the hierarchical Morse complex to capture the structural relationships among regions segmented within each sample and shape descriptors to characterize their metric properties. With this data structure, we cast the similarity problem as a sequence of optimizations, each minimizing differences in structure and geometry at a given resolution. The sequence of optimizations begins by aligning the fine‐scale segmentations of the two samples. Following optimization minimizes differences across incrementally coarser levels, producing a fully synchronized hierarchical representation of the two samples. In addition, we introduce a visualization framework that enables interactive exploration and manual editing of the matched hierarchies, thereby allowing an expert user to further improve the quality of the comparison. We apply our workflow to characterize changes in grain structure for energetic materials undergoing aging, match segmentations for materials under different stress conditions, and perform image registration that outperforms state‐of‐the‐art techniques.

The article discusses the transformative impact of Generative AI (GenAI) to the field of vulnerability assessment (VA) and risk management (RM) right from the beginning of their life cycle to the end in cybersecurity (CS). Through a systematic review of over 100 publications (2021-2025), we develop a comprehensive taxonomy classifying GenAI’s dual offensive and defensive applications in VA/RM. The survey spells out the dominant techniques of GenAI and also points towards challenging aspects, which include security, explainability, and trustworthiness. The resultant findings reinforce the belief that GenAI could help resolve many traditional VA/RM challenges, thus providing fertile ground for research and practice in this area.

The massive data generated by scientists daily serve as both a major catalyst for new discoveries and innovations, as well as a significant roadblock that restricts access to the data. Our paper introduces a new approach to removing Big Data barriers and democratizing access to petascale data for the broader scientific community. Our novel data fabric abstraction layer allows user-friendly querying of scientific information while hiding the complexities of dealing with file systems or cloud services. We enable FAIR (Findable, Accessible, Interoperable, and Reusable) access to datasets such as NASA's petascale climate datasets. Our paper presents an approach to managing, visualizing, and analyzing petabytes of data within a browser on equipment ranging from the top NASA supercomputer to commodity hardware like a laptop. Our novel data fabric abstraction utilizes state-of-the art progressive compression algorithms and machine-learning insights to power scalable visualization dashboards for petascale data. The result provides users with the ability to identify extreme events or trends dynamically, expanding access to scientific data and further enabling discoveries. We validate our approach by improving the ability of climate scientists to visually explore their data via three fully interactive dashboards. We further validate our approach by deploying the dashboards and simplified training materials in the classroom at a minority-serving institution. These dashboards, released in simplified form to the general public, contribute significantly to a broader push to democratize the access and use of climate data.

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

Given the constantly increasing number of newly published vulnerabilities, manually assessing their scores (e.g., under the Common Vulnerability Scoring System) has become unfeasible. Recently, learning-based systems have been proposed to automatically predict vulnerability scores. Such systems use vulnerability indexing databases to train deep learning algorithms. However, their practical applicability has important limitations, including a high dependency on the quality and diversity of training data, and high computational requirements. In addition, vulnerability descriptions often do not follow the standard templates and are not rich enough with respect to the expected features. In this paper, we propose a novel architecture that takes advantage of both generative artificial intelligence and lightweight deep learning techniques to provide an efficient and effective solution for automated vulnerability scoring. Data extracted from the National Vulnerability Dataset is fed into a large language model layer, whose output (i.e., an augmented dataset) is then used in a lightweight fine-tuned BERTsmall layer. We provide the results of an extensive experimental assessment of the effect of both each layer of the architecture and end-to-end performances. The results suggest that the combination of GPT3.5-Turbo and BERTsmall provides the most effective accuracy-time trade-off. We also compare the performance of the proposed architecture with other LLMs, BERT models, and cutting-edge approaches. The results show good improvements in prediction quality also when compared to a recent technique that incorporates data from 66 different sources, including the NVD.

Advanced manufacturing creates increasingly complex objects with material compositions that are often difficult to characterize by a single modality. Our collaborating domain scientists are going beyond traditional methods by employing both X-ray and neutron computed tomography to obtain complementary representations expected to better resolve material boundaries. However, the use of two modalities creates its own challenges for visualization, requiring either complex adjustments of bimodal transfer functions or the need for multiple views. Together with experts in nondestructive evaluation, we designed a novel interactive bimodal visualization approach to create a combined view of the co-registered X-ray and neutron acquisitions of industrial objects. Using an automatic topological segmentation of the bivariate histogram of X-ray and neutron values as a starting point, the system provides a simple yet effective interface to easily create, explore, and adjust a bimodal visualization. We propose a widget with simple brushing interactions that enables the user to quickly correct the segmented histogram results. Our semiautomated system enables domain experts to intuitively explore large bimodal datasets without the need for either advanced segmentation algorithms or knowledge of visualization techniques. We demonstrate our approach using synthetic examples, industrial phantom objects created to stress bimodal scanning techniques, and real-world objects, and we discuss expert feedback.

The increasing demand for larger and higher fidelity simulations has made Adaptive Mesh Refinement (AMR) and unstructured mesh techniques essential to focus compute effort and memory cost on just the areas of interest in the simulation domain. The distribution of these meshes over the compute nodes is often determined by balancing compute, memory, and network costs, leading to distributions with jagged nonconvex boundaries that fit together much like puzzle pieces. It is expensive, and sometimes impossible, to re-partition the data posing a challenge for in situ and post hoc visualization as the data cannot be rendered using standard sort-last compositing techniques that require a convex and disjoint data partitioning. We present a new distributed volume rendering and compositing algorithm, Approximate Puzzlepiece Compositing, that enables fast and high-accuracy in-place rendering of AMR and unstructured meshes. Our approach builds on Moment-Based Ordered-Independent Transparency to achieve a scalable, order-independent compositing algorithm that requires little communication and does not impose requirements on the data partitioning. We evaluate the image quality and scalability of our approach on synthetic data and two large-scale unstructured meshes on HPC systems by comparing to state-of-the-art sort-last compositing techniques, highlighting our approach's minimal overhead at higher core counts. We demonstrate that Approximate Puzzlepiece Compositing provides a scalable, high-performance, and high-quality distributed rendering approach applicable to the complex data distributions encountered in large-scale CFD simulations.

Deep learning approaches have provided state-of-the-art performance in many applications by relying on large and overparameterized neural networks. However, such networks are very brittle and are difficult to deploy on resource-limited platforms. Model pruning, i.e., reducing the size of the network, is a widely adopted strategy that can lead to a more robust and compact model. Many heuristics exist for model pruning, but our understanding of the pruning process remains limited due to the black-box nature of a neural network model. Empirical studies show that some heuristics improve performance whereas others can make models more brittle. This work aims to shed light on how different pruning methods alter the network's internal feature representation and the corresponding impact on model performance. To facilitate a comprehensive comparison and characterization of the high-dimensional model feature space, we introduce a visual geometric analysis of feature representations. We evaluated a set of critical geometric concepts decomposed from the commonly adopted classification loss and used them to design a visualization system to compare and highlight the impact of pruning on model performance and feature representation. The proposed tool provides an environment for an in-depth comparison of pruning methods and a comprehensive understanding of how the model responds to common data corruption. By leveraging the proposed visualization, machine learning researchers can reveal the similarities between pruning methods and redundancy in robustness evaluation benchmarks, obtain geometric insights about the differences between pruned models that achieve superior robustness performance, and identify samples that are robust or fragile to model pruning and common data corruption.

Abstract With recent advances in multi‐modal foundation models, the previously text‐only large language models (LLM) have evolved to incorporate visual input, opening up unprecedented opportunities for various applications in visualization. Compared to existing work on LLM‐based visualization works that generate and control visualization with textual input and output only, the proposed approach explores the utilization of the visual processing ability of multi‐modal LLMs to develop Autonomous Visualization Agents (AVAs) that can evaluate the generated visualization and iterate on the result to accomplish user‐defined objectives defined through natural language. We propose the first framework for the design of AVAs and present several usage scenarios intended to demonstrate the general applicability of the proposed paradigm. Our preliminary exploration and proof‐of‐concept agents suggest that this approach can be widely applicable whenever the choices of appropriate visualization parameters require the interpretation of previous visual output. Our study indicates that AVAs represent a general paradigm for designing intelligent visualization systems that can achieve high‐level visualization goals, which pave the way for developing expert‐level visualization agents in the future.

Scientific simulations and observations using particles have been creating large datasets that require effective and efficient data reduction to store, transfer, and analyze. However, current approaches either compress only small data well while being inefficient for large data, or handle large data but with insufficient compression. Toward effective and scalable compression/decompression of particle positions, we introduce new kinds of particle hierarchies and corresponding traversal orders that quickly reduce reconstruction error while being fast and low in memory footprint. Our solution to compression of large-scale particle data is a flexible block-based hierarchy that supports progressive, random-access, and error-driven decoding, where error estimation heuristics can be supplied by the user. For low-level node encoding, we introduce new schemes that effectively compress both uniform and densely structured particle distributions. Our proposed methods thus target all three phases of a tree-based particle compression pipeline, namely tree construction, tree traversal, and node encoding. The improved efficacy and flexibility of these methods over existing compressors are demonstrated through extensive experimentation, using a wide range of scientific particle datasets.

In many scientific endeavors, increasingly abstract representations of data allow for new interpretive methodologies and conceptualization of phenomena. For example, moving from raw imaged pixels to segmented and reconstructed objects allows researchers new insights and means to direct their studies toward relevant areas. Thus, the development of new and improved methods for segmentation remains an active area of research. With advances in machine learning and neural networks, scientists have been focused on employing deep neural networks such as U-Net to obtain pixel-level segmentations, namely, defining associations between pixels and corresponding/referent objects and gathering those objects afterward. Topological analysis, such as the use of the Morse-Smale complex to encode regions of uniform gradient flow behavior, offers an alternative approach: first, create geometric priors, and then apply machine learning to classify. This approach is empirically motivated since phenomena of interest often appear as subsets of topological priors in many applications. Using topological elements not only reduces the learning space but also introduces the ability to use learnable geometries and connectivity to aid the classification of the segmentation target. In this article, we describe an approach to creating learnable topological elements, explore the application of ML techniques to classification tasks in a number of areas, and demonstrate this approach as a viable alternative to pixel-level classification, with similar accuracy, improved execution time, and requiring marginal training data.

High-performance computing (HPC) systems play a critical role in facilitating scientific discoveries. Their scale and complexity (e.g., the number of computational units and software stack) continue to grow as new systems are expected to process increasingly more data and reduce computing time. However, with more processing elements, the probability that these systems will experience a random bit-flip error that corrupts a program's output also increases, which is often recognized as silent data corruption. Analyzing the resiliency of HPC applications in extreme-scale computing to silent data corruption is crucial but difficult. An HPC application often contains a large number of computation units that need to be tested, and error propagation caused by error corruption is complex and difficult to interpret. To accommodate this challenge, we propose an interactive visualization system that helps HPC researchers understand the resiliency of HPC applications and compare their error propagation. Our system models an application's error propagation to study a program's resiliency by constructing and visualizing its fault tolerance boundary. Coordinating with multiple interactive designs, our system enables domain experts to efficiently explore the complicated spatial and temporal correlation between error propagations. At the end, the system integrated a nonmonotonic error propagation analysis with an adjustable graph propagation visualization to help domain experts examine the details of error propagation and answer such questions as why an error is mitigated or amplified by program execution.

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

Processing, managing and publishing the substantial volume of data collected through modern remote sensing technologies in a format that is easy for researchers - across broad skill levels and scientific domains - to view and use presents a formidable challenge. As a prime example, the massive scale of image mosaics produced by NEON’s Airborne Observation Platform (AOP), often several to hundreds of gigabytes in volume, demands efficient data management strategies. Additionally, these aerial mosaics frequently exhibit seams due to variations in lighting conditions during the data acquisition process. These seams undermine the integrity of subsequent scientific analyses, introducing distortions that hinder accurate interpretation of ecological patterns. Finally, one of NEON’s core objectives is to make these data broadly accessible to users, including those who are not yet versed in working with remote sensing data or who wish to view the datasets without needing to download and process them.In response to these challenges, we have developed a comprehensive data management pipeline that enables interactive access for analysis and visualization of NEON’s aerial mosaic collection. This pipeline automates data ingestion, conversion, and publication in a streamable format, facilitating seamless user interaction through web viewers and programming APIs. Moreover, we have implemented a portable blending algorithm aimed at eliminating these problematic seams from large aerial mosaics. This algorithm, grounded in the Conjugate Gradient (CG) method, has been implemented both in CUDA and using the modern SYCL programming model for enhanced portability across diverse computing platforms.Experimental results demonstrate scalable performance across both CPU and GPU architectures. This work not only addresses the challenges of large aerial data management and seam removal but also opens avenues for more accurate and comprehensive scientific investigations within the NEON ecosystem.

The National Science Data Fabric (NSDF) is our solution to the problem of addressing the data-sharing needs of the growing data science community. NSDF is designed to make sharing data across geographically distributed sites easier for users who lack technical expertise and infrastructure. By developing an easy-to-install software stack, we promote the FAIR data-sharing principles in NSDF while leveraging existing high-speed data transfer infrastructures such as Globus and XRootD. This work shows how we leverage latency and throughput information between geo-distributed NSDF sites with NSDF entry points to optimize the automatic coordination of data placement and transfer across the data fabric, which can further improve the efficiency of data sharing.

Topological analysis reveals meaningful structure in data from a variety of domains. Tasks such as image segmentation can be effectively performed on an image’s topological connectivity using graph neural networks (GNNs). We propose two methods for using GNNs to learn from the hierarchical information captured by complexes at multiple levels of topological persistence: one modifies the training procedure of an existing GNN, and one extends the message passing across all levels of the complex. Experiments on real-world data from three domains show the performance benefits to GNNs from using a hierarchical topological structure.

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

Scientific datasets are often analyzed and visualized using isosurfaces. The connected components at or above the isovalue defining these isosurfaces are called superlevel-set components. The vertex set of these superlevel-set components can be used to compute local statistics, such as mean temperature or histogram per component, or to segment the data. However, in datasets produced by acquisition devices or simulations, noise induces many spurious components that clutter the visualization and analysis results. Many of these spurious components would disappear if the data values were slightly adjusted. The notion of persistence captures the stability of a component with respect to function value changes, and so we are interested in computing persistence quickly. Locality of computation is critical for parallel scalability, minimization of communication in a distributed environment, or an out-of-core processing. The recently introduced merge forest attained high performance by exploiting locality, thereby avoiding communication until needed to resolve a feature query. We extend the merge forest to support persistence-based queries and study the locality of these queries by evaluating the traversals of regions of data during a query. We confirm that the majority of evaluated datasets have the property that the noise is mostly local, and thus can be efficiently eliminated without performing a global analysis. Finally, we compare the query running times with those of a triplet merge tree because a triplet merge tree answers all proposed queries in constant time and can be constructed from a merge tree in linear time.

Advanced manufacturing techniques, such as additive manufacturing, enable the design of increasingly complex components for a wide range of industrial applications. However, this complexity makes qualification of the parts, determining whether a part is within some margin of error from the initial design, difficult. To inspect and qualify complex internal geometries that are not accessible with an external probe, parts are typically scanned with computed tomography (CT), and manually compared to the computer-aided design (CAD) model using visual inspections. Matching the CAD model to the 3D reconstructed object is challenging in a traditional desktop environment due to the lack of depth perception and 3D interaction. An additional challenge comes from the geometric complexity of CAD meshes and large-scale CT scans. We present a virtual reality (VR) system for manual qualification, providing a novel defect visualization method. First, we describe a semiautomatic CAD-to-Scan Registration approach in VR using a finite element mesh. Second, we introduce the Defect Box, which enables full-resolution inspection for massive scans and CAD-CT comparison of local defect regions. Finally, our system includes intuitive 3D Metrology methods that enable natural interactions for the measurement of features and defects in VR. We demonstrate our approach on both real and synthetic data and discuss feedback from four expert users in nondestructive qualification.

