Understanding large amounts of spatiotemporal data from particle-based simulations, such as molecular dynamics, often relies on the computation and analysis of aggregate measures. These, however, by virtue of aggregation, hide structural information about the space time localization of the studied phenomena. This leads to degenerate cases where the measures fail to capture distinct behaviour. In order to drill into these aggregate values, we propose a multi-scale visual exploration technique. Our novel representation, based on partial domain aggregation, enables the construction of a continuous scale-space for discrete datasets and the simultaneous exploration of scales in both space and time. We link these two scale-spaces in a scale-space space-time cube and model linked views as orthogonal slices through this cube, thus enabling the rapid identification of spatio-temporal patterns at multiple scales. To demonstrate the effectiveness of our approach, we showcase an advanced exploration of a protein-ligand simulation.
Substantial work has been done on the visualization of trajectory-based simulation data, including projects such as OVITO @cite_34 , Trillion Particles @cite_23 , Multiscale HIV @cite_13 . These are primarily concerned with the sheer volume of the data and its direct visualization, rather than the computation of derived properties and their temporal analysis.
@cite_34 @cite_13 @cite_23
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Petascale plasma physics simulations have recently entered the regime of simulating trillions of particles. These unprecedented simulations generate massive amounts of data, posing significant challenges in storage, analysis, and visualization. In this paper, we present parallel I O, analysis, and visualization results from a VPIC trillion particle simulation running on 120,000 cores, which produces 30TB of data for a single timestep. We demonstrate the successful application of H5Part, a particle data extension of parallel HDF5, for writing the dataset at a significant fraction of system peak I O rates. To enable efficient analysis, we develop hybrid parallel FastQuery to index and query data using multi-core CPUs on distributed memory hardware. We show good scalability results for the FastQuery implementation using up to 10,000 cores. Finally, we apply this indexing query-driven approach to facilitate the first-ever analysis and visualization of the trillion particle dataset. Current approaches for visual--inertial odometry (VIO) are able to attain highly accurate state estimation via nonlinear optimization. However, real-time optimization quickly becomes infeasible as the trajectory grows over time; this problem is further emphasized by the fact that inertial measurements come at high rate, hence, leading to the fast growth of the number of variables in the optimization. In this paper, we address this issue by preintegrating inertial measurements between selected keyframes into single relative motion constraints. Our first contribution is a preintegration theory that properly addresses the manifold structure of the rotation group. We formally discuss the generative measurement model as well as the nature of the rotation noise and derive the expression for the maximum a posteriori state estimator. Our theoretical development enables the computation of all necessary Jacobians for the optimization and a posteriori bias correction in analytic form. The second contribution is to show that the preintegrated inertial measurement unit model can be seamlessly integrated into a visual--inertial pipeline under the unifying framework of factor graphs. This enables the application of incremental-smoothing algorithms and the use of a structureless model for visual measurements, which avoids optimizing over the 3-D points, further accelerating the computation. We perform an extensive evaluation of our monocular VIO pipeline on real and simulated datasets. The results confirm that our modeling effort leads to an accurate state estimation in real time, outperforming state-of-the-art approaches. We introduce a novel projection-based visualization method for high-dimensional data sets by combining concepts from MDS and the geometry of the hyperbolic spaces. This approach hyperbolic multi-dimensional scaling (H-MDS) is a synthesis of two important concepts for explorative data analysis and visualization: (i) multi-dimensional scaling uses proximity or pair distance data to generate a low-dimensional, spatial presentation of the data; (ii) previous work on the "hyperbolic tree browser" demonstrated the extraordinary advantages for an interactive display of graph-like data in the two-dimensional hyperbolic space (H2).In the new approach, H-MDS maps proximity data directly into the H2. This removes the restriction to "quasihierarchical", graph-based data--a major limitation of (ii). Since a suitable distance function can convert all kinds of data to proximity (or distance-based) data, this type of data can be considered the most general.We review important properties of the hyperbolic space and, in particular, the circular Poincare model of the H2. It enables effective human-computer interaction: by mouse dragging the "focus", the user can navigate in the data without loosing the context. In H2 the "fish-eye" behavior originates not simply by a non-linear view transformation but rather by extraordinary, non-Euclidean properties of the H2. Especially, the exponential growth of length and area of the underlying space makes the H2 a prime target for mapping hierarchical and (now also) high-dimensional data.Several high-dimensional mapping examples including synthetic and real-world data are presented. Since high-dimensional data produce "ring"-shaped displays, we present methods to enhance the display by modulating the dissimilarity contrast. This is demonstrated for an application for unstructured text: i.e., by using multiple film critiques from news:rec.art.movies.reviews and www.imdb.com, each movie is placed within the H2--creating a "space of movies" for interactive exploration. The Next Generation Simulation (NGSIM) trajectory data sets provide longitudinal and lateral positional information for all vehicles in certain spatiotemporal regions. Velocity and acceleration information cannot be extracted directly because the noise in the NGSIM positional information is greatly increased by the necessary numerical differentiations. A smoothing algorithm is proposed for positions, velocities, and accelerations that can also be applied near the boundaries. The smoothing time interval is estimated on the basis of velocity time series and the variance of the processed acceleration time series. The velocity information obtained in this way is then applied to calculate the density function of the two-dimensional distribution of velocity and inverse distance and the density of the distribution corresponding to the "microscopic" fundamental diagram. It is also used to calculate the distributions of time gaps and times to collision, conditioned to several ranges of velocities and velocity diff...