The Stay Centered project at Technische Universitat Chemnitz has the goal to improve the overall security of air traffic controllers. Therefore, we attempt to empirically comprehend the usual controller workspace and their dyadic team structure. Within this context, the following paper describes actual interfaces and visualization, discusses recent research within this field and outlines the project's intention.

Abstract The operation of an airline is a very complex task and disruptions to the planned operation can occur on very short notice. Already a small disruption like a delay of some minutes can cost the airline a tremendous amount of money. Hence, it is crucial to proactively control all operations of the airline and efficiently prioritize and handle disruptions. Due to the complex setting and the need for ad hoc decisions this task can only be carried out by human operation controllers. In the field of airline operations control there exists already a vast variety of different software in productive use. We analyze the different approaches from two of the market leaders and identify problematic design choices. We take into account this analysis and develop a set of rules for an intuitive visualization of airline disruption data. Finally, we introduce our tool for visualizing such data which complies to these rules. The visualization enables the user to gain a fast overview over the current problem situation and to intuitively prioritize different problems and problem hierarchies. The efficiency of the design is evaluated with the help of a user study which shows that the new system significantly outperforms the current state of the art.

Abstract Visualization of high‐dimensional data requires a mapping to a visual space. Whenever the goal is to preserve similarity relations a frequent strategy is to use 2D projections, which afford intuitive interactive exploration, e.g., by users locating and selecting groups and gradually drilling down to individual objects. In this paper, we propose a framework for projecting high‐dimensional data to 3D visual spaces, based on a generalization of the Least‐Square Projection (LSP). We compare projections to 2D and 3D visual spaces both quantitatively and through a user study considering certain exploration tasks. The quantitative analysis confirms that 3D projections outperform 2D projections in terms of precision. The user study indicates that certain tasks can be more reliably and confidently answered with 3D projections. Nonetheless, as 3D projections are displayed on 2D screens, interaction is more difficult. Therefore, we incorporate suitable interaction functionalities into a framework that supports 3D transformations, predefined optimal 2D views, coordinated 2D and 3D views, and hierarchical 3D cluster definition and exploration. For visually encoding data clusters in a 3D setup, we employ color coding of projected data points as well as four types of surface renderings. A second user study evaluates the suitability of these visual encodings. Several examples illustrate the framework's applicability for both visual exploration of multidimensional abstract (non‐spatial) data as well as the feature space of multi‐variate spatial data.

Abstract Signed distance functions (SDF) to explicit or implicit surface representations are intensively used in various computer graphics and visualization algorithms. Among others, they are applied to optimize collision detection, are used to reconstruct data fields or surfaces, and, in particular, are an obligatory ingredient for most level set methods. Level set methods are common in scientific visualization to extract surfaces from scalar or vector fields. Usual approaches for the construction of an SDF to a surface are either based on iterative solutions of a special partial differential equation or on marching algorithms involving a polygonization of the surface. We propose a novel method for a non‐iterative approximation of an SDF and its derivatives in a vicinity of a manifold. We use a second‐order algebraic fitting scheme to ensure high accuracy of the approximation. The manifold is defined (explicitly or implicitly) as an isosurface of a given volumetric scalar field. The field may be given at a set of irregular and unstructured samples. Stability and reliability of the SDF generation is achieved by a proper scaling of weights for the Moving Least Squares approximation, accurate choice of neighbors, and appropriate handling of degenerate cases. We obtain the solution in an explicit form, such that no iterative solving is necessary, which makes our approach fast.

Abstract Point clusters occur in both spatial and non‐spatial data. In the former context they may represent segmented particle data, in the latter context they may represent clusters in scatterplots. In order to visualize such point clusters, enclosing surfaces lead to much better comprehension than pure point renderings. We propose a flexible system for the generation of enclosing surfaces for 3D point clusters. We developed a GPU‐based 3D discrete Voronoi diagram computation that supports all surface extractions. Our system provides three different types of enclosing surfaces. By generating a discrete distance field to the point cluster and extracting an isosurface from the field, an enclosing surface with any distance to the point cluster can be generated. As a second type of enclosing surfaces, a hull of the point cluster is extracted. The generation of the hull uses a projection of the discrete Voronoi diagram of the point cluster to an isosurface to generate a polygonal surface. Generated hulls of non‐convex clusters are also non‐convex. The third type of enclosing surfaces can be created by computing a distance field to the hull and extracting an isosurface from the distance field. This method exhibits reduced bumpiness and can extract surfaces arbitrarily close to the point cluster without losing connectedness. We apply our methods to the visualization of multidimensional spatial and non‐spatial data. Multidimensional clusters are extracted and projected into a 3D visual space, where the point clusters are visualized. The respective clusters can also be visualized in object space when dealing with multidimensional particle data.