Repositories are increasingly used for publishing and sharing scientific data. The Materials Commons is a data repository that follows the FAIR (Findable, Accessible, Inter-operable, Reusable) principles. We demonstrate the challenges with FAIR and how Materials Commons solves them. We also discuss the Nationals Science Data Fabric (NSDF) [1], a project that is democratizing data access, and show how Materials Commons with the NSDF software stack accelerates data access and scientific research.

In MPI, collective routines MPI_Alltoall and MPI_Alltoallv play an important role in facilitating all-to-all inter-process data exchange. MPI_Alltoallv is a generalization of MPI_Alltoall, supporting the exchange of non-uniform distributions of data. Popular implementations of MPI, such as MPICH and OpenMPI, implement MPI_Alltoall using a combination of techniques such as the Spread-out algorithm and the Bruck algorithm. Spread-out has a linear complexity in P, compared to Bruck's logarithmic complexity (P: process count); a selection between these two techniques is made at runtime based on the data block size. However, MPI_Alltoallv is typically implemented using only variants of the spread-out algorithm, and therefore misses out on the performance benefits that the log-time Bruck algorithm offers (especially for smaller data loads).

Computational resources are increasingly provisioned to users through cloud-like interfaces. Both academic and commercial cloud offerings exist, but no single standardized interface for common actions such as configuration, launching, and termination of virtual resources exists. This imposes huge technical burden on domain scientist that attempt to take advantage of these resources; even expert users spend considerable time to port their applications from one cloud platform to another.

This work presents NSDF-FUSE, a testbed for evaluating settings and performance of FUSE-based file systems on top of S3-compatible object storage; the testbed is part of a suite of services from the National Science Data Fabric (NSDF) project (an NSF-funded project that is delivering cyberinfrastructures for data scientists). We demonstrate how NSDF-FUSE can be deployed to evaluate eight different mapping packages that mount S3-compatible object storage to a file system, as well as six data patterns representing different I/O operations on two cloud platforms. NSDF-FUSE is open-source and can be easily extended to run with other software mapping packages and different cloud platforms.

Morse complexes are gradient-based topological descriptors with close connections to Morse theory. They are widely applicable in scientific visualization as they serve as important abstractions for gaining insights into the topology of scalar fields. Data uncertainty inherent to scalar fields due to randomness in their acquisition and processing, however, limits our understanding of Morse complexes as structural abstractions. We, therefore, explore uncertainty visualization of an ensemble of 2D Morse complexes that arises from scalar fields coupled with data uncertainty. We propose several statistical summary maps as new entities for quantifying structural variations and visualizing positional uncertainties of Morse complexes in ensembles. Specifically, we introduce three types of statistical summary maps - the probabilistic map, the significance map, and the survival map - to characterize the uncertain behaviors of gradient flows. We demonstrate the utility of our proposed approach using wind, flow, and ocean eddy simulation datasets.

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

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

In the study of packed granular materials, the performance of a sample (e.g., the detonation of a high-energy explosive) often correlates to measurements of a fluid flowing through it. The "effective surface area," the surface area accessible to the airflow, is typically measured using a permeametry apparatus that relates the flow conductance to the permeable surface area via the Carman-Kozeny equation. This equation allows calculating the flow rate of a fluid flowing through the granules packed in the sample for a given pressure drop. However, Carman-Kozeny makes inherent assumptions about tunnel shapes and flow paths that may not accurately hold in situations where the particles possess a wide distribution in shapes, sizes, and aspect ratios, as is true with many powdered systems of technological and commercial interest. To address this challenge, we replicate these measurements virtually on micro-CT images of the powdered material, introducing a new Pore Network Model based on the skeleton of the Morse-Smale complex. Pores are identified as basins of the complex, their incidence encodes adjacency, and the conductivity of the capillary between them is computed from the cross-section at their interface. We build and solve a resistive network to compute an approximate laminar fluid flow through the pore structure. We provide two means of estimating flow-permeable surface area: (i) by direct computation of conductivity, and (ii) by identifying dead-ends in the flow coupled with isosurface extraction and the application of the Carman-Kozeny equation, with the aim of establishing consistency over a range of particle shapes, sizes, porosity levels, and void distribution patterns.

Scientific phenomena are being simulated at ever-increasing resolution and fidelity thanks to advances in modern supercomputers. These simulations produce a deluge of data, putting unprecedented demand on the end-to-end data-movement pipeline that consists of parallel writes for checkpoint and analysis dumps and parallel localized reads for exploratory analysis and visualization tasks. Parallel I/O libraries are often optimized for uniformly distributed large-sized accesses, whereas reads for analysis and visualization benefit from data layouts that enable random-access and multiresolution queries. While multiresolution layouts enable interactive exploration of massive datasets, efficiently writing such layouts in parallel is challenging, and straightforward methods for creating a multiresolution hierarchy can lead to inefficient memory and disk access. In this paper, we propose a compressed, hierarchical layout that facilitates efficient parallel writes, while being efficient at serving random access, multiresolution read queries for post-hoc analysis and visualization. To efficiently write data to such a layout in parallel is challenging due to potential load-balancing issues at both the data transformation and disk I/O steps. Data is often not readily distributed in a way that facilitates efficient transformations necessary for creating a multi resolution hierar-chy. Further, when compression or data reduction is applied, the compressed data chunks may end up with different sizes, confounding efficient parallel I/O. To overcome both these issues, we present a novel two-phase load-balancing strategy to optimize both memory and disk access patterns unique to writing non-uniform multiresolution data. We implement these strategies in a parallel I/O library and evaluate the efficacy of our approach by using real-world simulation data and a novel approach to micro benchmarking on the Theta Supercomputer of Argonne National Laboratory.

Topological analysis is used in several domains to identify and characterize important features in scientific data, and is now one of the established classes of techniques of proven practical use in scientific computing. The growth in parallelism and problem size tackled by modern simulations poses a particular challenge for these approaches. Fundamentally, the global encoding of topological features necessitates interprocess communication that limits their scaling. In this paper, we extend a new topological paradigm to the case of distributed computing, where the construction of a global merge tree is replaced by a distributed data structure, the merge forest, trading slower individual queries on the structure for faster end-to-end performance and scaling. Empirically, the queries that are most negatively affected also tend to have limited practical use. Our experimental results demonstrate the scalability of both the merge forest construction and the parallel queries needed in scientific workflows, and contrast this scalability with the two established alternatives that construct variations of a global tree.

Large-scale simulations on nonuniform particle distributions that evolve over time are widely used in cosmology, molecular dynamics, and engineering. Such data are often saved in an unstructured format that neither preserves spatial locality nor provides metadata for accelerating spatial or attribute subset queries, leading to poor performance of visualization tasks. Furthermore, the parallel I/O strategy used typically writes a file per process or a single shared file, neither of which is portable or scalable across different HPC systems. We present a portable technique for scalable, spatially aware adaptive aggregation that preserves spatial locality in the output. We evaluate our approach on two supercomputers, Stampede2 and Summit, and demonstrate that it outperforms prior approaches at scale, achieving up to 2.5 x faster writes and reads for nonuniform distributions. Furthermore, the layout written by our method is directly suitable for visual analytics, supporting low-latency reads and attribute-based filtering with little overhead.

Aggressive technology scaling trends have worsened the transient fault problem in high-performance computing (HPC) systems. Some faults are benign, but others can lead to silent data corruption (SDC), which represents a serious problem; a fault introducing an error that is not readily detected nto an HPC simulation. Due to the insidious nature of SDCs, researchers have worked to understand their impact on applications. Previous studies have relied on expensive fault injection campaigns with uniform sampling to provide overall SDC rates, but this solution does not provide any feedback on the code regions without samples.

Abstract Single particle tracking (SPT) of fluorescent molecules provides significant insights into the diffusion and relative motion of tagged proteins and other structures of interest in biology. However, despite the latest advances in high‐resolution microscopy, individual particles are typically not distinguished from clusters of particles. This lack of resolution obscures potential evidence for how merging and splitting of particles affect their diffusion and any implications on the biological environment. The particle tracks are typically decomposed into individual segments at observed merge and split events, and analysis is performed without knowing the true count of particles in the resulting segments. Here, we address the challenges in analyzing particle tracks in the context of cancer biology. In particular, we study the tracks of KRAS protein, which is implicated in nearly 20% of all human cancers, and whose clustering and aggregation have been linked to the signaling pathway leading to uncontrolled cell growth. We present a new analysis approach for particle tracks by representing them as tracking graphs and using topological events – merging and splitting, to disambiguate the tracks. Using this analysis, we infer a lower bound on the count of particles as they cluster and create conditional distributions of diffusion speeds before and after merge and split events. Using thousands of time‐steps of simulated and in‐vitro SPT data, we demonstrate the efficacy of our method, as it offers the biologists a new, detailed look into the relationship between KRAS clustering and diffusion speeds.

Extraction of multiscale features using scale-space is one of the fundamental approaches to analyze scalar fields. However, similar techniques for vector fields are much less common, even though it is well known that, for example, turbulent flows contain cascades of nested vortices at different scales. The challenge is that the ideas related to scale-space are based upon iteratively smoothing the data to extract features at progressively larger scale, making it difficult to extract overlapping features. Instead, we consider spatial regions of influence in vector fields as scale, and introduce a new approach for the multiscale analysis of vector fields. Rather than smoothing the flow, we use the natural Helmholtz-Hodge decomposition to split it into small-scale and large-scale components using progressively larger neighborhoods. Our approach creates a natural separation of features by extracting local flow behavior, for example, a small vortex, from large-scale effects, for example, a background flow. We demonstrate our technique on large-scale, turbulent flows, and show multiscale features that cannot be extracted using state-of-the-art techniques.

To address the problem of ever-growing scientific data sizes making data movement a major hindrance to analysis, we introduce a novel encoding for scalar fields: a unified tree of resolution and precision, specifically constructed so that valid cuts correspond to sensible approximations of the original field in the precision-resolution space. Furthermore, we introduce a highly flexible encoding of such trees that forms a parameterized family of data hierarchies. We discuss how different parameter choices lead to different trade-offs in practice, and show how specific choices result in known data representation schemes such as zfp [52], idx [58], and jpeg2000 [76]. Finally, we provide system-level details and empirical evidence on how such hierarchies facilitate common approximate queries with minimal data movement and time, using real-world data sets ranging from a few gigabytes to nearly a terabyte in size. Experiments suggest that our new strategy of combining reductions in resolution and precision is competitive with state-of-the-art compression techniques with respect to data quality, while being significantly more flexible and orders of magnitude faster, and requiring significantly reduced resources.

The trend of rapid technology scaling is expected to make the hardware of high-performance computing (HPC) systems more susceptible to computational errors due to random bit flips. Some bit flips may cause a program to crash or have a minimal effect on the output, but others may lead to silent data corruption (SDC), i.e., undetected yet significant output errors. Classical fault injection analysis methods employ uniform sampling of random bit flips during program execution to derive a statistical resiliency profile. However, summarizing such fault injection result with sufficient detail is difficult, and understanding the behavior of the fault-corrupted program is still a challenge. In this article, we introduce SpotSDC, a visualization system to facilitate the analysis of a program's resilience to SDC. SpotSDC provides multiple perspectives at various levels of detail of the impact on the output relative to where in the source code the flipped bit occurs, which bit is flipped, and when during the execution it happens. SpotSDC also enables users to study the code protection and provide new insights to understand the behavior of a fault-injected program. Based on lessons learned, we demonstrate how what we found can improve the fault injection campaign method.

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

Presents the messages from the VIS 2020 conference General Chairs.

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

Topological approaches to data analysis can answer complex questions about the number, connectivity, and scale of intrinsic features in scalar data. However, the global nature of many topological structures makes their computation challenging at scale, and thus often limits the size of data that can be processed. One key quality to achieving scalability and performance on modern architectures is data locality, i.e., a process operates on data that resides in a nearby memory system, avoiding frequent jumps in data access patterns. From this perspective, topological computations are particularly challenging because the implied data structures represent features that can span the entire data set, often requiring a global traversal phase that limits their scalability. Traditionally, expensive preprocessing is considered an acceptable trade-off as it accelerates all subsequent queries. Most published use cases, however, explore only a fraction of all possible queries, most often those returning small, local features. In these cases, much of the global information is not utilized, yet computing it dominates the overall response time. We address this challenge for merge trees, one of the most commonly used topological structures. In particular, we propose an alternative representation, the merge forest, a collection of local trees corresponding to regions in a domain decomposition. Local trees are connected by a bridge set that allows us to recover any necessary global information at query time. The resulting system couples (i) a preprocessing that scales linearly in practice with (ii) fast runtime queries that provide the same functionality as traditional queries of a global merge tree. We test the scalability of our approach on a shared-memory parallel computer and demonstrate how data structure locality enables the analysis of large data with an order of magnitude performance improvement over the status quo. Furthermore, a merge forest reduces the memory overhead compared to a global merge tree and enables the processing of data sets that are an order of magnitude larger than possible with previous algorithms.

With the rapid adoption of machine learning techniques for large-scale applications in science and engineering comes the convergence of two grand challenges in visualization. First, the utilization of black box models (e.g., deep neural networks) calls for advanced techniques in exploring and interpreting model behaviors. Second, the rapid growth in computing has produced enormous datasets that require techniques that can handle millions or more samples. Although some solutions to these interpretability challenges have been proposed, they typically do not scale beyond thousands of samples, nor do they provide the high-level intuition scientists are looking for. Here, we present the first scalable solution to explore and analyze high-dimensional functions often encountered in the scientific data analysis pipeline. By combining a new streaming neighborhood graph construction, the corresponding topology computation, and a novel data aggregation scheme, namely topology aware datacubes, we enable interactive exploration of both the topological and the geometric aspect of high-dimensional data. Following two use cases from high-energy-density (HED) physics and computational biology, we demonstrate how these capabilities have led to crucial new insights in both applications.

Metallic open-cell foams are promising structural materials with applications in multifunctional systems such as biomedical implants, energy absorbers in impact, noise mitigation, and batteries. There is a high demand for means to understand and correlate the design space of material performance metrics to the material structure in terms of attributes such as density, ligament and node properties, void sizes, and alignments. Currently, X-ray Computed Tomography (CT) scans of these materials are segmented either manually or with skeletonization approaches that may not accurately model the variety of shapes present in nodes and ligaments, especially irregularities that arise from manufacturing, image artifacts, or deterioration due to compression. In this paper, we present a new workflow for analysis of open-cell foams that combines a new density measurement to identify nodal structures, and topological approaches to identify ligament structures between them. Additionally, we provide automated measurement of foam properties. We demonstrate stable extraction of features and time-tracking in an image sequence of a foam being compressed. Our approach allows researchers to study larger and more complex foams than could previously be segmented only manually, and enables the high-throughput analysis needed to predict future foam performance.

The National Science Foundation's Large Facilities are major, multi-user research facilities that operate and manage sophisticated and diverse research instruments and platforms (e.g., large telescopes, interferometers, distributed sensor arrays) that serve a variety of scientific disciplines, from astronomy and physics to geology and biology and beyond. Large Facilities are increasingly dependent on advanced cyberinfrastructure (i.e., computing, data, and software systems; networking; and associated human capital) to enable the broad delivery and analysis of facility-generated data. These cyberinfrastructure tools enable scientists and the public to gain new insights into fundamental questions about the structure and history of the universe, the world we live in today, and how our environment may change in the coming decades. This paper describes a pilot project that aims to develop a model for a Cyberinfrastructure Center of Excellence (CI CoE) that facilitates community building and knowledge sharing and that disseminates and applies best practices and innovative solutions for facility CI.

