Parallel hierarchical visualization of large time-varying 3D vector fields

The paper discusses CAVEvis and a related set of tools for the interactive visualization and exploration of large sets of time-varying scalar and vector fields using the CAVE virtual reality environment. Since visualization of large data sets can be very time-consuming in both computation and rendering time, the task is distributed over multiple machines, each of which is specialized for some aspect of the visualization process. All modules must run asynchronously to maintain the highest level of interactivity. A model of distributed visualization is introduced that addresses important issues related to the management of time-dependent data, module synchronization, and interactivity bottlenecks.

Although many types of computational simulations produce time-varying vector fields, subsequent analysis is often limited to single time slices due to excessive costs. Fortunately, a new approach using a Lagrangian representation can enable time-varying vector field analysis while mitigating these costs. With this approach, a Lagrangian representation is calculated while the simulation code is running, and the result is explored after the simulation. Importantly, the effectiveness of this approach varies based on the nature of the vector field, requiring in-depth investigation for each application area. With this study, we evaluate the effectiveness for previously unexplored cosmology and seismology applications. We do this by considering encumbrance (on the simulation) and accuracy (of the reconstructed result). To inform encumbrance, we integrated in situ infrastructure with two simulation codes, and evaluated on representative HPC environments, performing Lagrangian in situ reduction using GPUs as well as CPUs. To inform accuracy, our study conducted a statistical analysis across a range of spatiotemporal configurations as well as a qualitative evaluation. In all, we demonstrate effectiveness for both cosmology and seismology—time-varying vector fields from these domains can be reduced to less than 1% of the total data via Lagrangian representations, while maintaining accurate reconstruction and requiring under 10% of total execution time in over 80% of our experiments.

A very important subproblem in the task assignment problem for unmanned air vehicles is the evaluation of costs for the state transitions of a directed graph. Usually a Dubins vehicle flying in the absence of wind is considered in the computation of costs. However, when a prevailing wind vector field is considered, the costs taken on very different values and the task assignment problem can have very different solutions. In this paper, we consider the problem of constructing minimum-time trajectories for a Dubins vehicle in the presence of a time-varying wind vector field. We present results on the existence and uniqueness of minimum-time solutions for a Dubins vehicle flying in a general time-varying wind vector field under some technical conditions. These results extend the conclusions of the well-known Dubins theorem. We also propose an algorithm for obtaining the minimum-time solution for an unmanned air vehicle and prove its convergence. We also present the results of numerical experiments that show that the importance of considering wind vector fields while planning the tour for an unmanned air vehicle.

Navigating in a vector field is a challenging problem for many autonomous vehicles. This article focuses on a High-Altitude Pseudo-Satellite (HAPS) operating in a wind field with wind magnitude comparable to its airspeed. In addition to navigating from a start to a goal point, the HAPS is expected to carry out patrolling missions spanning long hours/ days, within which the physical environment (e.g. wind field, weather-critical no-go areas, fly zones etc.) vary, resulting in either an improvement or a deterioration of mission fulfillment. A time-dependent hybrid mission planning framework is proposed in this work which consists firstly of a hierarchical strategic planner that produces very quickly multiple sequences of tasks (or rather plans) that are ranked with roughly estimated objective or penalty values, and secondly of a tactical planner that refines the values of each premature plan to help the operator assess the plans better. The framework was implemented on the long-term offline planner for HAPS in patrolling missions. Test results using an independent six degrees-of-freedoms HAPS simulator and historical weather data are provided and analyzed.

L1 adaptive backstepping control for path-following of underactuated marine surface ships

Widefield calcium imaging has recently emerged as a powerful experimental technique to record coordinated large-scale brain activity. These measurements present a unique opportunity to characterize spatiotemporally coherent structures that underlie neural activity across many regions of the brain. In this work, we leverage analytic techniques from fluid dynamics to develop a visualization framework that highlights features of flow across the cortex, mapping wavefronts that may be correlated with behavioural events. First, we transform the time series of widefield calcium images into time-varying vector fields using optic flow. Next, we extract concise diagrams summarizing the dynamics, which we refer to as FLOW (flow lines in optical widefield imaging) portraits. These FLOW portraits provide an intuitive map of dynamic calcium activity, including regions of initiation and termination, as well as the direction and extent of activity spread. To extract these structures, we use the finite-time Lyapunov exponent technique developed to analyse time-varying manifolds in unsteady fluids. Importantly, our approach captures coherent structures that are poorly represented by traditional modal decomposition techniques. We demonstrate the application of FLOW portraits on three simple synthetic datasets and two widefield calcium imaging datasets, including cortical waves in the developing mouse and spontaneous cortical activity in an adult mouse.

Spatiotemporal Response Properties of Optic-Flow Processing Neurons

An important subproblem in the area of cooperative control of multiple, autonomous, unmanned air vehicles is the determination of the minimum-time optimal paths for the agents to fly from one destination to the next. The tasks for the air vehicles are usually tightly coupled in time, and hence estimates of the times taken for each air vehicle to fly from one destination to the next is highly critical for correct assignment of tasks. In this article, we discuss the existence and uniqueness of minimum time solutions for the trajectory planning problem for a Micro Air Vehicle (MAV) under wind conditions. We show that there exists a minimum time solution for the trajectory planning problem with a minimum turn radius constraint for the air vehicle, and for a non-zero, time-varying wind vector field satisfying certain easily checked sufficient conditions. We also prove uniqueness for almost every combination of initial and final conditions in the case of a wind vector field that can vary with time but is constant in the spatial variable at each time instant.