Data sets resulting from physical simulations typically contain a multitude of physical variables. It is, therefore, desirable that visualization methods take into account the entire multi-field volume data rather than concentrating on one variable. We present a visualization approach based on surface extraction from multi-field particle volume data. The surfaces segment the data with respect to the underlying multi-variate function. Decisions on segmentation properties are based on the analysis of the multi-dimensional feature space. The feature space exploration is performed by an automated multi-dimensional hierarchical clustering method, whose resulting density clusters are shown in the form of density level sets in a 3D star coordinate layout. In the star coordinate layout, the user can select clusters of interest. A selected cluster in feature space corresponds to a segmenting surface in object space. Based on the segmentation property induced by the cluster membership, we extract a surface from the volume data. Our driving applications are Smoothed Particle Hydrodynamics (SPH) simulations, where each particle carries multiple properties. The data sets are given in the form of unstructured point-based volume data. We directly extract our surfaces from such data without prior resampling or grid generation. The surface extraction computes individual points on the surface, which is supported by an efficient neighborhood computation. The extracted surface points are rendered using point-based rendering operations. Our approach combines methods in scientific visualization for object-space operations with methods in information visualization for feature-space operations.

Smooth surface extraction using partial differential equations (PDEs) is a well-known and widely used technique for visualizing volume data. Existing approaches operate on gridded data and mainly on regular structured grids. When considering unstructured point-based volume data where sample points do not form regular patterns nor are they connected in any form, one would typically resample the data over a grid prior to applying the known PDE-based methods. We propose an approach that directly extracts smooth surfaces from unstructured point-based volume data without prior resampling or mesh generation. When operating on unstructured data one needs to quickly derive neighborhood information. The respective information is retrieved by partitioning the 3D domain into cells using a kd-tree and operating on its cells. We exploit neighborhood information to estimate gradients and mean curvature at every sample point using a four-dimensional least-squares fitting approach. Gradients and mean curvature are required for applying the chosen PDE-based method that combines hyperbolic advection to an isovalue of a given scalar field and mean curvature flow. Since we are using an explicit time-integration scheme, time steps and neighbor locations are bounded to ensure convergence of the process. To avoid small global time steps, we use asynchronous local integration. We extract the surface by successively fitting a smooth auxiliary function to the data set. This auxiliary function is initialized as a signed distance function. For each sample and for every time step we compute the respective gradient, the mean curvature, and a stable time step. With these informations the auxiliary function is manipulated using an explicit Euler time integration. The process successively continues with the next sample point in time. If the norm of the auxiliary function gradient in a sample exceeds a given threshold at some time, the auxiliary function is reinitialized to a signed distance function. After convergence of the evolution, the resulting smooth surface is obtained by extracting the zero isosurface from the auxiliary function using direct isosurface extraction from unstructured point-based volume data and rendering the extracted surface using point-based rendering methods.

Isosurface extraction is a standard visualization method for scalar volume data and has been subject to research for decades. Nevertheless, to our knowledge, no isosurface extraction method exists that directly extracts surfaces from scattered volume data without 3D mesh generation or reconstruction over a structured grid. We propose a method based on spatial domain partitioning using a kd-tree and an indexing scheme for efficient neighbor search. Our approach consists of a geometry extraction and a rendering step. The geometry extraction step computes points on the isosurface by linearly interpolating between neighboring pairs of samples. The neighbor information is retrieved by partitioning the 3D domain into cells using a kd-tree. The cells are merely described by their index and bitwise index operations allow for a fast determination of potential neighbors. We use an angle criterion to select appropriate neighbors from the small set of candidates. The output of the geometry step is a point cloud representation of the isosurface. The final rendering step uses point-based rendering techniques to visualize the point cloud. Our direct isosurface extraction algorithm for scattered volume data produces results of quality close to the results from standard isosurface extraction algorithms for gridded volume data (like marching cubes). In comparison to 3D mesh generation algorithms (like Delaunay tetrahedrization), our algorithm is about one order of magnitude faster for the examples used in this paper.