Particle data are used across a diverse set of large scale simulations, for example, in cosmology, molecular dynamics and combustion. At scale these applications generate tremendous amounts of data, which is often saved in an unstructured format that does not preserve spatial locality; resulting in poor read performance for post-processing analysis and visualization tasks, which typically make spatial queries. In this work, we explore some of the challenges of large scale particle data management, and introduce new techniques to perform scalable, spatially-aware write and read operations. We propose an adaptive aggregation technique to improve the performance of data aggregation, for both uniform and non-uniform particle distributions. Furthermore, we enable efficient read operations by employing a level of detail re-ordering and a multi-resolution layout. Finally, we demonstrate the scalability of our techniques with experiments on large scale simulation workloads up to 256K cores on two different leadership supercomputers, Mira and Theta.

We present a general high-performance technique for ray tracing generalized tube primitives. Our technique efficiently supports tube primitives with fixed and varying radii, general acyclic graph structures with bifurcations, and correct transparency with interior surface removal. Such tube primitives are widely used in scientific visualization to represent diffusion tensor imaging tractographies, neuron morphologies, and scalar or vector fields of 3D flow. We implement our approach within the OSPRay ray tracing framework, and evaluate it on a range of interactive visualization use cases of fixed- and varying-radius streamlines, pathlines, complex neuron morphologies, and brain tractographies. Our proposed approach provides interactive, high-quality rendering, with low memory overhead.

Abstract Image‐ and data‐parallel rendering across multiple nodes on high‐performance computing systems is widely used in visualization to provide higher frame rates, support large data sets, and render data in situ. Specifically for in situ visualization, reducing bottlenecks incurred by the visualization and compositing is of key concern to reduce the overall simulation runtime. Moreover, prior algorithms have been designed to support either image‐ or data‐parallel rendering and impose restrictions on the data distribution, requiring different implementations for each configuration. In this paper, we introduce the Distributed FrameBuffer, an asynchronous image‐processing framework for multi‐node rendering. We demonstrate that our approach achieves performance superior to the state of the art for common use cases, while providing the flexibility to support a wide range of parallel rendering algorithms and data distributions. By building on this framework, we extend the open‐source ray tracing library OSPRay with a data‐distributed API, enabling its use in data‐distributed and in situ visualization applications.

Topological techniques have proven to be a powerful tool in the analysis and visualization of large-scale scientific data. In particular, the Morse-Smale complex and its various components provide a rich framework for robust feature definition and computation. Consequently, there now exist a number of approaches to compute Morse-Smale complexes for large-scale data in parallel. However, existing techniques are based on discrete concepts which produce the correct topological structure but are known to introduce grid artifacts in the resulting geometry. Here, we present a new approach that combines parallel streamline computation with combinatorial methods to construct a high-quality discrete Morse-Smale complex. In addition to being invariant to the orientation of the underlying grid, this algorithm allows users to selectively build a subset of features using high-quality geometry. In particular, a user may specifically select which ascending/descending manifolds are reconstructed with improved accuracy, focusing computational effort where it matters for subsequent analysis. This approach computes Morse-Smale complexes for larger data than previously feasible with significant speedups. We demonstrate and validate our approach using several examples from a variety of different scientific domains, and evaluate the performance of our method.

There currently exist two dominant strategies to reduce data sizes in analysis and visualization: reducing the precision of the data, e.g., through quantization, or reducing its resolution, e.g., by subsampling. Both have advantages and disadvantages and both face fundamental limits at which the reduced information ceases to be useful. The paper explores the additional gains that could be achieved by combining both strategies. In particular, we present a common framework that allows us to study the trade-off in reducing precision and/or resolution in a principled manner. We represent data reduction schemes as progressive streams of bits and study how various bit orderings such as by resolution, by precision, etc., impact the resulting approximation error across a variety of data sets as well as analysis tasks. Furthermore, we compute streams that are optimized for different tasks to serve as lower bounds on the achievable error. Scientific data management systems can use the results presented in this paper as guidance on how to store and stream data to make efficient use of the limited storage and bandwidth in practice.

With the recent advances in deep learning, neural network models have obtained state-of-the-art performances for many linguistic tasks in natural language processing. However, this rapid progress also brings enormous challenges. The opaque nature of a neural network model leads to hard-to-debug-systems and difficult-to-interpret mechanisms. Here, we introduce a visualization system that, through a tight yet flexible integration between visualization elements and the underlying model, allows a user to interrogate the model by perturbing the input, internal state, and prediction while observing changes in other parts of the pipeline. We use the natural language inference problem as an example to illustrate how a perturbation-driven paradigm can help domain experts assess the potential limitation of a model, probe its inner states, and interpret and form hypotheses about fundamental model mechanisms such as attention.

The rapid growth in simulation data requires large-scale parallel implementations of scientific analysis and visualization algorithms, both to produce results within an acceptable timeframe and to enable in situ deployment. However, efficient and scalable implementations, especially of more complex analysis approaches, require not only advanced algorithms, but also an in-depth knowledge of the underlying runtime. Furthermore, different machine configurations and different applications may favor different runtimes, i.e., MPI vs Charm++ vs Legion, etc., and different hardware architectures. This diversity makes developing and maintaining a broadly applicable analysis software infrastructure challenging. We address some of these problems by explicitly separating the implementation of individual tasks of an algorithm from the dataflow connecting these tasks. In particular, we present an embedded domain specific language (EDSL) to describe algorithms using a new task graph abstraction. This task graph is then executed on top of one of several available runtimes (MPI, Charm++, Legion) using a thin layer of library calls. We demonstrate the flexibility and performance of this approach using three different large scale analysis and visualization use cases, i.e., topological analysis, rendering and compositing dataflow, and image registration of large microscopy scans. Despite the unavoidable overheads of a generic solution, our approach demonstrates performance portability at scale, and, in some cases, outperforms hand-optimized implementations.

Abstract Parallel simulation codes often suffer from performance bottlenecks due to network congestion, leaving millions of dollars of investments underutilized. Given a network topology, it is critical to understand how different applications, job placements, routing schemes, etc., are affected by and contribute to network congestion, especially for large and complex networks. Understanding and optimizing communication on large‐scale networks is an active area of research. Domain experts often use exploratory tools to develop both intuitive and formal metrics for network health and performance. This paper presentsTreeScope, an interactive, web‐based visualization tool for exploring network traffic on large‐scale fat‐tree networks.TreeScopeencodes the network topology using a tailored matrix‐based representation and provides detailed visualization of all traffic in the network. We report on the design process ofTreeScope, which has been received positively by network researchers as well as system administrators. Through case studies of real and simulated data, we demonstrate howTreeScope's visual design and interactive support for complex queries on network traffic can provide experts with new insights into the occurrences and causes of congestion in the network.

Abstract We introduce Flexible Live‐Wire, a generalization of the Live‐Wire interactive segmentation technique with floating anchors. In our approach, the user input for Live‐Wire is no longer limited to the setting of pixel‐level anchor nodes, but can use more general anchor sets. These sets can be of any dimension, size, or connectedness. The generality of the approach allows the design of a number of user interactions while providing the same functionality as the traditional Live‐Wire. In particular, we experiment with this new flexibility by designing four novel Live‐Wire interactions based on specific primitives: paint, pinch, probable, and pick anchors. These interactions are only a subset of the possibilities enabled by our generalization. Moreover, we discuss the computational aspects of this approach and provide practical solutions to alleviate any additional overhead. Finally, we illustrate our approach and new interactions through several example segmentations.

Constructing distributed representations for words through neural language models and using the resulting vector spaces for analysis has become a crucial component of natural language processing (NLP). However, despite their widespread application, little is known about the structure and properties of these spaces. To gain insights into the relationship between words, the NLP community has begun to adapt high-dimensional visualization techniques. In particular, researchers commonly use t-distributed stochastic neighbor embeddings (t-SNE) and principal component analysis (PCA) to create two-dimensional embeddings for assessing the overall structure and exploring linear relationships (e.g., word analogies), respectively. Unfortunately, these techniques often produce mediocre or even misleading results and cannot address domain-specific visualization challenges that are crucial for understanding semantic relationships in word embeddings. Here, we introduce new embedding techniques for visualizing semantic and syntactic analogies, and the corresponding tests to determine whether the resulting views capture salient structures. Additionally, we introduce two novel views for a comprehensive study of analogy relationships. Finally, we augment t-SNE embeddings to convey uncertainty information in order to allow a reliable interpretation. Combined, the different views address a number of domain-specific tasks difficult to solve with existing tools.

Tracing neurons in large-scale microscopy data is crucial to establishing a wiring diagram of the brain, which is needed to understand how neural circuits in the brain process information and generate behavior. Automatic techniques often fail for large and complex datasets, and connectomics researchers may spend weeks or months manually tracing neurons using 2D image stacks. We present a design study of a new virtual reality (VR) system, developed in collaboration with trained neuroanatomists, to trace neurons in microscope scans of the visual cortex of primates. We hypothesize that using consumer-grade VR technology to interact with neurons directly in 3D will help neuroscientists better resolve complex cases and enable them to trace neurons faster and with less physical and mental strain. We discuss both the design process and technical challenges in developing an interactive system to navigate and manipulate terabyte-sized image volumes in VR. Using a number of different datasets, we demonstrate that, compared to widely used commercial software, consumer-grade VR presents a promising alternative for scientists.

Atmospheric sciences is the study of physical and chemical phenomena occurring within the Earth's atmosphere. The study entails understanding the state of the Earth's atmosphere, how it is changing over time and why. Understanding how various weather events develop and evolve is often conducted through retrospective analysis of past atmospheric events. Atmospheric scientists can then utilize tools to better predict potential hazards and provide earlier warnings for events that may impact life and property. Several atmospheric state variables can be measured to identify high-impact events, one of which is surface atmospheric pressure. Many weather events are characterized by variations in surface pressure from the mean pressure value (i.e., pressure-perturbations). Accordingly, there is significant interest in extracting and tracking pressure-perturbations both spatially and temporally to better understand the evolution of weather events. Here, we present a visualization and analysis environment that allows interactive exploration of pressure-perturbation data sets. Our system, for the first time, enables atmospheric scientists to interactively explore the spatiotemporal behaviors of pressure-perturbations for a range of values and provides support to leverage other conventional data sets such as radar imagery and wind observations. It also allows atmospheric scientists to evaluate model and parameter sensitivity, which is difficult if not impossible with conventional visualization tools in atmospheric sciences. Finally, we demonstrate the utility of our approach for retrospective analysis using different case studies of recorded severe weather events.

Hierarchical data representations have been shown to be effective tools for coping with large-scale scientific data. Writing hierarchical data on supercomputers, however, is challenging as it often involves all-to-one communication during aggregation of low-resolution data which tends to span the entire network domain, resulting in several bottlenecks. We introduce the concept of indexing templates, which succinctly describe data organization and can be used to alter movement of data in beneficial ways. We present two techniques, domain partitioning and localized aggregation, that leverage indexing templates to alleviate congestion and synchronization overheads during data aggregation. We report experimental results that show significant I/O speedup using our proposed schemes on two of today's fastest supercomputers, Mira and Shaheen II, using the Uintah and S3D simulation frameworks.

Abstract This paper presents a novel approach to visualize the uncertainty in graph‐based segmentations of scalar data. Segmentation of 2D scalar data has wide application in a variety of scientific and medical domains. Typically, a segmentation is presented as a single unambiguous boundary although the solution is often uncertain due to noise or blur in the underlying data as well as imprecision in user input. Our approach provides insight into this uncertainty by computing the “min‐path stability”, a scalar measure analyzing the stability of the segmentation given a set of input constraints. Our approach is efficient, easy to compute, and can be generally applied to either graph cuts or live‐wire (even partial) segmentations. In addition to its general applicability, our new approach to graph cuts uncertainty visualization improves on the time complexity of the current state‐of‐the‐art with an additional fast approximate solution. We also introduce a novel query enabled by our approach which provides users with alternate segmentations by efficiently extracting local minima of the segmentation optimization. Finally, we evaluate our approach and demonstrate its utility on data from scientific and medical applications.

Massive simulations and arrays of sensing devices, in combination with increasing computing resources, have generated large, complex, high-dimensional datasets used to study phenomena across numerous fields of study. Visualization plays an important role in exploring such datasets. We provide a comprehensive survey of advances in high-dimensional data visualization that focuses on the past decade. We aim at providing guidance for data practitioners to navigate through a modular view of the recent advances, inspiring the creation of new visualizations along the enriched visualization pipeline, and identifying future opportunities for visualization research.

Multifield data are common in visualization. However, reducing these data to comprehensible geometry is a challenging problem. Fiber surfaces, an analogy of isosurfaces to bivariate volume data, are a promising new mechanism for understanding multifield volumes. In this work, we explore direct ray casting of fiber surfaces from volume data without any explicit geometry extraction. We sample directly along rays in domain space, and perform geometric tests in range space where fibers are defined, using a signed distance field derived from the control polygons. Our method requires little preprocess, and enables real-time exploration of data, dynamic modification and pixel-exact rendering of fiber surfaces, and support for higher-order interpolation in domain space. We demonstrate this approach on several bivariate datasets, including analysis of multi-field combustion data.

Exploration of atomic trajectories is fundamental to understanding and characterizing complex chemical systems important in many applications. For instance, any new insight into the mechanisms of ionic migration in catalytic materials could lead to a substantial increase in battery performance. A new statistical measure, called the relative-angle distribution, has been proposed to understand complex motion - whether Brownian, ballistic, or diffusive. The relative-angle distribution can be represented as a collection of 1D histograms, but is currently created in a slow, offline process, making any parameter exploration a tedious and time-consuming task. Furthermore, the resulting plot can hide uncertainty in both the data and the visualization. As a result, once rastered or printed at a fixed resolution, these histograms can be misleading. We present a new analysis tool for the exploration of atomic trajectories that combines an interactive histogram visualization with uncertainty information for both data and plotting errors, and is also linked to an interactive 3D display of trajectories. Our tool enables a holistic exploration of trajectories previously not feasible, with the potential for significant scientific impact. In collaboration with domain experts, we have deployed our tool ta analyze molecular dynamics simulations of lithium-ion diffusion. Users have found that the tool significantly accelerates the exploration process and have used it to validate a number of previously unconfirmed hypotheses.

In nuclear engineering, understanding the safety margins of the nuclear reactor via simulations is arguably of paramount importance in predicting and preventing nuclear accidents. It is therefore crucial to perform sensitivity analysis to understand how changes in the model inputs affect the outputs. Modern nuclear simulation tools rely on numerical representations of the sensitivity information — inherently lacking in visual encodings — offering limited effectiveness in communicating and exploring the generated data. In this paper, we design a framework for sensitivity analysis and visualization of multidimensional nuclear simulation data using partition-based, topology-inspired regression models and report on its efficacy. We rely on the established Morse-Smale regression technique, which allows us to partition the domain into monotonic regions where easily interpretable linear models can be used to assess the influence of inputs on the output variability. The underlying computation is augmented with an intuitive and interactive visual design to effectively communicate sensitivity information to nuclear scientists. Our framework is being deployed into the multipurpose probabilistic risk assessment and uncertainty quantification framework RAVEN (Reactor Analysis and Virtual Control Environment). We evaluate our framework using a simulation dataset studying nuclear fuel performance.

