Spatio‐Temporal Contours from Deep Volume Raycasting

We visualize contours for spatio‐temporal processes to indicate where and when non‐continuous changes occur or spatial bounds are encountered. All time steps are comprised densely in one visualization, with contours allowing to efficiently analyze processes in the data even in case of spatial or temporal overlap. Contours are determined on the basis of deep raycasting that collects samples across time and depth along each ray. For each sample along a ray, its closest neighbors from adjacent rays are identified, considering time, depth, and value in the process. Large distances are represented as contours in image space, using color to indicate temporal occurrence. This contour representation can easily be combined with volume rendering‐based techniques, providing both full spatial detail for individual time steps and an outline of the whole time series in one view. Our view‐dependent technique supports efficient progressive computation, and requires no prior assumptions regarding the shape or nature of processes in the data. We discuss and demonstrate the performance and utility of our approach via a variety of data sets, comparison and combination with an alternative technique, and feedback by a domain scientist.     

Visualizing the Phase Space of Heterogeneous Inertial Particles in 2D Flows

In many scientific disciplines, the motion of finite‐sized objects in fluid flows plays an important role, such as in brownout engineering, sediment transport, oceanology or meteorology. These finite‐sized objects are called inertial particles and, in contrast to traditional tracer particles, their motion depends on their current position, their own particle velocity, the time and their size. Thus, the visualization of their motion becomes a high‐dimensional problem that entails computational and perceptual challenges. So far, no visualization explored and visualized the particle trajectories under variation of all seeding parameters. In this paper, we propose three coordinated views that visualize the different aspects of the high‐dimensional space in which the particles live. We visualize the evolution of particles over time, showing that particles travel different distances in the same time, depending on their size. The second view provides a clear illustration of the trajectories of different particle sizes and allows the user to easily identify differences due to particle size. Finally, we embed the trajectories in the space‐velocity domain and visualize their distance to an attracting manifold using ribbons. In all views, we support interactive linking and brushing, and provide abstraction through density volumes that are shown by direct volume rendering and isosurface slabs. Using our method, users gain deeper insights into the dynamics of inertial particles in 2D fluids, including size‐dependent separation, preferential clustering and attraction. We demonstrate the effectiveness of our method in multiple steady and unsteady 2D flows.     

An Approximate Parallel Vectors Operator for Multiple Vector Fields

The Parallel Vectors (PV) Operator extracts the locations of points where two vector fields are parallel. In general, these features are line structures. The PV operator has been used successfully for a variety of problems, which include finding vortex‐core lines or extremum lines. We present a new generic feature extraction method for multiple 3D vector fields: The Approximate Parallel Vectors (APV) Operator extracts lines where all fields are approximately parallel. The definition of the APV operator is based on the application of PV for two vector fields that are derived from the given set of fields. The APV operator enables the direct visualization of features of vector field ensembles without processing fields individually and without causing visual clutter. We give a theoretical analysis of the APV operator and demonstrate its utility for a number of ensemble data.     

An Interactive Visualization System for Large Sets of Phase Space Trajectories

We introduce a visual analysis system with GPU acceleration techniques for large sets of trajectories from complex dynamical systems. The approach is based on an interactive Boolean combination of subsets into a Focus+Context phase‐space visualization. We achieve high performance through efficient bitwise algorithms utilizing runtime generated GPU shaders and kernels. This enables a higher level of interactivity for visualizing the large multivariate trajectory data. We explain how our design meets a set of carefully considered analysis requirements, provide performance results, and demonstrate utility through case studies with many‐particle simulation data from two application areas.     

Designing Animated Transitions to Convey Aggregate Operations

Data can be aggregated in many ways before being visualized in charts, profoundly affecting what a chart conveys. Despite this importance, the type of aggregation is often communicated only via axis titles. In this paper, we investigate the use of animation to disambiguate different types of aggregation and communicate the meaning of aggregate operations. We present design rationales for animated transitions depicting aggregate operations and present the results of an experiment assessing the impact of these different transitions on identification tasks. We find that judiciously staged animated transitions can improve subjects' accuracy at identifying the aggregation performed, though sometimes with longer response times than with static transitions. Through an analysis of participants' rankings and qualitative responses, we find a consistent preference for animation over static transitions and highlight visual features subjects report relying on to make their judgments. We conclude by extending our animation designs to more complex charts of aggregated data such as box plots and bootstrapped confidence intervals.     

