Oceanographers rely on visual analysis to interpret model simulations, identify events and phenomena, and track dynamic ocean processes. The ever increasing resolution and complexity of ocean data due to its dynamic nature and multivariate relationships demands a scalable and adaptable visualization tool for interactive exploration. We introduce pyParaOcean, a scalable and interactive visualization system designed specifically for ocean data analysis. pyParaOcean offers specialized modules for common oceanographic analysis tasks, including eddy identification and salinity movement tracking. These modules seamlessly integrate with ParaView as filters, ensuring a user-friendly and easy-to-use system while leveraging the parallelization capabilities of ParaView and a plethora of inbuilt general-purpose visualization functionalities. The creation of an auxiliary dataset stored as a Cinema database helps address I/O and network bandwidth bottlenecks while supporting the generation of quick overview visualizations. We present a case study on the Bay of Bengal to demonstrate the utility of the system and scaling studies to evaluate the efficiency of the system.

We present theory and practice for robust implementations of bi-variate Jacobi set and Reeb space algorithms. Robustness is a fundamental topic in computational geometry that deals with the issues of numerical errors and degenerate cases in algorithm implementations. Computational topology already uses some robustness techniques for the development of scalar field algorithms, such as those for computing critical points, merge trees, contour trees, Reeb graphs, Morse-Smale complexes, and persistent homology. In most cases, robustness can be ensured with floating-point arithmetic, and degenerate cases can be resolved with a standard symbolic perturbation technique called Simulation of Simplicity. However, this becomes much more complex for topological data structures of multifields, such as Jacobi sets and Reeb spaces. The geometric predicates used in their computation require exact arithmetic and a more involved treatment of degenerate cases to ensure correctness. Neither of these challenges has been fully addressed in the literature so far. In this paper, we describe how exact arithmetic and symbolic perturbation schemes can be used to enable robust implementations of bivariate Jacobi set and Reeb space algorithms. In the process, we develop a method for automatically evaluating predicates that can be expressed as large symbolic polynomials, which are difficult to factor appropriately by hand, as is typically done in the computational geometry literature. We provide implementations of all proposed approaches and evaluate their efficiency.

Photon-Counting Computed Tomography (PCCT) is a novel imaging modality that simultaneously acquires volumetric data at multiple X-ray energy levels, generating separate volumes that capture energy-dependent attenuation properties. Attenuation refers to the reduction in X-ray intensity as it passes through different tissues or materials, which depends on their density and atomic composition. This spectral information enhances tissue and material differentiation, enabling more accurate diagnosis and analysis. However, the resulting multivolume datasets are often complex and redundant, making visualization and interpretation challenging. To address these challenges, we propose a method for fusing spectral PCCT data into a single representative volume that enables direct volume rendering and segmentation by leveraging both shared and complementary information across different channels. Our approach starts by computing 2D histograms between pairs of volumes to identify those that exhibit prominent structural features. These histograms reveal relationships and variations that may be difficult to discern from individual volumes alone. Next, we construct an extremum graph from the 2D histogram of two minimally correlated yet complementary volumes—selected to capture both shared and distinct features—thereby maximizing the information content. The graph captures the topological distribution of histogram extrema. By extracting prominent structure within this graph and projecting each grid point in histogram space onto it, we reduce the dimensionality to one, producing a unified volume. This representative volume retains key structural and material characteristics from the original spectral data while significantly reducing the analysis scope from multiple volumes to one. The result is a topology-aware, information-rich fusion of multi-energy CT datasets that facilitates more effective visualization and segmentation.

Electronic transitions in molecules due to the absorption or emission of light is a complex quantum mechanical process. Their study plays an important role in the design of novel materials. A common yet challenging task in the study is to determine the nature of electronic transitions, namely which subgroups of the molecule are involved in the transition by donating or accepting electrons, followed by an investigation of the variation in the donor-acceptor behavior for different transitions or conformations of the molecules. In this paper, we present a novel approach for the analysis of a bivariate field and show its applicability to the study of electronic transitions. This approach is based on two novel operators, the continuous scatterplot (CSP) lens operator and the CSP peel operator, that enable effective visual analysis of bivariate fields. Both operators can be applied independently or together to facilitate analysis. The operators motivate the design of control polygon inputs to extract fiber surfaces of interest in the spatial domain. The CSPs are annotated with a quantitative measure to further support the visual analysis. We study different molecular systems and demonstrate how the CSP peel and CSP lens operators help identify and study donor and acceptor characteristics in molecular systems.