The increasing gap between available compute power and I/O capabilities is resulting in simulation pipelines running on leadership computing facilities being reformulated. In particular, in-situ processing is complementing conventional post-process analysis, however, it can be performed by using the same compute resources as the simulation or using secondary dedicated resources. In this paper, we focus on three different in-situ analysis strategies, which use the same compute resources as the ongoing simulation but different data movement strategies. We evaluate the costs incurred by these strategies in terms of run time, scalability and power/energy consumption. Furthermore, we extrapolate power behavior to peta-scale and investigate different design choices through projections. Experimental evaluation at full machine scale on Titan supports that using fewer cores per node for in-situ analysis is the optimum choice in terms of scalability. Hence, further research effort should be devoted towards developing in-situ analysis techniques following this strategy in future high-end systems.

The dragonfly topology is a popular choice for building high-radix, low-diameter, hierarchical networks with high-bandwidth links. On Cray installations of the dragonfly network, job placement policies and routing inefficiencies can lead to significant network congestion for a single job and multi-job workloads. In this paper, we explore the effects of job placement, parallel workloads and network configurations on network health to develop a better understanding of inter-job interference. We have developed a functional network simulator, Damselfly, to model the network behavior of Cray Cascade, and a visual analytics tool, DragonView, to analyze the simulation output. We simulate several parallel workloads based on five representative communication patterns on up to 131,072 cores. Our simulations and visualizations provide unique insight into the buildup of network congestion and present a trade-off between deployment dollar costs and performance of the network.

Abstract Linear projections are one of the most common approaches to visualize high‐dimensional data. Since the space of possible projections is large, existing systems usually select a small set of interesting projections by ranking a large set of candidate projections based on a chosen quality measure. However, while highly ranked projections can be informative, some lower ranked ones could offer important complementary information. Therefore, selection based on ranking may miss projections that are important to provide a global picture of the data. The proposed work fills this gap by presenting the Grassmannian Atlas, a framework that captures the global structures of quality measures in the space of all projections, which enables a systematic exploration of many complementary projections and provides new insights into the properties of existing quality measures.

Large-scale molecular dynamics (MD) simulations are commonly used for simulating the synthesis and ion diffusion of battery materials. A good battery anode material is determined by its capacity to store ion or other diffusers. However, modeling of ion diffusion dynamics and transport properties at large length and long time scales would be impossible with current MD codes. To analyze the fundamental properties of these materials, therefore, we turn to geometric and topological analysis of their structure. In this paper, we apply a novel technique inspired by discrete Morse theory to the Delaunay triangulation of the simulated geometry of a thermally annealed carbon nanosphere. We utilize our computed structures to drive further geometric analysis to extract the interstitial diffusion structure as a single mesh. Our results provide a new approach to analyze the geometry of the simulated carbon nanosphere, and new insights into the role of carbon defect size and distribution in determining the charge capacity and charge dynamics of these carbon based battery materials.

Vector field topology has been successfully applied to represent the structure of steady vector fields. Critical points, one of the essential components of vector field topology, play an important role in describing the complexity of the extracted structure. Simplifying vector fields via critical point cancellation has practical merit for interpreting the behaviors of complex vector fields such as turbulence. However, there is no effective technique that allows direct cancellation of critical points in 3D. This work fills this gap and introduces the first framework to directly cancel pairs or groups of 3D critical points in a hierarchical manner with a guaranteed minimum amount of perturbation based on their robustness, a quantitative measure of their stability. In addition, our framework does not require the extraction of the entire 3D topology, which contains non-trivial separation structures, and thus is computationally effective. Furthermore, our algorithm can remove critical points in any subregion of the domain whose degree is zero and handle complex boundary configurations, making it capable of addressing challenging scenarios that may not be resolved otherwise. We apply our method to synthetic and simulation datasets to demonstrate its effectiveness.

We present an algorithm to compute an approximation of the generalized Voronoi diagram (GVD) on arbitrary collections of 2D or 3D geometric objects. In particular, we focus on datasets with closely spaced objects; GVD approximation is expensive and sometimes intractable on these datasets using previous algorithms. With our approach, the GVD can be computed using commodity hardware even on datasets with many, extremely tightly packed objects. Our approach is to subdivide the space with an octree that is represented with an adjacency structure. We then use a novel adaptive distance transform to compute the distance function on octree vertices. The computed distance field is sampled more densely in areas of close object spacing, enabling robust and parallelizable GVD surface generation. We demonstrate our method on a variety of data and show example applications of the GVD in 2D and 3D.

Abstract We introduce a novel interactive framework for visualizing and exploring high‐dimensional datasets based on subspace analysis and dynamic projections. We assume the high‐dimensional dataset can be represented by a mixture of low‐dimensional linear subspaces with mixed dimensions, and provide a method to reliably estimate the intrinsic dimension and linear basis of each subspace extracted from the subspace clustering. Subsequently, we use these bases to define unique 2D linear projections as viewpoints from which to visualize the data. To understand the relationships among the different projections and to discover hidden patterns, we connect these projections through dynamic projections that create smooth animated transitions between pairs of projections. We introduce the view transition graph, which provides flexible navigation among these projections to facilitate an intuitive exploration. Finally, we provide detailed comparisons with related systems, and use real‐world examples to demonstrate the novelty and usability of our proposed framework.

Abstract Image boundaries are a fundamental component of many interactive digital photography techniques, enabling applications such as segmentation, panoramas, and seamless image composition. Interactions for image boundaries often rely on two complementary but separate approaches: editing via painting or clicking constraints. In this work, we provide a novel, unified approach for interactive editing of pairwise image boundaries that combines the ease of painting with the direct control of constraints. Rather than a sequential coupling, this new formulation allows full use of both interactions simultaneously, giving users unprecedented flexibility for fast boundary editing. To enable this new approach, we provide technical advancements. In particular, we detail a reformulation of image boundaries as a problem of finding cycles, expanding and correcting limitations of the previous work. Our new formulation provides boundary solutions for painted regions with performance on par with state‐of‐the‐art specialized, paint‐only techniques. In addition, we provide instantaneous exploration of the boundary solution space with user constraints. Finally, we provide examples of common graphics applications impacted by our new approach.

Gigapixel panoramas are an increasingly popular digital image application. They are often created as a mosaic of many smaller images. The mosaic acquisition can take many hours causing the individual images to differ in exposure and lighting conditions. A blending operation is often necessary to give the appearance of a seamless image. The blending quality depends on the magnitude of discontinuity along the image boundaries. Often, new boundaries, or seams, are first computed that minimize this transition. Current techniques based on multi-labeling Graph Cuts are too slow and memory intensive for gigapixel sized panoramas. In this paper, we present a parallel, out-of-core seam computing technique that is fast, has small memory footprint, and is capable of running efficiently on different types of parallel systems. Its maximum memory usage is configurable, in the form of a cache, which can improve performance by reducing redundant disk I/O and computations. It shows near-perfect scaling on symmetric multiprocessing systems and good scaling on clusters and distributed shared memory systems. Our technique improves the time required to compute seams for gigapixel imagery from many hours (or even days) to just a few minutes, while still producing boundaries with energy that is on-par with Graph Cuts.

We present an efficient, flexible, adaptive-resolution I/O framework that is suitable for both uniform and Adaptive Mesh Refinement (AMR) simulations. In an AMR setting, current solutions typically represent each resolution level as an independent grid which often results in inefficient storage and performance. Our technique coalesces domain data into a unified, multiresolution representation with fast, spatially aggregated I/O. Furthermore, our framework easily extends to importance-driven storage of uniform grids, for example, by storing regions of interest at full resolution and nonessential regions at lower resolution for visualization or analysis. Our framework, which is an extension of the PIDX framework, achieves state of the art disk usage and I/O performance regardless of resolution of the data, regions of interest, and the number of processes that generated the data. We demonstrate the scalability and efficiency of our framework using the Uintah and S3D large-scale combustion codes on the Mira and Edison supercomputers.

The ever increasing amount of data generated by scientific simulations coupled with system I/O constraints are fueling a need for in-situ analysis techniques. Of particular interest are approaches that produce reduced data representations while maintaining the ability to redefine, extract, and study features in a post-process to obtain scientific insights. This paper presents two variants of in-situ feature extraction techniques using segmented merge trees, which encode a wide range of threshold based features. The first approach is a fast, low communication cost technique that generates an exact solution but has limited scalability. The second is a scalable, local approximation that nevertheless is guaranteed to correctly extract all features up to a predefined size. We demonstrate both variants using some of the largest combustion simulations available on leadership class supercomputers. Our approach allows state-of-the-art, feature-based analysis to be performed in-situ at significantly higher frequency than currently possible and with negligible impact on the overall simulation runtime.

Abstract Extracting features from complex, time‐dependent flow fields remains a significant challenge despite substantial research efforts, especially because most flow features of interest are defined with respect to a given reference frame. Pathline‐based techniques, such as the FTLE field, are complex to implement and resource intensive, whereas scalar transforms, such as λ2, often produce artifacts and require somewhat arbitrary thresholds. Both approaches aim to analyze the flow in a more suitable frame, yet neither technique explicitly constructs one. This paper introduces a new data‐driven technique to compute internal reference frames for large‐scale complex flows. More general than uniformly moving frames, these frames can transform unsteady fields, which otherwise require substantial processing of resources, into a sequence of individual snapshots that can be analyzed using the large body of steady‐flow analysis techniques. Our approach is simple, theoretically well‐founded, and uses an embarrassingly parallel algorithm for structured as well as unstructured data. Using several case studies from fluid flow and turbulent combustion, we demonstrate that internal frames are distinguished, result in temporally coherent structures, and can extract well‐known as well as notoriously elusive features one snapshot at a time.

Abstract Recently, dissipation elements have been gaining popularity as a mechanism for measurement of fundamental properties of turbulent flow, such as turbulence length scales and zonal partitioning. Dissipation elements segment a domain according to the source and destination of streamlines in the gradient flow field of a scalar function f : → ℝ. They have traditionally been computed by numerically integrating streamlines from the center of each voxel in the positive and negative gradient directions, and grouping those voxels whose streamlines terminate at the same extremal pair. We show that the same structures map well to combinatorial topology concepts developed recently in the visualization community. Namely, dissipation elements correspond to sets of cells of the Morse‐Smale complex. The topology‐based formulation enables a more exploratory analysis of the nature of dissipation elements, in particular, in understanding their stability with respect to small scale variations. We present two examples from combustion science that raise significant questions about the role of small scale perturbation and indeed the definition of dissipation elements themselves.

Abstract Dimension reduction techniques are essential for feature selection and feature extraction of complex high‐dimensional data. These techniques, which construct low‐dimensional representations of data, are typically geometrically motivated, computationally efficient and approximately preserve certain structural properties of the data. However, they are often used as black box solutions in data exploration and their results can be difficult to interpret. To assess the quality of these results, quality measures, such as co‐ranking [ LV09 ], have been proposed to quantify structural distortions that occur between high‐dimensional and low‐dimensional data representations. Such measures could be evaluated and visualized point‐wise to further highlight erroneous regions [ MLGH13 ]. In this work, we provide an interactive visualization framework for exploring high‐dimensional data via its two‐dimensional embeddings obtained from dimension reduction, using a rich set of user interactions. We ask the following question: what new insights do we obtain regarding the structure of the data, with interactive manipulations of its embeddings in the visual space? We augment the two‐dimensional embeddings with structural abstractions obtained from hierarchical clusterings, to help users navigate and manipulate subsets of the data. We use point‐wise distortion measures to highlight interesting regions in the domain, and further to guide our selection of the appropriate level of clusterings that are aligned with the regions of interest. Under the static setting, point‐wise distortions indicate the level of structural uncertainty within the embeddings. Under the dynamic setting, on‐the‐fly updates of point‐wise distortions due to data movement and data deletion reflect structural relations among different parts of the data, which may lead to new and valuable insights.

The Helmholtz-Hodge decomposition (HHD), which describes a flow as the sum of an incompressible, an irrotational, and a harmonic flow, is a fundamental tool for simulation and analysis. Unfortunately, for bounded domains, the HHD is not uniquely defined, traditionally, boundary conditions are imposed to obtain a unique solution. However, in general, the boundary conditions used during the simulation may not be known known, or the simulation may use open boundary conditions. In these cases, the flow imposed by traditional boundary conditions may not be compatible with the given data, which leads to sometimes drastic artifacts and distortions in all three components, hence producing unphysical results. This paper proposes the natural HHD, which is defined by separating the flow into internal and external components. Using a completely data-driven approach, the proposed technique obtains uniqueness without assuming boundary conditions a priori. As a result, it enables a reliable and artifact-free analysis for flows with open boundaries or unknown boundary conditions. Furthermore, our approach computes the HHD on a point-wise basis in contrast to the existing global techniques, and thus supports computing inexpensive local approximations for any subset of the domain. Finally, the technique is easy to implement for a variety of spatial discretizations and interpolated fields in both two and three dimensions.

Morse-Smale (MS) complexes have been gaining popularity as a tool for feature-driven data analysis and visualization. However, the quality of their geometric embedding and the sole dependence on the input scalar field data can limit their applicability when expressing application-dependent features. In this paper we introduce a new combinatorial technique to compute an MS complex that conforms to both an input scalar field and an additional, prior segmentation of the domain. The segmentation constrains the MS complex computation guaranteeing that boundaries in the segmentation are captured as separatrices of the MS complex. We demonstrate the utility and versatility of our approach with two applications. First, we use streamline integration to determine numerically computed basins/mountains and use the resulting segmentation as an input to our algorithm. This strategy enables the incorporation of prior flow path knowledge, effectively resulting in an MS complex that is as geometrically accurate as the employed numerical integration. Our second use case is motivated by the observation that often the data itself does not explicitly contain features known to be present by a domain expert. We introduce edit operations for MS complexes so that a user can directly modify their features while maintaining all the advantages of a robust topology-based representation.

As scientific applications target exascale, challenges related to data and energy are becoming dominating concerns. For example, coupled simulation workflows are increasingly adopting in-situ data processing and analysis techniques to address costs and overheads due to data movement and I/O. However it is also critical to understand these overheads and associated trade-offs from an energy perspective. The goal of this paper is exploring data-related energy/performance trade-offs for end-to-end simulation workflows running at scale on current high-end computing systems. Specifically, this paper presents: (1) an analysis of the data-related behaviors of a combustion simulation workflow with an in-situ data analytics pipeline, running on the Titan system at ORNL; (2) a power model based on system power and data exchange patterns, which is empirically validated; and (3) the use of the model to characterize the energy behavior of the workflow and to explore energy/performance trade-offs on current as well as emerging systems.

Parallel I/O library performance can vary greatly in response to user-tunable parameter values such as aggregator count, file count, and aggregation strategy. Unfortunately, manual selection of these values is time consuming and dependent on characteristics of the target machine, the underlying file system, and the dataset itself. Some characteristics, such as the amount of memory per core, can also impose hard constraints on the range of viable parameter values. In this work we address these problems by using machine learning techniques to model the performance of the PIDX parallel I/O library and select appropriate tunable parameter values. We characterize both the network and I/O phases of PIDX on a Cray XE6 as well as an IBM Blue Gene/P system. We use the results of this study to develop a machine learning model for parameter space exploration and performance prediction.