Analysis of Long Molecular Dynamics Simulations Using Interactive Focus+Context Visualization

Analyzing molecular dynamics (MD) simulations is a key aspect to understand protein dynamics and function. With increasing computational power, it is now possible to generate very long and complex simulations, which are cumbersome to explore using traditional 3D animations of protein movements. Guided by requirements derived from multiple focus groups with protein engineering experts, we designed and developed a novel interactive visual analysis approach for long and crowded MD simulations. In this approach, we link a dynamic 3D focus+context visualization with a 2D chart of time series data to guide the detection and navigation towards important spatio‐temporal events. The 3D visualization renders elements of interest in more detail and increases the temporal resolution dependent on the time series data or the spatial region of interest. In case studies with different MD simulation data sets and research questions, we found that the proposed visual analysis approach facilitates exploratory analysis to generate, confirm, or reject hypotheses about causalities. Finally, we derived design guidelines for interactive visual analysis of complex MD simulation data.     

Towards Glyphs for Uncertain Symmetric Second‐Order Tensors

Measured data often incorporates some amount of uncertainty, which is generally modeled as a distribution of possible samples. In this paper, we consider second‐order symmetric tensors with uncertainty. In the 3D case, this means the tensor data consists of 6 coefficients – uncertainty, however, is encoded by 21 coefficients assuming a multivariate Gaussian distribution as model. The high dimension makes the direct visualization of tensor data with uncertainty a difficult problem, which was until now unsolved. The contribution of this paper consists in the design of glyphs for uncertain second‐order symmetric tensors in 2D and 3D. The construction consists of a standard glyph for the mean tensor that is augmented by a scalar field that represents uncertainty. We show that this scalar field and therefore the displayed glyph encode the uncertainty comprehensively, i.e., there exists a bijective map between the glyph and the parameters of the distribution. Our approach can extend several classes of existing glyphs for symmetric tensors to additionally encode uncertainty and therefore provides a possible foundation for further uncertain tensor glyph design. For demonstration, we choose the well‐known superquadric glyphs, and we show that the uncertainty visualization satisfies all their design constraints.     

DimSUM: Dimension and Scale Unifying Map for Visual Abstraction of DNA Origami Structures

We present a novel visualization concept for DNA origami structures that integrates a multitude of representations into a Dimension and Scale Unifying Map (DimSUM). This novel abstraction map provides means to analyze, smoothly transition between, and interact with many visual representations of the DNA origami structures in an effective way that was not possible before. DNA origami structures are nanoscale objects, which are challenging to model in silico. In our holistic approach we seamlessly combine three‐dimensional realistic shape models, two‐dimensional diagrammatic representations, and ordered alignments in one‐dimensional arrangements, with semantic transitions across many scales. To navigate through this large, two‐dimensional abstraction map we highlight locations that users frequently visit for certain tasks and datasets. Particularly interesting viewpoints can be explicitly saved to optimize the workflow. We have developed DimSUM together with domain scientists specialized in DNA nanotechnology. In the paper we discuss our design decisions for both the visualization and the interaction techniques. We demonstrate two practical use cases in which our approach increases the specialists’ understanding and improves their effectiveness in the analysis. Finally, we discuss the implications of our concept for the use of controlled abstraction in visualization in general.     

Baseball Timeline: Summarizing Baseball Plays Into a Static Visualization

In sports, Play Diagrams are the standard way to represent and convey information. They are widely used by coaches, managers, journalists and fans in general. There are situations where diagrams may be hard to understand, for example, when several actions are packed in a certain region of the field or there are just too many actions to be transformed in a clear depiction of the play. The representation of how actions develop through time, in particular, may be hardly achieved on such diagrams. The time, and the relationship among the actions of the players through time, is critical on the depiction of complex plays. In this context, we present a study on how player actions may be clearly depicted on 2D diagrams. The study is focused on Baseball plays, a sport where diagrams are heavily used to summarize the actions of the players. We propose a new and simple approach to represent spatiotemporal information in the form of a timeline. We designed our visualization with a requirement driven approach, conducting interviews and fulfilling the needs of baseball experts and expert‐fans. We validate our approach by presenting a detailed analysis of baseball plays and conducting interviews with four domain experts.     

Bridging the Data Analysis Communication Gap Utilizing a Three‐Component Summarized Line Graph

Communication‐minded visualizations are designed to provide their audience—managers, decision‐makers, and the public—with new knowledge. Authoring such visualizations effectively is challenging because the audience often lacks the expertise, context, and time that professional analysts have at their disposal to explore and understand datasets. We present a novel summarized line graph visualization technique designed specifically for data analysts to communicate data to decision‐makers more effectively and efficiently. Our summarized line graph reduces a large and detailed dataset of multiple quantitative time‐series into (1) representative data that provides a quick takeaway of the full dataset; (2) analytical highlights that distinguish specific insights of interest; and (3) a data envelope that summarizes the remaining aggregated data. Our summarized line graph achieved the best overall results when evaluated against line graphs, band graphs, stream graphs, and horizon graphs on four representative tasks.     

