Search

High performance computing simulations often produce datasets defined over unstructured grids. Those grids allow for the local refinement of the resolution and can accommodate arbitrary boundary geometry. From a visualization standpoint, however, such grids have a high storage cost, require special spatial data structures, and make the computation of high-quality derivatives challenging. Rectilinear grids, in contrast, have a negligible memory footprint and readily support smooth data reconstruction, though with reduced geometric flexibility. The present work is concerned with the creation of an accurate reconstruction of large unstructured datasets on rectilinear grids. We present an efficient method to automatically determine the geometry of a rectilinear grid upon which a low-error data reconstruction can be achieved with a given reconstruction kernel. Using this rectilinear grid, we address the potential ill-posedness of the data fitting problem, as well as the necessary balance between smoothness and accuracy, through a bi-level smoothness regularization. To tackle the computational challenge posed by very large input datasets and high-resolution reconstructions, we propose a block-based approach that allows us to obtain a seamless global approximation solution from a set of independently computed sparse least-squares problems. Results are presented for several 3D datasets that demonstrate the quality of the visualization results that our reconstruction enables, at a greatly reduced computational and memory cost.

The choice of knot vector has immense influence on the resulting accuracy of a B-spline approximation of a curve. However, despite the significance of this problem and the various solutions that were proposed in the literature, optimizing the number and placement of knots remains a difficult task. This paper presents a novel method for the approximation of a curve by a B-spline of arbitrary order, which automatically determines a knot vector that achieves high approximation quality. At the core of our approach is a feature function that characterizes the amount and spatial distribution of geometric details in the input curve by estimating its derivatives. Knots are then selected in such a way as to evenly distribute the feature contents across their intervals. A comparison to the state of the art for a wide variety of curves shows that our method is faster and achieves more accurate reconstruction results, while typically reducing the number of necessary knots.

We present a technique to automatically characterize the geometry of important anatomical structures in diffusion weighted MRI (DWI) data. Our approach is based on the interpretation of diffusion data as a superimposition of multiple line fields that each form a continuum of space filling curves. Using a dense tractography computation, our method quantifies the spatial variations of the geometry of these curves and use the resulting measure to characterize salient structures as edges. Anatomically, these structures have a boundary-like nature and yield a clear picture of major fiber bundles. In particular, the application of our algorithm to high angular resolution imaging (HARDI) data yields a precise geometric description of subtle anatomical configurations associated with the local presence of multiple fiber orientations. We evaluate our technique and study its robustness to noise in the context of a phantom dataset and present results obtained with two diffusion weighted brain images.

Poincare maps supply vital descriptions of dynamical behavior in spacecraft trajectory analysis, but the puncture plot, the standard display method for maps, typically requires significant external effort to extract topology. This investigation presents adaptations of topology-based methods to compute map structures in multi-body dynamical environments. In particular, a scalar field visualization technique enhances the contrast between quasi-periodic and chaotic regimes. Also, an autonomous method is outlined to extract map topology in the planar circular restricted three-body problem. The resulting topological skeleton supplies a network of design options through the interconnectivity of orbital structures.

A low-dimensional center-of-mass dynamical model is devised as a simplified means of approximately predicting some important aspects of the motion of a vertical column comprised of a large number of particles subjected to gravity and periodic vertical tapping. This model is investigated first as a continuous dynamical system using analytical, simulation and visualization techniques. Then, by employing an approach analogous to that used to approximate the dynamics of a bouncing ball on an oscillating flat plate, it is modeled as a discrete dynamical system and analyzed to determine bifurcations and transitions to chaotic motion along with other properties. The predictions of the analysis are then compared–primarily qualitatively–with visualization and simulation results of the reduced continuous model, and ultimately with simulations of the complete system dynamics.