Abstract Analyzing critical points and their temporal evolutions plays a crucial role in understanding the behavior of vector fields. A key challenge is to quantify the stability of critical points: more stable points may represent more important phenomena or vice versa. The topological notion of robustness is a tool which allows us to quantify rigorously the stability of each critical point. Intuitively, the robustness of a critical point is the minimum amount of perturbation necessary to cancel it within a local neighborhood, measured under an appropriate metric. In this paper, we introduce a new analysis and visualization framework which enables interactive exploration of robustness of critical points for both stationary and time‐varying 2D vector fields. This framework allows the end‐users, for the first time, to investigate how the stability of a critical point evolves over time. We show that this depends heavily on the global properties of the vector field and that structural changes can correspond to interesting behavior. We demonstrate the practicality of our theories and techniques on several datasets involving combustion and oceanic eddy simulations and obtain some key insights regarding their stable and unstable features.

The Helmholtz-Hodge decomposition (HHD) is one of the fundamental theorems of fluids describing the decomposition of a flow field into its divergence-free, curl-free, and harmonic components. Solving for the HHD is intimately connected to the choice of boundary conditions which determine the uniqueness and orthogonality of the decomposition. This article points out that one of the boundary conditions used in a recent paper "Meshless Helmholtz-Hodge Decomposition" is, in general, invalid and provides an analytical example demonstrating the problem. We hope that this clarification on the theory will foster further research in this area and prevent undue problems in applying and extending the original approach.

The Helmholtz-Hodge Decomposition (HHD) describes the decomposition of a flow field into its divergence-free and curl-free components. Many researchers in various communities like weather modeling, oceanology, geophysics, and computer graphics are interested in understanding the properties of flow representing physical phenomena such as incompressibility and vorticity. The HHD has proven to be an important tool in the analysis of fluids, making it one of the fundamental theorems in fluid dynamics. The recent advances in the area of flow analysis have led to the application of the HHD in a number of research communities such as flow visualization, topological analysis, imaging, and robotics. However, because the initial body of work, primarily in the physics communities, research on the topic has become fragmented with different communities working largely in isolation often repeating and sometimes contradicting each others results. Additionally, different nomenclature has evolved which further obscures the fundamental connections between fields making the transfer of knowledge difficult. This survey attempts to address these problems by collecting a comprehensive list of relevant references and examining them using a common terminology. A particular focus is the discussion of boundary conditions when computing the HHD. The goal is to promote further research in the field by creating a common repository of techniques to compute the HHD as well as a large collection of example applications in a broad range of areas.

As the visualization field matures, an increasing number of general toolkits are developed to cover a broad range of applications. However, no general tool can incorporate the latest capabilities for all possible applications, nor can the user interfaces and workflows be easily adjusted to accommodate all user communities. As a result, users will often chose either substandard solutions presented in familiar, customized tools or assemble a patchwork of individual applications glued through ad-hoc scripts and extensive, manual intervention. Instead, we need the ability to easily and rapidly assemble the best-in-task tools into custom interfaces and workflows to optimally serve any given application community. Unfortunately, creating such meta-applications at the API or SDK level is difficult, time consuming, and often infeasible due to the sheer variety of data models, design philosophies, limits in functionality, and the use of closed commercial systems. In this paper, we present the ManyVis framework which enables custom solutions to be built both rapidly and simply by allowing coordination and communication across existing unrelated applications. ManyVis allows users to combine software tools with complementary characteristics into one virtual application driven by a single, custom-designed interface.

We demonstrate the application of topological analysis techniques to the rather unexpected domain of software visualization. We collect a memory reference trace from a running program, recasting the linear flow of trace records as a high-dimensional point cloud in a metric space. We use topological persistence to automatically detect significant circular structures in the point cloud, which represent recurrent or cyclical runtime program behaviors. We visualize such recurrences using radial plots to display their time evolution, offering multi-scale visual insights, and detecting potential candidates for memory performance optimization. We then present several case studies to demonstrate some key insights obtained using our techniques.

Topology-based techniques are useful for multiscale exploration of the feature space of scalar-valued functions, such as those derived from the output of large-scale simulations. The Morse-Smale (MS) complex, in particular, allows robust identification of gradient-based features, and therefore is suitable for analysis tasks in a wide range of application domains. In this paper, we develop a two-stage algorithm to construct the 1-skeleton of the Morse-Smale complex in parallel, the first stage independently computing local features per block and the second stage merging to resolve global features. Our implementation is based on MPI and a distributed-memory architecture. Through a set of scalability studies on the IBM Blue Gene/P supercomputer, we characterize the performance of the algorithm as block sizes, process counts, merging strategy, and levels of topological simplification are varied, for datasets that vary in feature composition and size. We conclude with a strong scaling study using scientific datasets computed by combustion and hydrodynamics simulations.

With the onset of extreme-scale computing, I/O constraints make it increasingly difficult for scientists to save a sufficient amount of raw simulation data to persistent storage. One potential solution is to change the data analysis pipeline from a post-process centric to a concurrent approach based on either in-situ or in-transit processing. In this context computations are considered in-situ if they utilize the primary compute resources, while in-transit processing refers to offloading computations to a set of secondary resources using asynchronous data transfers. In this paper we explore the design and implementation of three common analysis techniques typically performed on large-scale scientific simulations: topological analysis, descriptive statistics, and visualization. We summarize algorithmic developments, describe a resource scheduling system to coordinate the execution of various analysis workflows, and discuss our implementation using the DataSpaces and ADIOS frameworks that support efficient data movement between in-situ and in-transit computations. We demonstrate the efficiency of our lightweight, flexible framework by deploying it on the Jaguar XK6 to analyze data generated by S3D, a massively parallel turbulent combustion code. Our framework allows scientists dealing with the data deluge at extreme scale to perform analyses at increased temporal resolutions, mitigate I/O costs, and significantly improve the time to insight.

The placement of tasks in a parallel application on specific nodes of a supercomputer can significantly impact performance. Traditionally, this task mapping has focused on reducing the distance between communicating tasks on the physical network. This minimizes the number of hops that point-to-point messages travel and thus reduces link sharing between messages and contention. However, for applications that use collectives over sub-communicators, this heuristic may not be optimal. Many collectives can benefit from an increase in bandwidth even at the cost of an increase in hop count, especially when sending large messages. For example, placing communicating tasks in a cube configuration rather than a plane or a line on a torus network increases the number of possible paths messages might take. This increases the available bandwidth which can lead to significant performance gains. We have developed Rubik, a tool that provides a simple and intuitive interface to create a wide variety of mappings for structured communication patterns. Rubik supports a number of elementary operations such as splits, tilts, or shifts, that can be combined into a large number of unique patterns. Each operation can be applied to disjoint groups of processes involved in collectives to increase the effective bandwidth. We demonstrate the use of Rubik for improving performance of two parallel codes, pF3D and Qbox, which use collectives over sub-communicators.

Hierarchical, multiresolution data representations enable interactive analysis and visualization of large-scale simulations. One promising application of these techniques is to store high performance computing simulation output in a hierarchical Z (HZ) ordering that translates data from a Cartesian coordinate scheme to a one-dimensional array ordered by locality at different resolution levels. However, when the dimensions of the simulation data are not an even power of 2, parallel HZ ordering produces sparse memory and network access patterns that inhibit I/O performance. This work presents a new technique for parallel HZ ordering of simulation datasets that restructures simulation data into large (power of 2) blocks to facilitate efficient I/O aggregation. We perform both weak and strong scaling experiments using the S3D combustion application on both Cray-XE6 (65,536 cores) and IBM Blue Gene/P (131,072 cores) platforms. We demonstrate that data can be written in hierarchical, multiresolution format with performance competitive to that of native data-ordering methods.

Abstract Analysis and visualization of complex vector fields remain major challenges when studying large scale simulation of physical phenomena. The primary reason is the gap between the concepts of smooth vector field theory and their computational realization. In practice, researchers must choose between either numerical techniques, with limited or no guarantees on how they preserve fundamental invariants, or discrete techniques which limit the precision at which the vector field can be represented. We propose a new representation of vector fields that combines the advantages of both approaches. In particular, we represent a subset of possible streamlines by storing their paths as they traverse the edges of a triangulation. Using only a finite set of streamlines creates a fully discrete version of a vector field that nevertheless approximates the smooth flow up to a user controlled error bound. The discrete nature of our representation enables us to directly compute and classify analogues of critical points, closed orbits, and other common topological structures. Further, by varying the number of divisions (quantizations) used per edge, we vary the resolution used to represent the field, allowing for controlled precision. This representation is compact in memory and supports standard vector field operations.

A fundamental step in stitching several pictures to form a larger mosaic is the computation of boundary seams that minimize the visual artifacts in the transition between images. Current seam computation algorithms use optimization methods that may be slow, sequential, memory intensive, and prone to finding suboptimal solutions related to local minima of the chosen energy function. Moreover, even when these techniques perform well, their solution may not be perceptually ideal (or even good). Such an inflexible approach does not allow the possibility of user-based improvement. This paper introduces the Panorama Weaving technique for seam creation and editing in an image mosaic. First, Panorama Weaving provides a procedure to create boundaries for panoramas that is fast, has low memory requirements and is easy to parallelize. This technique often produces seams with lower energy than the competing global technique. Second, it provides the first interactive technique for the exploration of the seam solution space. This powerful editing capability allows the user to automatically extract energy minimizing seams given a sparse set of constraints. With a variety of empirical results, we show how Panorama Weaving allows the computation and editing of a wide range of digital panoramas including unstructured configurations.

Robust analysis of vector fields has been established as an important tool for deriving insights from the complex systems these fields model. Traditional analysis and visualization techniques rely primarily on computing streamlines through numerical integration. The inherent numerical errors of such approaches are usually ignored, leading to inconsistencies that cause unreliable visualizations and can ultimately prevent in-depth analysis. We propose a new representation for vector fields on surfaces that replaces numerical integration through triangles with maps from the triangle boundaries to themselves. This representation, called edge maps, permits a concise description of flow behaviors and is equivalent to computing all possible streamlines at a user defined error threshold. Independent of this error streamlines computed using edge maps are guaranteed to be consistent up to floating point precision, enabling the stable extraction of features such as the topological skeleton. Furthermore, our representation explicitly stores spatial and temporal errors which we use to produce more informative visualizations. This work describes the construction of edge maps, the error quantification, and a refinement procedure to adhere to a user defined error bound. Finally, we introduce new visualizations using the additional information provided by edge maps to indicate the uncertainty involved in computing streamlines and topological structures.

The broad goals of verifiable visualization rely on correct algorithmic implementations. We extend a framework for verification of isosurfacing implementations to check topological properties. Specifically, we use stratified Morse theory and digital topology to design algorithms which verify topological invariants. Our extended framework reveals unexpected behavior and coding mistakes in popular publicly available isosurface codes.

Topological techniques have proven highly successful in analyzing and visualizing scientific data. As a result, significant efforts have been made to compute structures like the Morse-Smale complex as robustly and efficiently as possible. However, the resulting algorithms, while topologically consistent, often produce incorrect connectivity as well as poor geometry. These problems may compromise or even invalidate any subsequent analysis. Moreover, such techniques may fail to improve even when the resolution of the domain mesh is increased, thus producing potentially incorrect results even for highly resolved functions. To address these problems we introduce two new algorithms: (i) a randomized algorithm to compute the discrete gradient of a scalar field that converges under refinement; and (ii) a deterministic variant which directly computes accurate geometry and thus correct connectivity of the MS complex. The first algorithm converges in the sense that on average it produces the correct result and its standard deviation approaches zero with increasing mesh resolution. The second algorithm uses two ordered traversals of the function to integrate the probabilities of the first to extract correct (near optimal) geometry and connectivity. We present an extensive empirical study using both synthetic and real-world data and demonstrates the advantages of our algorithms in comparison with several popular approaches.

In this paper, we characterize the range of features that can be extracted from an Morse-Smale complex and describe a unified query language to extract them. We provide a visual dictionary to guide users when defining features in terms of these queries. We demonstrate our topology-rich visualization pipeline in a tool that interactively queries the MS complex to extract features at multiple resolutions, assigns rendering attributes, and combines traditional volume visualization with the extracted features. The flexibility and power of this approach is illustrated with examples showing novel features.

The performance of massively parallel applications is often heavily impacted by the cost of communication among compute nodes. However, determining how to best use the network is a formidable task, made challenging by the ever increasing size and complexity of modern supercomputers. This paper applies visualization techniques to aid parallel application developers in understanding the network activity by enabling a detailed exploration of the flow of packets through the hardware interconnect. In order to visualize this large and complex data, we employ two linked views of the hardware network. The first is a 2D view, that represents the network structure as one of several simplified planar projections. This view is designed to allow a user to easily identify trends and patterns in the network traffic. The second is a 3D view that augments the 2D view by preserving the physical network topology and providing a context that is familiar to the application developers. Using the massively parallel multi-physics code pF3D as a case study, we demonstrate that our tool provides valuable insight that we use to explain and optimize pF3D's performance on an IBM Blue Gene/P system.

Creating high-quality quad meshes from triangulated surfaces is a highly nontrivial task that necessitates consideration of various application specific metrics of quality. In our work, we follow the premise that automatic reconstruction techniques may not generate outputs meeting all the subjective quality expectations of the user. Instead, we put the user at the center of the process by providing a flexible, interactive approach to quadrangulation design. By combining scalar field topology and combinatorial connectivity techniques, we present a new framework, following a coarse to fine design philosophy, which allows for explicit control of the subjective quality criteria on the output quad mesh, at interactive rates. Our quadrangulation framework uses the new notion of Reeb atlas editing, to define with a small amount of interactions a coarse quadrangulation of the model, capturing the main features of the shape, with user prescribed extraordinary vertices and alignment. Fine grain tuning is easily achieved with the notion of connectivity texturing, which allows for additional extraordinary vertices specification and explicit feature alignment, to capture the high-frequency geometries. Experiments demonstrate the interactivity and flexibility of our approach, as well as its ability to generate quad meshes of arbitrary resolution with high-quality statistics, while meeting the user’s own subjective requirements.

We present a combinatorial algorithm for the general topological simplification of scalar fields on surfaces. Given a scalar field f, our algorithm generates a simplified field g that provably admits only critical points from a constrained subset of the singularities of f, while guaranteeing a small distance ||f - g||∞ for data-fitting purpose. In contrast to previous algorithms, our approach is oblivious to the strategy used for selecting features of interest and allows critical points to be removed arbitrarily. When topological persistence is used to select the features of interest, our algorithm produces a standard ϵ-simplification. Our approach is based on a new iterative algorithm for the constrained reconstruction of sub- and sur-level sets. Extensive experiments show that the number of iterations required for our algorithm to converge is rarely greater than 2 and never greater than 5, yielding O(n log(n)) practical time performances. The algorithm handles triangulated surfaces with or without boundary and is robust to the presence of multi-saddles in the input. It is simple to implement, fast in practice and more general than previous techniques. Practically, our approach allows a user to arbitrarily simplify the topology of an input function and robustly generate the corresponding simplified function. An appealing application area of our algorithm is in scalar field design since it enables, without any threshold parameter, the robust pruning of topological noise as selected by the user. This is needed for example to get rid of inaccuracies introduced by numerical solvers, thereby providing topological guarantees needed for certified geometry processing. Experiments show this ability to eliminate numerical noise as well as validate the time efficiency and accuracy of our algorithm. We provide a lightweight C++ implementation as supplemental material that can be used for topological cleaning on surface meshes.

Robust analysis of vector fields has been established as an important tool for deriving insights from the complex systems these fields model. Many analysis techniques rely on computing streamlines, a task often hampered by numerical instabilities. Approaches that ignore the resulting errors can lead to inconsistencies that may produce unreliable visualizations and ultimately prevent in-depth analysis. We propose a new representation for vector fields on surfaces that replaces numerical integration through triangles with linear maps defined on its boundary. This representation, called edge maps, is equivalent to computing all possible streamlines at a user defined error threshold. In spite of this error, all the streamlines computed using edge maps will be pairwise disjoint. Furthermore, our representation stores the error explicitly, and thus can be used to produce more informative visualizations. Given a piecewise-linear interpolated vector field, a recent result [15] shows that there are only 23 possible map classes for a triangle, permitting a concise description of flow behaviors. This work describes the details of computing edge maps, provides techniques to quantify and refine edge map error, and gives qualitative and visual comparisons to more traditional techniques.