Towards Easy Comparison of Local Businesses Using Online Reviews

With the rapid development of e‐commerce, there is an increasing number of online review websites, such as Yelp, to help customers make better purchase decisions. Viewing online reviews, including the rating score and text comments by other customers, and conducting a comparison between different businesses are the key to making an optimal decision. However, due to the massive amount of online reviews, the potential difference of user rating standards, and the significant variance of review time, length, details and quality, it is difficult for customers to achieve a quick and comprehensive comparison. In this paper, we present E‐Comp, a carefully‐designed visual analytics system based on online reviews, to help customers compare local businesses at different levels of details. More specifically, intuitive glyphs overlaid on maps are designed for quick candidate selection. Grouped Sankey diagram visualizing the rating difference by common customers is chosen for more reliable comparison of two businesses. Augmented word cloud showing adjective‐noun word pairs, combined with a temporal view, is proposed to facilitate in‐depth comparison of businesses in terms of different time periods, rating scores and features. The effectiveness and usability of E‐Comp are demonstrated through a case study and in‐depth user interviews.     

Exploring Online Learners' Interactive Dynamics by Visually Analyzing Their Time‐anchored Comments

MOOCs (Massive Open Online Courses) are increasingly prevalent as an online educational resource open to everyone and have attracted hundreds of thousands learners enrolling these online courses. At such scale, there is potentially rich information of learners' behaviors embedded in the interactions between learners and videos that may help instructors and content producers adjust the instructions and refine the online courses. However, the lack of tools to visualize information from interactive data, including messages left to the videos at particular timestamps as well as the temporal variations of learners' online participation and perceived experience, has prevented people from gaining more insights from video‐watching logs. In this paper, we focus on extracting and visualizing useful information from time‐anchored comments that learners left to specific time points of the videos when watching them. Timestamps as a kind of metadata of messages can be useful to recover the interactive dynamics of learners occurring around the videos. Therefore, we present a visualization system to analyze and categorize time‐anchored comments based on topics and content types. Our system integrates visualization methods of temporal text data, namely ToPIN and ThemeRiver, which can help people understand the quality and quantity of online learners' feedback and their states of learning. To evaluate the proposed system, we visualized time‐anchored commenting data from two online course videos, and conducted two user studies participated by course instructors and third‐party educational evaluators. The results validate the usefulness of the approach and show how the quantitative and qualitative visualizations can be used to gain interesting insights around learners' online learning behaviors.     

Core Lines in 3D Second‐Order Tensor Fields

Vortices are important features in vector fields that show a swirling behavior around a common core. The concept of a vortex core line describes the center of this swirling behavior. In this work, we examine the extension of this concept to 3D second‐order tensor fields. Here, a behavior similar to vortices in vector fields can be observed for trajectories of the eigenvectors. Vortex core lines in vector fields were defined by Sujudi and Haimes to be the locations where stream lines are parallel to an eigenvector of the Jacobian. We show that a similar criterion applied to the eigenvector trajectories of a tensor field yields structurally stable lines that we call tensor core lines. We provide a formal definition of these structures and examine their mathematical properties. We also present a numerical algorithm for extracting tensor core lines in piecewise linear tensor fields. We find all intersections of tensor core lines with the faces of a dataset using a simple and robust root finding algorithm. Applying this algorithm to tensor fields obtained from structural mechanics simulations shows that it is able to effectively detect and visualize regions of rotational or hyperbolic behavior of eigenvector trajectories.     

Efficient Optimal Overlap Removal: Algorithms and Experiments

Motivated by visualizing spatial data using proportional symbols, we study the following problem: given a set of overlapping squares of varying sizes, minimally displace the squares as to remove the overlap while maintaining the orthogonal order on their centers. Though this problem is NP‐hard, we show that rotating the squares by 45 degrees into diamonds allows for a linear or convex quadratic program. It is thus efficiently solvable even for relatively large instances. This positive result and the flexibility offered by constraint programming allow us to study various trade‐offs for overlap removal. Specifically, we model and evaluate through computational experiments the relations between displacement, scale and order constraints for static data, and between displacement and temporal coherence for time‐varying data. Finally, we also explore the generalization of our methodology to other shapes.     