We present a new efficient and scalable method for the high quality reconstruction of the flow map from sparse samples. The flow map describes the transport of massless particles along the flow. As such, it is a fundamental concept in the analysis of transient flow phenomena and all so-called Lagrangian flow visualization techniques require its approximation. The flow map is generally obtained by integrating a dense 1D, 2D, or 3D set of particles across the domain of definition of the flow. Despite its embarrassingly parallel nature, this computation creates a performance bottleneck in the analysis of large-scale datasets that existing adaptive techniques alleviate only partially. Our iterative approximation method significantly improves upon the state of the art by precisely modeling the flow behavior around automatically detected geometric structures embedded in the flow, thus effectively restricting the sampling effort to interesting regions. Our data reconstruction is based on a modified version of Sibson's scattered data interpolation and allows us at each step to offer an intermediate dense approximation of the flow map and to seamlessly integrate regions that will be further refined in subsequent steps. We present a quantitative and qualitative evaluation of our method on different types of flow datasets and offer a detailed comparison with existing techniques.

Computational and experimental methodologies are integrated into a novel combined technique to define microstructure design criteria and maximize the properties of rhombohedral Bi0.5Na0.4K0.1TiO3, from untextured (1 MRD ), d33 = 155 pC/N, to textured (4.41 MRD s), d33 = 227 pC/N. Two-dimensional orientation maps obtained using electron backscatter diffraction on sequential parallel layers are used to computationally reconstruct three-dimensional samples, simulate the local piezoelectric grain interactions, and thus demonstrate that superior lead-free piezoelectric microstructures can be fabricated by engineering its associated crystallographic and polarization texture. Computer-generated material representations, based on the experimentally determined microstructures, were used to simulate the crystallographic orientation of each grain, as function a macroscopic polarization and crystallographic texture. Computer-generated material representations, based on the experimentally determined microstructures, were used to simulate the crystallographic orientation of each grain, as function a macroscopic polarization and crystallographic texture. The method takes advantage of the anisotropy of the properties of the underlying single-crystal phases and delivers a guide to search for material anisotropy |microstructure parameters that are optimal in piezoelectric performance and reliability, and thus establish practical links between structure and macroscopic length scales.

This paper introduces a new feature analysis and visualization method for multifield datasets. Our approach applies a surface-centric model to characterize salient features and form an effective, schematic representation of the data. We propose a simple, geometrically motivated, multifield feature definition. This definition relies on an iterative algorithm that applies existing theory of skeleton derivation to fuse the structures from the constitutive fields into a coherent data description, while addressing noise and spurious details. This paper also presents a new method for non-rigid surface registration between the surfaces of consecutive time steps. This matching is used in conjunction with clustering to discover the interaction patterns between the different fields and their evolution over time. We document the unified visual analysis achieved by our method in the context of several multifield problems from large-scale time-varying simulations.

We report our findings on the evolution of solids fraction in a tapped system of inelastic, frictional spheres as a function of the applied acceleration obtained via discrete element simulations. Animations of the simulation data reveal the propagation of a wave initiated from the base that causes local rearrangements of the particles ultimately leading to the development of a dense microstructure. We also describe the analysis of dynamical models capable of predicting the simulated behavior, and advanced visualization techniques for revealing the dynamics.

The dynamics of a vertical stack of particles subject to gravity and a sequence of small, periodically applied taps is considered. First, the motion of the particles, assumed to be identical, is modeled as a system of ordinary differential equations, which is analyzed with an eye to observing connections with finite-dimensional Hamiltonian systems. Then, two approaches to obtaining approximate continuum models for large numbers of particles are described: the long-wave approximation that yields partial differential equations and the BSR method that employs integro-partial differential models. These approximate continuum models, which comprise infinite-dimensional dynamical systems, are studied with a focus on nonlinear wave type behavior, which naturally leads to investigating links to infinite-dimensional Hamiltonian systems. Several examples are solved numerically to show similarities among the solution properties of the finite-dimensional (lattice-dynamics), and the approximate long-wave and BSR continuum models. Extensions to higher dimensions and more general dynamically driven particle configurations are also sketched.