The IDX data format provides efficient, cache oblivious, and progressive access to large-scale scientific datasets by storing the data in a hierarchical Z (HZ) order. Data stored in IDX format can be visualized in an interactive environment allowing for meaningful explorations with minimal resources. This technology enables real-time, interactive visualization and analysis of large datasets on a variety of systems ranging from desktops and laptop computers to portable devices such as iPhones/iPads and over the web. While the existing ViSUS API for writing IDX data is serial, there are obvious advantages of applying the IDX format to the output of large scale scientific simulations. We have therefore developed PIDX - a parallel API for writing data in an IDX format. With PIDX it is now possible to generate IDX datasets directly from large scale scientific simulations with the added advantage of real-time monitoring and visualization of the generated data. In this paper, we provide an overview of the IDX file format and how it is generated using PIDX. We then present a data model description and a novel aggregation strategy to enhance the scalability of the PIDX library. The S3D combustion application is used as an example to demonstrate the efficacy of PIDX for a real-world scientific simulation. S3D is used for fundamental studies of turbulent combustion requiring exceptionally high fidelity simulations. PIDX achieves up to 18 GiB/s I/O throughput at 8,192 processes for S3D to write data out in the IDX format. This allows for interactive analysis and visualization of S3D data, thus, enabling in situ analysis of S3D simulation.

This video presents a visualization of a recent algorithm to compute discrete gradient fields on regular cell complexes. Discrete gradient fields are used in practical methods that robustly translate smooth Morse theory to combinatorial domains. We describe the stages of the algorithm, highlighting both its simplicity and generality.

Gradient domain processing is a computationally expensive image processing technique. Its use for processing massive images, giga or terapixels in size, can take several hours with serial techniques. To address this challenge, parallel algorithms are being developed to make this class of techniques applicable to the largest images available with running times that are more acceptable to the users. To this end we target the most ubiquitous form of computing power available today, which is small or medium scale clusters of commodity hardware. Such clusters are continuously increasing in scale, not only in the number of nodes, but also in the amount of parallelism available within each node in the form of multicore CPUs and GPUs. In this paper we present a hybrid parallel implementation of gradient domain processing for seamless stitching of gigapixel panoramas that utilizes MPI, threading and a CUDA based GPU component. We demonstrate the performance and scalability of our implementation by presenting results from two GPU clusters processing two large data sets.

To exploit the capabilities of current and future systems, developers must understand the interplay between on-node performance, domain decomposition, and an application's intrinsic communication patterns. While tools exist to gather and analyze data for each of these components individually, the resulting information is generally processed in isolation and presented in an abstract, categorical fashion unintuitive to most users. In this paper we present the HAC model, in which we identify the three domains of performance data most familiar to the user: (i)the application domain containing the application's working set, (ii) the hardware domain of the compute and network devices, and (iii) the communication domain of logical data transfers. We show that taking data from each of these domains and projecting, visualizing, and correlating it to the other domains can give valuable insights into the behavior of parallel application codes. The HAC abstraction opens the door for a new generation of tools that can help users more easily and intuitively associate performance data with root causes in the hardware system, the application's structure, and in its communication behavior, and by doing so leads to an improved understanding of the performance of their codes.

This article presents a simple framework for progressive processing of high-resolution images with minimal resources. We demonstrate this framework's effectiveness by implementing an adaptive, multi-resolution solver for gradient-based image processing that, for the first time, is capable of handling gigapixel imagery in real time. With our system, artists can use commodity hardware to interactively edit massive imagery and apply complex operators, such as seamless cloning, panorama stitching, and tone mapping. We introduce a progressive Poisson solver that processes images in a purely coarse-to-fine manner, providing near instantaneous global approximations for interactive display (see Figure 1). We also allow for data-driven adaptive refinements to locally emulate the effects of a global solution. These techniques, combined with a fast, cache-friendly data access mechanism, allow the user to interactively explore and edit massive imagery, with the illusion of having a full solution at hand. In particular, we demonstrate the interactive modification of gigapixel panoramas that previously required extensive offline processing. Even with massive satellite images surpassing a hundred gigapixels in size, we enable repeated interactive editing in a dynamically changing environment. Images at these scales are significantly beyond the purview of previous methods yet are processed interactively using our techniques. Finally our system provides a robust and scalable out-of-core solver that consistently offers high-quality solutions while maintaining strict control over system resources.

We present a new framework for feature-based statistical analysis of large-scale scientific data and demonstrate its effectiveness by analyzing features from Direct Numerical Simulations (DNS) of turbulent combustion. Turbulent flows are ubiquitous and account for transport and mixing processes in combustion, astrophysics, fusion, and climate modeling among other disciplines. They are also characterized by coherent structure or organized motion, i.e. nonlocal entities whose geometrical features can directly impact molecular mixing and reactive processes. While traditional multi-point statistics provide correlative information, they lack nonlocal structural information, and hence, fail to provide mechanistic causality information between organized fluid motion and mixing and reactive processes. Hence, it is of great interest to capture and track flow features and their statistics together with their correlation with relevant scalar quantities, e.g. temperature or species concentrations. In our approach we encode the set of all possible flow features by pre-computing merge trees augmented with attributes, such as statistical moments of various scalar fields, e.g. temperature, as well as length-scales computed via spectral analysis. The computation is performed in an efficient streaming manner in a pre-processing step and results in a collection of meta-data that is orders of magnitude smaller than the original simulation data. This meta-data is sufficient to support a fully flexible and interactive analysis of the features, allowing for arbitrary thresholds, providing per-feature statistics, and creating various global diagnostics such as Cumulative Density Functions (CDFs), histograms, or time-series. We combine the analysis with a rendering of the features in a linked-view browser that enables scientists to interactively explore, visualize, and analyze the equivalent of one terabyte of simulation data. We highlight the utility of this new framework for combustion science; however, it is applicable to many other science domains.

Large-scale simulations are increasingly being used to study complex scientific and engineering phenomena. As a result, advanced visualization and data analysis are also becoming an integral part of the scientific process. Often, a key step in extracting insight from these large simulations involves the definition, extraction, and evaluation of features in the space and time coordinates of the solution. However, in many applications, these features involve a range of parameters and decisions that will affect the quality and direction of the analysis. Examples include particular level sets of a specific scalar field, or local inequalities between derived quantities. A critical step in the analysis is to understand how these arbitrary parameters/decisions impact the statistical properties of the features, since such a characterization will help to evaluate the conclusions of the analysis as a whole. We present a new topological framework that in a single-pass extracts and encodes entire families of possible features definitions as well as their statistical properties. For each time step we construct a hierarchical merge tree a highly compact, yet flexible feature representation. While this data structure is more than two orders of magnitude smaller than the raw simulation data it allows us to extract a set of features for any given parameter selection in a postprocessing step. Furthermore, we augment the trees with additional attributes making it possible to gather a large number of useful global, local, as well as conditional statistic that would otherwise be extremely difficult to compile. We also use this representation to create tracking graphs that describe the temporal evolution of the features over time. Our system provides a linked-view interface to explore the time-evolution of the graph interactively alongside the segmentation, thus making it possible to perform extensive data analysis in a very efficient manner. We demonstrate our framework by extracting and analyzing burning cells from a large-scale turbulent combustion simulation. In particular, we show how the statistical analysis enabled by our techniques provides new insight into the combustion process.

Large observations and simulations in scientific research give rise to high-dimensional data sets that present many challenges and opportunities in data analysis and visualization. Researchers in application domains such as engineering, computational biology, climate study, imaging and motion capture are faced with the problem of how to discover compact representations of high-dimensional data while preserving their intrinsic structure. In many applications, the original data is projected onto low-dimensional space via dimensionality reduction techniques prior to modeling. One problem with this approach is that the projection step in the process can fail to preserve structure in the data that is only apparent in high dimensions. Conversely, such techniques may create structural illusions in the projection, implying structure not present in the original high-dimensional data. Our solution is to utilize topological techniques to recover important structures in high-dimensional data that contains non-trivial topology. Specifically, we are interested in high-dimensional branching structures. We construct local circle-valued coordinate functions to represent such features. Subsequently, we perform dimensionality reduction on the data while ensuring such structures are visually preserved. Additionally, we study the effects of global circular structures on visualizations. Our results reveal never-before-seen structures on real-world data sets from a variety of applications.

We consider the problem of extracting discrete two-dimensional vortices from a turbulent flow. In our approach we use a reference model describing the expected physics and geometry of an idealized vortex. The model allows us to derive a novel correlation between the size of the vortex and its strength, measured as the square of its strain minus the square of its vorticity. For vortex detection in real models we use the strength parameter to locate potential vortex cores, then measure the similarity of our ideal analytical vortex and the real vortex core for different strength thresholds. This approach provides a metric for how well a vortex core is modeled by an ideal vortex. Moreover, this provides insight into the problem of choosing the thresholds that identify a vortex. By selecting a target coefficient of determination (i.e., statistical confidence), we determine on a per-vortex basis what threshold of the strength parameter would be required to extract that vortex at the chosen confidence. We validate our approach on real data from a global ocean simulation and derive from it a map of expected vortex strengths over the global ocean.

In preparation for the Intergovernmental Panel on Climate Change (IPCC) Fifth Assessment Report, the climate community will run the Coupled Model Intercomparison Project phase 5 (CMIP-5) experiments, which are designed to answer crucial questions about future regional climate change and the results of carbon feedback for different mitigation scenarios. The CMIP-5 experiments will generate petabytes of data that must be replicated seamlessly, reliably, and quickly to hundreds of research teams around the globe. As an end-to-end test of the technologies that will be used to perform this task, a multi-disciplinary team of researchers moved a small portion (10 TB) of the multimodel Coupled Model Intercomparison Project, Phase 3 data set used in the IPCC Fourth Assessment Report from three sources---the Argonne Leadership Computing Facility (ALCF), Lawrence Livermore National Laboratory (LLNL) and National Energy Research Scientific Computing Center (NERSC)---to the 2009 Supercomputing conference (SC09) show floor in Portland, Oregon, over circuits provided by DOE's ESnet. The team achieved a sustained data rate of 15 Gb/s on a 20 Gb/s network. More important, this effort provided critical feedback on how to deploy, tune, and monitor the middleware that will be used to replicate the upcoming petascale climate datasets. We report on obstacles overcome and the key lessons learned from this successful bandwidth challenge effort.

Abstract We propose a new framework design for exploiting multi‐core architectures in the context of visualization dataflow systems. Recent hardware advancements have greatly increased the levels of parallelism available with all indications showing this trend will continue in the future. Existing visualization dataflow systems have attempted to take advantage of these new resources, though they still have a number of limitations when deployed on shared memory multi‐core architectures. Ideally, visualization systems should be built on top of a parallel dataflow scheme that can optimally utilize CPUs and assign resources adaptively to pipeline elements. We propose the design of a flexible dataflow architecture aimed at addressing many of the shortcomings of existing systems including a unified execution model for both demand‐driven and event‐driven models; a resource scheduler that can automatically make decisions on how to allocate computing resources; and support for more general streaming data structures which include unstructured elements. We have implemented our system on top of VTK with backward compatibility. In this paper, we provide evidence of performance improvements on a number of applications.

This paper presents topology-based methods to robustly extract, analyze, and track features defined as subsets of isosurfaces. First, we demonstrate how features identified by thresholding isosurfaces can be defined in terms of the Morse complex. Second, we present a specialized hierarchy that encodes the feature segmentation independent of the threshold while still providing a flexible multiresolution representation. Third, for a given parameter selection, we create detailed tracking graphs representing the complete evolution of all features in a combustion simulation over several hundred time steps. Finally, we discuss a user interface that correlates the tracking information with interactive rendering of the segmented isosurfaces enabling an in-depth analysis of the temporal behavior. We demonstrate our approach by analyzing three numerical simulations of lean hydrogen flames subject to different levels of turbulence. Due to their unstable nature, lean flames burn in cells separated by locally extinguished regions. The number, area, and evolution over time of these cells provide important insights into the impact of turbulence on the combustion process. Utilizing the hierarchy, we can perform an extensive parameter study without reprocessing the data for each set of parameters. The resulting statistics enable scientists to select appropriate parameters and provide insight into the sensitivity of the results with respect to the choice of parameters. Our method allows for the first time to quantitatively correlate the turbulence of the burning process with the distribution of burning regions, properly segmented and selected. In particular, our analysis shows that counterintuitively stronger turbulence leads to larger cell structures, which burn more intensely than expected. This behavior suggests that flames could be stabilized under much leaner conditions than previously anticipated.

An important goal of scientific data analysis is to understand the behavior of a system or process based on a sample of the system. In many instances it is possible to observe both input parameters and system outputs, and characterize the system as a high-dimensional function. Such data sets arise, for instance, in large numerical simulations, as energy landscapes in optimization problems, or in the analysis of image data relating to biological or medical parameters. This paper proposes an approach to analyze and visualizing such data sets. The proposed method combines topological and geometric techniques to provide interactive visualizations of discretely sampled high-dimensional scalar fields. The method relies on a segmentation of the parameter space using an approximate Morse-Smale complex on the cloud of point samples. For each crystal of the Morse-Smale complex, a regression of the system parameters with respect to the output yields a curve in the parameter space. The result is a simplified geometric representation of the Morse-Smale complex in the high dimensional input domain. Finally, the geometric representation is embedded in 2D, using dimension reduction, to provide a visualization platform. The geometric properties of the regression curves enable the visualization of additional information about each crystal such as local and global shape, width, length, and sampling densities. The method is illustrated on several synthetic examples of two dimensional functions. Two use cases, using data sets from the UCI machine learning repository, demonstrate the utility of the proposed approach on real data. Finally, in collaboration with domain experts the proposed method is applied to two scientific challenges. The analysis of parameters of climate simulations and their relationship to predicted global energy flux and the concentrations of chemical species in a combustion simulation and their integration with temperature.

The advent of highly accurate, large scale volumetric simulations has made data analysis and visualization techniques an integral part of the modern scientific process. To develop new insights from raw data, scientists need the ability to define features of interest in a flexible manner and to understand how changes in the feature definition impact the subsequent analysis of the data. Therefore, simply exploring the raw data is not sufficient. This paper presents a new topological framework for the analysis of large scale, time-varying, turbulent combustion simulations. It allows the scientists to interactively explore the complete parameter space of fuel consumption thresholds for an entire time-dependent combustion simulation. By computing augmented merge trees and their corresponding data segmentations, the system allows the user complete flexibility to segment, select, and track burning cells through time thanks to a linked view interface. We developed this technique in the context of low-swirl turbulent pre-mixed same simulation analysis, where the topological abstractions enable an efficient tracking through time of the burning cells and provide new qualitative and quantitative insights into the dynamics of the combustion process.

Simulations that require massive amounts of computing power and generate tens of terabytes of data are now part of the daily lives of scientists. Analyzing and visualizing the results of these simulations as they are computed can lead not only to early insights but also to useful knowledge that can be provided as feedback to the simulation, avoiding unnecessary use of computing power. Our work is aimed at making advanced visualization tools available to scientists in a user-friendly, Web-based environment where they can be accessed anytime from anywhere. In the context of turbulent combustion for example, visualization is used to understand the coupling between turbulence and the turbulent mixing of scalars. Although isosurface generation is a useful technique in this scenario, computing and rendering isosurfaces one at a time is expensive and not particularly well-suited for such a Web-based framework. In this paper we propose the use of a summary structure, called contour tree, that captures the topological structure of a scalar field and guides the user in identifying useful isosurfaces. We have also designed an interface which has been integrated with a Web-based simulation monitoring system, that allows users to interact with and explore multiple isosurfaces.