Focus+Context Exploration of Hierarchical Embeddings

Hierarchical embeddings, such as HSNE, address critical visual and computational scalability issues of traditional techniques for dimensionality reduction. The improved scalability comes at the cost of the need for increased user interaction for exploration. In this paper, we provide a solution for the interactive visual Focus+Context exploration of such embeddings. We explain how to integrate embedding parts from different levels of detail, corresponding to focus and context groups, in a joint visualization. We devise an according interaction model that relates typical semantic operations on a Focus+Context visualization with the according changes in the level‐of‐detail‐hierarchy of the embedding, including also a mode for comparative Focus+Context exploration and extend HSNE to incorporate the presented interaction model. In order to demonstrate the effectiveness of our approach, we present a use case based on the visual exploration of multi‐dimensional images.     

Design and Automated Generation of Japanese Picture Puzzles

We introduce the generalized nonogram, an extension of the well‐known nonogram or Japanese picture puzzle. It is not based on a regular square grid but on a subdivision (arrangement) with differently shaped cells, bounded by straight lines or curves. To generate a good, clear puzzle from a filled line drawing, the arrangement that is formed for the puzzle must meet a number of criteria. Some of these relate to the puzzle and some to the geometry. We give an overview of these criteria and show that a puzzle can be generated by an optimization method like simulated annealing. Experimentally, we analyze the convergence of the method and the remaining penalty score on several input pictures along with various other design options.     

IGM‐Vis: Analyzing Intergalactic and Circumgalactic Medium Absorption Using Quasar Sightlines in a Cosmic Web Context

We introduce IGM‐Vis, a novel astrophysics visualization and data analysis application for investigating galaxies and the gas that surrounds them in context with their larger scale environment, the Cosmic Web. Environment is an important factor in the evolution of galaxies from actively forming stars to quiescent states with little, if any, discernible star formation activity. The gaseous halos of galaxies (the circumgalactic medium, or CGM) play a critical role in their evolution, because the gas necessary to fuel star formation and any gas expelled from widely observed galactic winds must encounter this interface region between galaxies and the intergalactic medium (IGM). We present a taxonomy of tasks typically employed in IGM/CGM studies informed by a survey of astrophysicists at various career levels, and demonstrate how these tasks are facilitated via the use of our visualization software. Finally, we evaluate the effectiveness of IGM‐Vis through two in‐depth use cases that depict real‐world analysis sessions that use IGM/CGM data.     

SurgeryCuts: Embedding Additional Information in Maps without Occluding Features

Visualizing contextual information to a map often comes at the expense of overplotting issues. Especially for use cases with relevant map features in the immediate vicinity of an information to add, occlusion of the relevant map context should be avoided. We present SurgeryCuts, a map manipulation technique for the creation of additional canvas area for contextual visualizations on maps. SurgeryCuts is occlusion‐free and does not shift, zoom or alter the map viewport. Instead, relevant parts of the map can be cut apart. The affected area is controlledly distorted using a parameterizable warping function fading out the map distortion depending on the distance to the cut. We define extended metrics for our approach and compare to related approaches. As well, we demonstrate the applicability of our approach at the example of tangible use cases and a comparative user study.     

Bird's‐Eye ‐ Large‐Scale Visual Analytics of City Dynamics using Social Location Data

The analysis of behavioral city dynamics, such as temporal patterns of visited places and citizens' mobility routines, is an essential task for urban and transportation planning. Social media applications such as Foursquare and Twitter provide access to large‐scale and up‐to‐date dynamic movement data that not only help to understand the social life and pulse of a city but also to maintain and improve urban infrastructure. However, the fast growth rate of this data poses challenges for conventional methods to provide up‐to‐date, flexible analysis. Therefore, planning authorities barely consider it. We present a system and design study to leverage social media data that assist urban and transportation planners to achieve better monitoring and analysis of city dynamics such as visited places and mobility patterns in large metropolitan areas. We conducted a goal‐and‐task analysis with urban planning experts. To address these goals, we designed a system with a scalable data monitoring back‐end and an interactive visual analytics interface. The monitoring component uses intelligent pre‐aggregation to allow dynamic queries in near real‐time. The visual analytics interface leverages unsupervised learning to reveal clusters, routines, and unusual behavior in massive data, allowing to understand patterns in time and space. We evaluated our approach based on a qualitative user study with urban planning experts which demonstrates that intuitive integration of advanced analytical tools with visual interfaces is pivotal in making behavioral city dynamics accessible to practitioners. Our interviews also revealed areas for future research.     

The Dependent Vectors Operator

In this paper, we generalize the parallel vectors operator due to Peikert and Roth to arbitrary dimension, i.e., to four‐dimensional fields and beyond. Whereas the original operator tested for parallelism of two (derived) 2D or 3D vector fields, we reformulate the concept in terms of linear dependency of sets of vector fields, and propose a generic technique to extract and filter the solution manifolds. We exemplify our approach for vortex cores, bifurcations, and ridges as well as valleys in higher dimensions.