The analysis of data that consists of multiple vector fields can be greatly facilitated by the simultaneous visualization of the vector fields. An effective visualization must accurately reflect the key physical structures of the fields in a way that does not allow for an unintended bias toward one distribution. While there are several effective techniques to visualize a single vector field through equally spaced streamlines, applying these techniques to individual vector fields and combining them in a single image yields undesirable artifacts. In this paper, we present strategies for the effective visualization of two vector fields through the use of streamlines.

This paper describes an approach for interactive visualization of mixed scalar and vector fields, in which vector icons are generated from pre-voxelized icon templates and volume-rendered together with the volumetric scalar data. This approach displays simultaneously the global structure of the scalar field and the detailed features of the vector field. Interactive visualization is achieved with incremental image update, by re-rendering only a small portion of the image wherever and whenever a change occurs. This technique supports a set of interactive visualization tools, including change of vector field visualization parameters, real-time animation of vector icons advected within the scalar field, a zooming lens, and a local probe. Subject Terms: data visualisation; interactive systems; graphical user interfaces; rendering (computer graphics); interactive visualization; scalar fields; vector fields; vector icons; pre-voxelized icon templates; volume-rendered; volumetric scalar data; incremental image update; real-time animation; zooming lens; local probe

Visualization of particle traces provides intuitive and efficient means for the exploration and analysis of complex vector fields. The paper presents a method suitable for the real-time visualization of arbitrarily large time-varying vector fields in virtual environments. We describe an out-of-core scheme in which two distinct pre-processing and rendering components enable real-time data streaming and visualization. The presented approach yields low-latency application start-up times and small memory footprints. The described system was used to implement a volumetric fog lance, which can emit up to 60000 particles into a flow field while maintaining an interactive frame rate of 60 frames per second. All algorithms were specifically designed to support commodity hardware. The proof-of-concept system is running on a low-cost Linux workstation equipped with a 120 GB E-IDE RAID (redundant array of inexpensive disk) system.

In this paper, we present an interactive texture-based method for visualizing three-dimensional unsteady vector fields. The visualization method uses a sparse and global representation of the flow, such that it does not suffer from the same perceptual issues as is the case for visualizing dense representations. The animation is made by injecting a collection of particles evenly distributed throughout the physical domain. These particles are then tracked along their path lines. At each time step, these particles are used as seed points to generate field lines using any vector field such as the velocity field or vorticity field. In this way, the animation shows the advection of particles while each frame in the animation shows the instantaneous vector field. In order to maintain a coherent particle density and to avoid clustering as time passes, we have developed a novel particle advection strategy which produces approximately evenly-spaced field lines at each time step. To improve rendering performance, we decouple the rendering stage from the preceding stages of the visualization method. This allows interactive exploration of multiple fields simultaneously, which sets the stage for a more complete analysis of the flow field. The final display is rendered using texture-based direct volume rendering.

Streamline1 is one of the most widely used method in vector field visualization. However, with the expansion of data size, the existing methods cannot ensure the efficiency while maintaining high accuracy. In order to analyse the vector field efficiently, this paper proposes an algorithm for streamline visualization in unstructured vector field while keeping both efficiency and accuracy based on Kipfer's algorithm[1]. First, all grids are classified according to their Jordan canonical form. Then the streamline expressions in each grid cell are deduced for each kind of the grids, and we found that the expressions can be represented in a uniform way. Finally, the exit point of the streamline in the grid cell is calculated by solving the equation composed of the streamline expression and the equation of each face of the tetrahedron. The exit point can be obtained quickly and accurately by using Newton iterative method. The experimental results show that our algorithm is more efficient for streamline visualization with the same accuracy than Kipfer's algorithm.

A new method for the simplification and the visualization of vector fields is presented based on the notion of centroidal Voronoi tessellations (CVT's). A CVT is a special Voronoi tessellation for which the generators of the Voronoi regions in the tessellation are also the centers of mass (or means) with respect to a prescribed density. A distance function in both the spatial and vector spaces is introduced to measure the similarity of the spatially distributed vector fields. Based on such a distance, vector fields are naturally clustered and their simplified representations are obtained. Our method combines simple geometric intuitions with the rigorously established optimality properties of the CVTs. It is simple to describe, easy to understand and implement. Numerical examples are also provided to illustrate the effectiveness and competitiveness of the CVT-based vector simplification and visualization methodology.

One major discipline of Scientific Visualization is the display of vector field data. We address the problem of visualizing vector fields containing critical points of higher order Poincare-Index. We use polynomial pieces so that the degree is high enough to get the right Poincare-Index at the location of the critical points. This is an essential improvement because nearly all visualization of vector fields up to now used piecewise linear interpolation and therefore can not show this kind of critical points. A description of vector fields in Clifford algebra opens the way to a better understanding of some plane polynomial vector fields. This is used to choose the polynomial approximations needed for the visualization.