This paper introduces an efficient algorithm for computing the Reeb graph of a scalar function f defined on a volumetric mesh M in R3. We introduce a procedure called "loop surgery" that transforms M into a mesh M' by a sequence of cuts and guarantees the Reeb graph of f(M') to be loop free. Therefore, loop surgery reduces Reeb graph computation to the simpler problem of computing a contour tree, for which well-known algorithms exist that are theoretically efficient (O(n log n)) and fast in practice. Inverse cuts reconstruct the loops removed at the beginning. The time complexity of our algorithm is that of a contour tree computation plus a loop surgery overhead, which depends on the number of handles of the mesh. Our systematic experiments confirm that for real-life data, this overhead is comparable to the computation of the contour tree, demonstrating virtually linear scalability on meshes ranging from 70 thousand to 3.5 million tetrahedra. Performance numbers show that our algorithm, although restricted to volumetric data, has an average speedup factor of 6,500 over the previous fastest techniques, handling larger and more complex data-sets.We demonstrate the versatility of our approach by extending fast topologically clean iso surface extraction to non simply-connected domains. We apply this technique in the context of pressure analysis for mechanical design. In this case, our technique produces results in matter of seconds even for the largest meshes. For the same models, previous Reeb graph techniques do not produce a result.

The Morse-Smale (MS) complex has proven to be a useful tool in extracting and visualizing features from scalar-valued data. However, efficient computation of the MS complex for large scale data remains a challenging problem. We describe a new algorithm and easily extensible framework for computing MS complexes for large scale data of any dimension where scalar values are given at the vertices of a closure-finite and weak topology (CW) complex, therefore enabling computation on a wide variety of meshes such as regular grids, simplicial meshes, and adaptive multiresolution (AMR) meshes. A new divide-and-conquer strategy allows for memory-efficient computation of the MS complex and simplification on-the-fly to control the size of the output. In addition to being able to handle various data formats, the framework supports implementation-specific optimizations, for example, for regular data. We present the complete characterization of critical point cancellations in all dimensions. This technique enables the topology based analysis of large data on off-the-shelf computers. In particular we demonstrate the first full computation of the MS complex for a 1 billion/1024(3) node grid on a laptop computer with 2Gb memory.

We consider the problem of generating a map between two triangulated meshes, M and M', with arbitrary and possibly differing genus. This problem has rarely been tackled in its generality. Early schemes considered only topological spheres. Recent algorithms allow inputs with an arbitrary number of tunnels but require M and M' to have equal genus, mapping tunnel to tunnel. Other schemes which allow more general inputs are not guaranteed to work and the authors do not provide a characterization of the input meshes that can be processed successfully. Moreover, the techniques have difficulty dealing with coarse meshes with many tunnels. In this paper we present the first robust approach to build a map between two meshes of arbitrary unequal genus. We also provide a simplified method for setting the initial alignment between M and M', reducing reliance on landmarks and allowing the user to select "landmark tunnels" in addition to the standard landmark vertices. After computing the map, we automatically derive a continuous deformation from M to M' using a variational implicit approach to describe the evolution of non-landmark tunnels. Overall, we achieve a cross parameterization scheme that is provably robust in the sense that it can mapM toM' without constraints on their relative genus or on the density of the triangulation with respect to the number of tunnels. To demonstrate the practical effectiveness of our scheme we provide a number of examples of inter-surface parameterizations between meshes of different genus and shape.

Reeb graphs are a fundamental data structure for understanding and representing the topology of shapes. They are used in computer graphics, solid modeling, and visualization for applications ranging from the computation of similarities and finding defects in complex models to the automatic selection of visualization parameters. We introduce an on-line algorithm that reads a stream of elements (vertices, triangles, tetrahedra, etc.) and continuously maintains the Reeb graph of all elements already reed. The algorithm is robust in handling non-manifold meshes and general in its applicability to input models of any dimension. Optionally, we construct a skeleton-like embedding of the Reeb graph, and/or remove topological noise to reduce the output size. For interactive multi-resolution navigation we also build a hierarchical data structure which allows real-time extraction of approximated Reeb graphs containing all topological features above a given error threshold. Our extensive experiments show both high performance and practical linear scalability for meshes ranging from thousands to hundreds of millions of triangles. We apply our algorithm to the largest, most general, triangulated surfaces available to us, including 3D, 4D and 5D simplicial meshes. To demonstrate one important application we use Reeb graphs to find and highlight topological defects in meshes, including some widely believed to be "clean."

Analysis of the results obtained from material simulations is important in the physical sciences. Our research was motivated by the need to investigate the properties of a simulated porous solid as it is hit by a projectile. This paper describes two techniques for the generation of distance fields containing a minimal number of topological features, and we use them to identify features of the material. We focus on distance fields defined on a volumetric domain considering the distance to a given surface embedded within the domain. Topological features of the field are characterized by its critical points. Our first method begins with a distance field that is computed using a standard approach, and simplifies this field using ideas from Morse theory. We present a procedure for identifying and extracting a feature set through analysis of the MS complex, and apply it to find the invariants in the clean distance field. Our second method proceeds by advancing a front, beginning at the surface, and locally controlling the creation of new critical points. We demonstrate the value of topologically clean distance fields for the analysis of filament structures in porous solids. Our methods produce a curved skeleton representation of the filaments that helps material scientists to perform a detailed qualitative and quantitative analysis of pores, and hence infer important material properties. Furthermore, we provide a set of criteria for finding the "difference" between two skeletal structures, and use this to examine how the structure of the porous solid changes over several timesteps in the simulation of the particle impact.

The Morse-Smale complex is an efficient representation of the gradient behavior of a scalar function, and critical points paired by the complex identify topological features and their importance. We present an algorithm that constructs the Morse-Smale complex in a series of sweeps through the data, identifying various components of the complex in a consistent manner. All components of the complex, both geometric and topological, are computed, providing a complete decomposition of the domain. Efficiency is maintained by representing the geometry of the complex in terms of point sets.

Unstructured tetrahedral meshes are commonly used in scientific computing to represent scalar, vector, and tensor fields in three dimensions. Visualization of these meshes can be difficult to perform interactively due to their size and complexity. By reducing the size of the data, we can accomplish real-time visualization necessary for scientific analysis. We propose a two-step approach for streaming simplification of large tetrahedral meshes. Our algorithm arranges the data on disk in a streaming, I/O-efficient format that allows coherent access to the tetrahedral cells. A quadric-based simplification is sequentially performed on small portions of the mesh in-core. Our output is a coherent streaming mesh which facilitates future processing. Our technique is fast, produces high quality approximations, and operates out-of-core to process meshes too large for main memory.

Scientific visualization and illustration tools are designed to help people understand the structure and complexity of scientific data with images that are as informative and intuitive as possible. In this context the use of metaphors plays an important role since they make complex information easily accessible by using commonly known concepts. In this paper we propose a new metaphor, called "Topological Landscapes," which facilitates understanding the topological structure of scalar functions. The basic idea is to construct a terrain with the same topology as a given dataset and to display the terrain as an easily understood representation of the actual input data. In this projection from an $n$-dimensional scalar function to a two-dimensional (2D) model we preserve function values of critical points, the persistence (function span) of topological features, and one possible additional metric property (in our examples volume). By displaying this topologically equivalent landscape together with the original data we harness the natural human proficiency in understanding terrain topography and make complex topological information easily accessible.

Topology provides a foundation for the development of mathematically sound tools for processing and exploration of scalar fields. Existing topology-based methods can be used to identify interesting features in volumetric data sets, to find seed sets for accelerated isosurface extraction, or to treat individual connected components as distinct entities for isosurfacing or interval volume rendering. We describe a framework for direct volume rendering based on segmenting a volume into regions of equivalent contour topology and applying separate transfer functions to each region. Each region corresponds to a branch of a hierarchical contour tree decomposition, and a separate transfer function can be defined for it. The novel contributions of our work are 1) a volume rendering framework and interface where a unique transfer function can be assigned to each subvolume corresponding to a branch of the contour tree, 2) a runtime method for adjusting data values to reflect contour tree simplifications, 3) an efficient way of mapping a spatial location into the contour tree to determine the applicable transfer function, and 4) an algorithm for hardware-accelerated direct volume rendering that visualizes the contour tree-based segmentation at interactive frame rates using graphics processing units (GPUs) that support loops and conditional branches in fragment programs.

We continue the study of topological persistence [5] by investigating the problem of simplifying a function f in a way that removes topological noise as determined by its persistence diagram [2]. To state our results, we call a function g an ε-simplification of another function f if ¦¦f−g¦¦∞≤ε, and the persistence diagrams of g are the same as those of f except all points within L1-distance at most ε from the diagonal have been removed. We prove that for functions f on a 2-manifold such ε-simplification exists, and we give an algorithm to construct them in the piecewise linear case.

The output from the massively parallel scientific simulations is so voluminous and complex that advanced visualization technologies are necessary to interpret the calculated results. Even though visualization technology has progressed significantly in recent years, we are barely capable of visualizing and analyzing terascale data to its full extent, and petascale datasets are on the horizon. This workshop aims at addressing this pressing issue by fostering communication between visualization researchers and practitioners. The workshop attendees will be introduced to the latest and greatest research innovations in large data visualization and also help direct further research direction through an open discussion session.

Resampling raw surface meshes is one of the most fundamental operations used by nearly all digital geometry processing systems. The vast majority of this work has focused on triangular remeshing, yet quadrilateral meshes are preferred for many surface PDE problems, especially fluid dynamics, and are best suited for defining Catmull-Clark subdivision surfaces. We describe a fundamentally new approach to the quadrangulation of manifold polygon meshes using Laplacian eigenfunctions, the natural harmonics of the surface. These surface functions distribute their extrema evenly across a mesh, which connect via gradient flow into a quadrangular base mesh. An iterative relaxation algorithm simultaneously refines this initial complex to produce a globally smooth parameterization of the surface. From this, we can construct a well-shaped quadrilateral mesh with very few extraordinary vertices. The quality of this mesh relies on the initial choice of eigenfunction, for which we describe algorithms and hueristics to efficiently and effectively select the harmonic most appropriate for the intended application.

We describe a new progressive technique that allows real-time rendering of extremely large tetrahedral meshes. Our approach uses a client-server architecture to incrementally stream portions of the mesh from a server to a client which refines the quality of the approximate rendering until it converges to a full quality rendering. The results of previous steps are re-used in each subsequent refinement, thus leading to an efficient rendering. Our novel approach keeps very little geometry on the client and works by refining a set of rendered images at each step. Our interactive representation of the dataset is efficient, light-weight, and high quality. We present a framework for the exploration of large datasets stored on a remote server with a thin client that is capable of rendering and managing full quality volume visualizations.

This paper describes an efficient combinatorial method for simplification of topological features in a 3D scalar function. The Morse-Smale complex, which provides a succinct representation of a function's associated gradient flow field, is used to identify topological features and their significance. The simplification process, guided by the Morse-Smale complex, proceeds by repeatedly applying two atomic operations that each remove a pair of critical points from the complex. Efficient storage of the complex results in execution of these atomic operations at interactive rates. Visualization of the simplified complex shows that the simplification preserves significant topological features while removing small features and noise.

When a heavy fluid is placed above a light fluid, tiny vertical perturbations in the interface create a characteristic structure of rising bubbles and falling spikes known as Rayleigh-Taylor instability. Rayleigh-Taylor instabilities have received much attention over the past half-century because of their importance in understanding many natural and man-made phenomena, ranging from the rate of formation of heavy elements in supernovae to the design of capsules for Inertial Confinement Fusion. We present a new approach to analyze Rayleigh-Taylor instabilities in which we extract a hierarchical segmentation of the mixing envelope surface to identify bubbles and analyze analogous segmentations of fields on the original interface plane. We compute meaningful statistical information that reveals the evolution of topological features and corroborates the observations made by scientists. We also use geometric tracking to follow the evolution of single bubbles and highlight merge/split events leading to the formation of the large and complex structures characteristic of the later stages. In particular we (i) Provide a formal definition of a bubble; (ii) Segment the envelope surface to identify bubbles; (iii) Provide a multi-scale analysis technique to produce statistical measures of bubble growth; (iv) Correlate bubble measurements with analysis of fields on the interface plane; (v) Track the evolution of individual bubbles over time. Our approach is based on the rigorous mathematical foundations of Morse theory and can be applied to a more general class of applications.

We present an approach to hierarchically encode the topology of functions over triangulated surfaces. Its Morse-Smale complex, a well known structure in computational topology, describes the topology of a function. Following concepts of Morse theory, a Morse-Smale complex (and therefore a function's topology) can be simplified by successively canceling pairs of critical points. We demonstrate how cancellations can be effectively encoded to produce a highly adaptive topology-based multi-resolution representation of a given function. Contrary to the approach, we avoid encoding the complete complex in a traditional mesh hierarchy. Instead, the information is split into a new structure we call a cancellation forest and a traditional dependency graph. The combination of this new structure with a traditional mesh hierarchy proofs to be significantly more flexible than the one previously reported. In particular, we can create hierarchies that are guaranteed to be of logarithmic height.

The 3D Morse-Smale complex is a fundamental topological construct that partitions the domain of a real-valued function into regions having uniform gradient flow behavior. In this paper, we consider the construction and selective presentation of cells of the Morse-Smale complex and their use in the analysis and visualization of scientific datasets. We take advantage of the fact that cells of different dimension often characterize different types of features present in the data. For example, critical points pinpoint changes in topology by showing where components of the level sets are created, destroyed or modified in genus. Edges of the Morse-Smale complex extract filament-like features that are not explicitly modeled in the original data. Interactive selection and rendering of portions of the Morse-Smale complex introduces fundamental data management challenges due to the unstructured nature of the complex even for structured inputs. We describe a data structure that stores the Morse-Smale complex and allows efficient selective traversal of regions of interest. Finally, we illustrate the practical use of this approach by applying it to cryo-electron microscopy data of protein molecules.

In this paper, we present a topological approach for simplifying continuous functions defined on volumetric domains. We introduce two atomic operations that remove pairs of critical points of the function and design a combinatorial algorithm that simplifies the Morse-Smale complex by repeated application of these operations. The Morse-Smale complex is a topological data structure that provides a compact representation of gradient flow between critical points of a function. Critical points paired by the Morse-Smale complex identify topological features and their importance. The simplification procedure leaves important critical points untouched, and is therefore useful for extracting desirable features. We also present a visualization of the simplified topology.

We present a novel method for computing cache-oblivious layouts of large meshes that improve the performance of interactive visualization and geometric processing algorithms. Given that the mesh is accessed in a reasonably coherent manner, we assume no particular data access patterns or cache parameters of the memory hierarchy involved in the computation. Furthermore, our formulation extends directly to computing layouts of multi-resolution and bounding volume hierarchies of large meshes.We develop a simple and practical cache-oblivious metric for estimating cache misses. Computing a coherent mesh layout is reduced to a combinatorial optimization problem. We designed and implemented an out-of-core multilevel minimization algorithm and tested its performance on unstructured meshes composed of tens to hundreds of millions of triangles. Our layouts can significantly reduce the number of cache misses. We have observed 2--20 times speedups in view-dependent rendering, collision detection, and isocontour extraction without any modification of the algorithms or runtime applications.