This paper presents a prototypical visualization for the analysis of light-induced dynamics in molecules. It utilizes topological distances to find temporal patterns in scalar fields representing the electronic structure of such molecules and to illustrate the evolution of their features. It also provides a means to correlate these findings to the geometric evolution of the molecules.

Diffusion-weighted magnetic resonance imaging (D-MRI) is a technique to measure the diffusion of water, in biological tissues. It is used to detect microscopic patterns, such as neural fibers in the living human brain, with many medical and neuroscience applications e.g. for fiber tracking. In this paper, we consider High-Angular Resolution Diffusion Imaging (HARDI) which provides one of the richest representations of water diffusion. It records the movement of water molecules by measuring diffusion under 64 or more directions. A key challenge is that it generates high-dimensional, large, and complex datasets. In our work, we develop a novel representation that exploits the inherent sparsity of the HARDI signal by approximating it as a linear sum of basic atoms in an overcomplete data-driven dictionary using only a sparse set of coefficients. We show that this approach can be efficiently integrated into the standard q-ball imaging pipeline to compute the diffusion orientation distribution function (ODF). Sparse representations have the potential to reduce the size of the data while also giving some insight into the data. To explore the results, we provide a visualization of the atoms of the dictionary and their frequency in the data to highlight the basic characteristics of the data. We present our proposed pipeline and demonstrate its performance on 5 HARDI datasets.

The recent high-pressure synthesis of pentazolates and the subsequent stabilization of the aromatic [N-5](-) anion at atmospheric pressure have had an immense impact on nitrogen chemistry. Other aromatic nitrogen species have also been actively sought, including the hexaazabenzene N-6 ring. Although a variety of configurations and geometries have been proposed based on ab initio calculations, one that stands out as a likely candidate is the aromatic hexazine anion [N-6](4-). Here we present the synthesis of this species, realized in the high-pressure potassium nitrogen compound K9N56 formed at high pressures (46 and 61 GPa) and high temperature (estimated to be above 2,000 K) by direct reaction between nitrogen and KN3 in a laser-heated diamond anvil cell. The complex structure of K9N56-composed of 520 atoms per unit cell-was solved based on synchrotron single-crystal X-ray diffraction and corroborated by density functional theory calculations. The observed hexazine anion [N-6](4-) is planar and proposed to be aromatic.

Merge trees, a type of topological descriptor, serve to identify and summarize the topological characteristics associated with scalar fields. They present a great potential for the analysis and visualization of time-varying data. First, they give compressed and topology-preserving representations of data instances. Second, their comparisons provide a basis for studying the relations among data instances, such as their distributions, clusters, outliers, and periodicities. A number of comparative measures have been developed for merge trees. However, these measures are often computationally expensive since they implicitly consider all possible correspondences between critical points of the merge trees. In this paper, we perform geometry-aware comparisons of merge trees. The main idea is to decouple the computation of a comparative measure into two steps: a labeling step that generates a correspondence between the critical points of two merge trees, and a comparison step that computes distances between a pair of labeled merge trees by encoding them as matrices. We show that our approach is general, computationally efficient, and practically useful. Our general framework makes it possible to integrate geometric information of the data domain in the labeling process. At the same time, it reduces the computational complexity since not all possible correspondences have to be considered. We demonstrate via experiments that such geometry-aware merge tree comparisons help to detect transitions, clusters, and periodicities of a time-varying dataset, as well as to diagnose and highlight the topological changes between adjacent data instances.

We propose a visual analysis method for the comparison and evaluation of structures in solid-state materials based on the electron density field using topological analysis. The work has been motivated by a material science application, specifically looking for new so-called layered materials whose physical properties are required in many modern technological developments. Due to the incredibly large search space, this is a slow and tedious process, requiring efficient data analysis to characterize and understand the material properties. The core of our proposed analysis pipeline is an abstract bar representation that serves as a concise signature of the material, supporting direct comparison and also an exploration of different material candidates.

In this work, we propose trait-based merge trees a generalization of merge trees to feature level sets, targeting the analysis of tensor field or general multi-variate data. For this, we employ the notion of traits defined in attribute space as introduced in the feature level sets framework. The resulting distance field in attribute space induces a scalar field in the spatial domain that serves as input for topological data analysis. The leaves in the merge tree represent those areas in the input data that are closest to the defined trait and thus most closely resemble the defined feature. Hence, the merge tree yields a hierarchy of features that allows for querying the most relevant and persistent features. The presented method includes different query methods for the tree which enable the highlighting of different aspects. We demonstrate the cross-application capabilities of this approach with three case studies from different domains.