We study the evolution of the Reeb graph of a time-varying continuous function defined in three-dimensional space. While maintaining the Reeb graph, we compress the evolving sequence into a single, partially persistent data structure. We envision this data structure as a useful tool in visualizing real-valued space-time data obtained from computational simulations of physical processes.

Data coming from complex simulation models reach easily dimensions much greater than available computational resources. Visualization of such data still represents the most intuitive and effective tool for scientific inspection of simulated phenomena. To ease this process several techniques have been adopted mainly concerning the use of hierarchical multi-resolution representations. In this paper we present the implementation of a hierarchical indexing schema for multiresolution data tailored to overwork the computational power of distributed environments.

We introduce local and global comparison measures for a collection of k /spl les/ d real-valued smooth functions on a common d-dimensional Riemannian manifold. For k = d = 2 we relate the measures to the set of critical points of one function restricted to the level sets of the other. The definition of the measures extends to piecewise linear functions for which they are easy to compute. The computation of the measures forms the centerpiece of a software tool which we use to study scientific datasets.

We combine topological and geometric methods to construct a multiresolution representation for a function over a two-dimensional domain. In a preprocessing stage, we create the Morse-Smale complex of the function and progressively simplify its topology by cancelling pairs of critical points. Based on a simple notion of dependency among these cancellations, we construct a hierarchical data structure supporting traversal and reconstruction operations similarly to traditional geometry-based representations. We use this data structure to extract topologically valid approximations that satisfy error bounds provided at runtime.

Given a Morse function f over a 2-manifold with or without boundary, the Reeb graph is obtained by contracting the connected components of the level sets to points. We prove tight upper and lower bounds on the number of loops in the Reeb graph that depend on the genus, the number of boundary components, and whether or not the 2-manifold is orientable. We also give an algorithm that constructs the Reeb graph in time O(nlogn), where n is the number of edges in the triangulation used to represent the 2-manifold and the Morse function.

We define the Morse-Smale complex of a Morse function over a 3-manifold as the overlay of the descending and ascending manifolds of all critical points. In the generic case, its 3-dimensional cells are shaped like crystals and are separated by quadrangular faces. In this paper, we give a combinatorial algorithm for constructing such complexes for piecewise linear data.

We combine topological and geometric methods to construct a multi-resolution data structure for functions over two-dimensional domains. Starting with the Morse-Smale complex, we construct a topological hierarchy by progressively canceling critical points in pairs. Concurrently, we create a geometric hierarchy by adapting the geometry to the changes in topology. The data structure supports mesh traversal operations similarly to traditional multi-resolution representations.

Multiresolution methods for representing data at multiple levels of detail are widely used for large-scale two- and three-dimensional data sets. We present a four-dimensional multiresolution approach for time-varying volume data. This approach supports a hierarchy with spatial and temporal scalability. The hierarchical data organization is based on /sup 4//spl radic/2 subdivision. The /sup n//spl radic/2-subdivision scheme only doubles the overall number of grid points in each subdivision step. This fact leads to fine granularity and high adaptivity, which is especially desirable in the spatial dimensions. For high-quality data approximation on each level of detail, we use quadrilinear B-spline wavelets. We present a linear B-spline wavelet lifting scheme based on /sup n//spl radic/2 subdivision to obtain narrow masks for the update rules. Narrow masks provide a basis for out-of-core data exploration techniques and view-dependent visualization of sequences of time steps.

We present an algorithm for interactively extracting and rendering isosurfaces of large volume datasets in a view-dependent fashion. A recursive tetrahedral mesh refinement scheme, based on longest edge bisection, is used to hierarchically decompose the data into a multiresolution structure. This data structure allows fast extraction of arbitrary isosurfaces to within user specified view-dependent error bounds. A data layout scheme based on hierarchical space filling curves provides access to the data in a cache coherent manner that follows the data access pattern indicated by the mesh refinement.

This paper introduces two efficient algorithms that compute the Contour Tree of a 3D scalar field /spl Fscr/ and its augmented version with the Betti numbers of each isosurface. The Contour Tree is a fundamental data structure in scientific visualization that is used to preprocess the domain mesh to allow optimal computation of isosurfaces with minimal overhead storage. The Contour Tree can also be used to build user interfaces reporting the complete topological characterization of a scalar field. The first part of the paper presents a new scheme that augments the Contour Tree with the Betti numbers of each isocontour in linear time. We show how to extend the scheme with the Betti number computation without increasing its complexity. Thus, we improve on the time complexity from our previous approach from O(m log m) to O(n log n+m), where m is the number of tetrahedra and n is the number of vertices in the domain of /spl Fscr/. The second part of the paper introduces a new divide-and-conquer algorithm that computes the Augmented Contour Tree with improved efficiency. The central part of the scheme computes the output Contour Tree by merging two intermediate Contour Trees and is independent of the interpolant. In this way we confine any knowledge regarding a specific interpolant to an oracle that computes the tree for a single cell. We have implemented this oracle for the trilinear interpolant and plan to replace it with higher order interpolants when needed. The complexity of the scheme is O(n+t log n), where t is the number of critical points of /spl Fscr/. For the first time we can compute the Contour Tree in linear time in many practical cases when t=O(n/sup 1-/spl epsi//). Lastly, we report the running times for a parallel implementation of our algorithm, showing good scalability with the number of processors.

In recent years subdivision methods have been one of the most successful techniques applied to the multi-resolution representation and visualization of surface meshes. Extension these techniques to the volumetric case would enable their use in a broad class of applications including solid modeling, scientific visualization and mesh generation. Unfortunately, major challenges remain unsolved both in the generalization of the combinatorial structure of the refinement procedure and in the analysis of the smoothness of the limit mesh. In this paper we mainly tackle the first part of the problem introducing a subdivision scheme that generalizes to 3D and higher dimensional meshes without the excessive vertex proliferation typical of tensor-product refinements. The main four qualities of our subdivision procedure are: (i) the rate of refinement does not grow with the dimension of the mesh, (ii) adaptive refinement of the mesh is possible without introducing special temporary cell decompositions, (iii) the cells of the base meshes can have virtually unrestricted topology, and (iv) ``sharp'' features of different dimensions can be incorporated naturally. We use a narrow averaging mask that is applied to the vertices of the mesh and/or to eventual functions defined on the mesh. The general study of the limit smoothness of the approach requires new analysis techniques that are beyond the scope of this paper. Categories and Subject Descriptors (according to ACM CCS): I.3.5 [Computer Graphics]: Curve, surface, solid, and object representations. Volumetric meshes, recursive subdivision methods.

We describe a general framework for out-of-core rendering and management of massive terrain surfaces. The two key components of this framework are: view-dependent refinement of the terrain mesh and a simple scheme for organizing the terrain data to improve coherence and reduce the number of paging events from external storage to main memory. Similar to several previously proposed methods for view-dependent refinement, we recursively subdivide a triangle mesh defined over regularly gridded data using longest-edge bisection. As part of this single, per-frame refinement pass, we perform triangle stripping, view frustum culling, and smooth blending of geometry using geomorphing. Meanwhile, our refinement framework supports a large class of error metrics, is highly competitive in terms of rendering performance, and is surprisingly simple to implement. Independent of our refinement algorithm, we also describe several data layout techniques for providing coherent access to the terrain data. By reordering the data in a manner that is more consistent with our recursive access pattern, we show that visualization of gigabyte-size data sets can be realized even on low-end, commodity PCs without the need for complicated and explicit data paging techniques. Rather, by virtue of dramatic improvements in multilevel cache coherence, we rely on the built-in paging mechanisms of the operating system to perform this task. The end result is a straightforward, simple-to-implement, pointerless indexing scheme that dramatically improves the data locality and paging performance over conventional matrix-based layouts.

In this paper we introduce a new indexing scheme for progressive traversal and visualization of large regular grids. We demonstrate the potential of our approach by providing a tool that displays at interactive rates planar slices of scalar field data with very modest computing resources. We obtain unprecedented results both in terms of absolute performance and, more importantly, in terms of scalability. On a laptop computer we provide real time interaction with a 20483 grid (8 Giga-nodes) using only 20MB of memory. On an SGI Onyx we slice interactively an 81923 grid (½ tera-nodes) using only 60MB of memory. The scheme relies simply on the determination of an appropriate reordering of the rectilinear grid data and a progressive construction of the output slice. The reordering minimizes the amount of I/O performed during the out-of-core computation. The progressive and asynchronous computation of the output provides flexible quality/speed tradeoffs and a time-critical and interruptible user interface.

We present an elegant and simple to implement framework for performing out-of-core visualization and view-dependent refinement of large terrain surfaces. Contrary to the trend of increasingly elaborate algorithms for large-scale terrain visualization, our algorithms and data structures have been designed with the primary goal of simplicity and efficiency of implementation. Our approach to managing large terrain data also departs from more conventional strategies based on data tiling. Rather than emphasizing how to segment and efficiently bring data in and out of memory, we focus on the manner in which the data is laid out to achieve good memory coherency for data accesses made in a top-down (coarse-to-fine) refinement of the terrain. We present and compare the results of using several different data indexing schemes, and propose a simple to compute index that yields substantial improvements in locality and speed over more commonly used data layouts. Our second contribution is a new and simple, yet easy to generalize method for view-dependent refinement. Similar to several published methods in this area, we use longest edge bisection in a top-down traversal of the mesh hierarchy to produce a continuous surface with subdivision connectivity. In tandem with the refinement, we perform view frustum culling and triangle stripping. These three components are done together in a single pass over the mesh. We show how this framework supports virtually any error metric, while still being highly memory and compute efficient.

Multi-resolution techniques enhance the ability of graphics and visual systems to overcome limitations in time, space and transmission costs. Numerous techniques have been presented which concentrate on creating level of detail models for static meshes. Time-dependent deformable meshes impose even greater difficulties on such systems. In this paper we describe a solution for using level of details for time dependent meshes. Our solution allows for both temporal and spatial level of details to be combined in an efficient manner. By separating low and high frequency temporal information, we gain the ability to create very fast coarse updates in the temporal dimension, which can be adaptively refined for greater details.

Multi-resolution techniques and models have been shown to be effective for the display and transmission of large static geometric object. Dynamic environments with internally deforming models and scientific simulations using dynamic meshes pose greater challenges in terms of time and space, and need the development of similar solutions. We introduce the T-DAG, an adaptive multi-resolution representation for dynamic meshes with arbitrary deformations including attribute, position, connectivity and topology changes. T-DAG stands for time-dependent directed acyclic graph which defines the structure supporting this representation. We also provide an incremental algorithm (in time) for constructing the T-DAG representation of a given input mesh. This enables the traversal and use of the multi-resolution dynamic model for partial playback while still constructing new time-steps.

We propose a new layering structure to partition an arbitrary triangular mesh (no-manifold and arbitrary-genus) into generalized triangle strips. An efficient and flexible encoding of the connectivity, vertex coordinates and attribute data yields excellent single-resolution compression. This scheme gracefully solves the "crack" problem and also prevents error propagation while providing efficient prediction coding for both geometry and photometry data such as positions, color, normal, and texture coordinates. We present an encoder and decoder. We introduce a layering scheme to partition input data, we address the coding of connectivity and geometry, and discuss the attribute coding. Experimental results are presented.

The recent growth in the size and availability of large triangular surface models has generated interest in compact multi-resolution progressive representation and data transmission. An ongoing challenge is to design an efficient data structure that encompasses both compactness of geometric representations and visual quality of progressive representations. We introduce a topological layering based data structure and an encoding scheme to build a compact progressive representation of an arbitrary triangular mesh (a 2D simplicial complex in 3D) with attached attribute data. This compact representation is composed of multiple levels of detail that can be progressively transmitted and displayed. The global topology, which is the number of holes and connected components, can be flexibly changed among successive levels while still achieving guaranteed size of the coarsest level mesh for very complex models. The flexibility in our encoding scheme also allows topology preserving progressivity.

Scalar fields arise in every scientific application. Existing scalar visualization techniques require that the user infers the global scalar structure from what is frequently an insufficient display of information. We present a visualization technique which numerically detects the structure at all scales, removing from the user the responsibility of extracting information implicit in the data, and presenting the structure explicitly for analysis. We further demonstrate how scalar topology detection proves useful for correct visualization and image processing applications such as image co-registration, isocontouring, and mesh compression.

For 2D or 3D meshes that represent a continuous function to the reals, the contours---or isosurfaces---of a specified value are an important way to visualize it. To find such contours, a seed set can be used for the starting points from which the traversal of the contours can start. This paper gives the first methods to obtain seed sets that are provably small in size. They are based on a variant of the contour tree (or topographic change tree). We give a new, simple algorithm to compute such a tree in regular and irregular meshes that requires O(n log n) time in 2D for meshes with n elements, and in O(n 2 ) time in higher dimensions. The additional storage overhead is proportial to the maximum size of any contour (linear in the worst case, but typically less). Given the contour tree, a minimum size seed set can be computed in polynomial time and storage. Since in practice at most linear storage is allowed, we develop a simple approximation algorithm giving a seed set of size at most...

The authors introduce the contour spectrum, a user interface component that improves qualitative user interaction and provides real-time exact quantification in the visualization of isocontours. The contour spectrum is a signature consisting of a variety of scalar data and contour attributes, computed over the range of scalar values /spl omega//spl isin/R. They explore the use of surface, area, volume, and gradient integral of the contour that are shown to be univariate B-spline functions of the scalar value /spl omega/ for multi-dimensional unstructured triangular grids. These quantitative properties are calculated in real-time and presented to the user as a collection of signature graphs (plots of functions of /spl omega/) to assist in selecting relevant isovalues /spl omega//sub 0/ for informative visualization. For time-varying data, these quantitative properties can also be computed over time, and displayed using a 2D interface, giving the user an overview of the time-varying function, and allowing interaction in both isovalue and time step. The effectiveness of the current system and potential extensions are discussed.

Introduction We present a locality-based algorithm to solve the problem of splitting a complex of convex polytopes with a hyperplane or a convex subset of it. The solution to this problem has several applications. One goal is to perform boolean set operations. The solution can also be used to decompose a polyhedron into convex polytopes [3] and to generate good meshes [4]. In higher dimensional spaces it can be used to efficiently compute isocontours of linear approximations of scalar fields (a basic technique of Scientific Visualization) [17, 19]. The approach taken here can also be included in a set of robust algorithms [11, 13, 15, 20, 27, 28] based on finite precision arithmetic. It is also defined in a dimension independent framework [5, 16, 24, 25]. The main contributions of this approach are: (i) it can be applied to polyhedral complexes of any dimension d; (ii) the algorithm is robust (it always produces valid output) and consistent (the topological structure of the resu

This article presents a functional programming approach to geometric design with embedded polyhedral complexes. Its main goals are to show the expressive power of the language as well as its usefulness for geometric design. The language, named PLASM (the Programming LAnguage for Solid Modeling), introduces a very high level approach to “constructive” or “generative” modeling. Geometrical objects are generated by evaluating some suitable language expressions. Because generating expressions can be easily combined, the language also extends the standard variational geometry approach by supporting classes of geometric objects with varying topology and shape. The design language PLASM can be roughly considered as a geometry-oriented extension of a subset of the functional language FL. The language takes a dimension-independent approach to geometry representation and algorithms. In particular it implements an algebraic calculus over embedded polyhedra of any dimension. The generated objects are always geometrically consistent because the validity of geometry is guaranteed at a syntactical level. Such an approach allows one to use a representation scheme which is weaker than those usually adopted in solid modelers, thus encompassing a broader geometric domain, which contains solids, surfaces, and wire-frames, as well as higher-dimensional objects.