We present a novel algorithm for the efficient extraction and visualization of high-quality ridge and valley surfaces from numerical datasets. Despite their rapidly increasing popularity in visualization, these so-called crease surfaces remain challenging to compute owing to their strongly nonlinear and non-orientable nature, and their complex boundaries. In this context, existing meshing techniques require an extremely dense sampling that is computationally prohibitive. Our proposed solution intertwines sampling and meshing steps to yield an accurate approximation of the underlying surfaces while ensuring the geometric quality of the resulting mesh. Using the computation power of the GPU, we propose a fast, parallel method for sampling. Additionally, we present a new front propagation meshing strategy that leverages CPU multiprocessing. Results are shown for synthetic, medical and fluid dynamics datasets.

In the development of magnetic confinement fusion which will potentially be a future source for low cost power, physicists must be able to analyze the magnetic field that confines the burning plasma. While the magnetic field can be described as a vector field, traditional techniques for analyzing the field's topology cannot be used because of its Hamiltonian nature. In this paper we describe a technique developed as a collaboration between physicists and computer scientists that determines the topology of a toroidal magnetic field using fieldlines with near minimal lengths. More specifically, we analyze the Poincaré map of the sampled fieldlines in a Poincaré section including identifying critical points and other topological features of interest to physicists. The technique has been deployed into an interactive parallel visualization tool which physicists are using to gain new insight into simulations of magnetically confined burning plasmas.

We introduce a versatile framework for characterizing and extracting salient structures in three-dimensional symmetric second-order tensor fields. The key insight is that degenerate lines in tensor fields, as defined by the standard topological approach, are exactly crease (ridge and valley) lines of a particular tensor invariant called mode. This reformulation allows us to apply well-studied approaches from scientific visualization or computer vision to the extraction of topological lines in tensor fields. More generally, this main result suggests that other tensor invariants, such as anisotropy measures like fractional anisotropy (FA), can be used in the same framework in lieu of mode to identify important structural properties in tensor fields. Our implementation addresses the specific challenge posed by the non-linearity of the considered scalar measures and by the smoothness requirement of the crease manifold computation. We use a combination of smooth reconstruction kernels and adaptive refinement strategy that automatically adjust the resolution of the analysis to the spatial variation of the considered quantities. Together, these improvements allow for the robust application of existing ridge line extraction algorithms in the tensor context of our problem. Results are proposed for a diffusion tensor MRI dataset, and for a benchmark stress tensor field used in engineering research.

We introduce a novel flow visualization method called Flow Charts, which uses a texture atlas approach for the visualization of flows defined over curved surfaces. In this scheme, the surface and its associated flow are segmented into overlapping patches, which are then parameterized and packed in the texture domain. This scheme allows accurate particle advection across multiple charts in the texture domain, providing a flexible framework that supports various flow visualization techniques. The use of surface parameterization enables flow visualization techniques requiring the global view of the surface over long time spans, such as Unsteady Flow LIC (UFLIC), particle-based Unsteady Flow Advection Convolution (UFAC), or dye advection. It also prevents visual artifacts normally associated with view-dependent methods. Represented as textures, Flow Charts can be naturally integrated into hardware accelerated flow visualization techniques for interactive performance.

Dye advection is widely used in experimental flow analysis but has seen less use for visualization in computational fluid dynamics. One possible reason for this disconnect is the inaccuracy of the texture-based approach, which is prone to artifacts caused by numeric diffusion and mass fluctuation. In this paper, we introduce a novel 2D dye advection scheme for flow visualization based on the concept of control volume analysis typically used in computational fluid dynamics. The evolution of dye patterns in the flow field is achieved by advecting individual control volumes, which collectively cover the entire spatial domain. The local variation of dye material, represented as a piecewise quasi-parabolic function, is integrated within each control volume resulting in mass conserving transport without excessive numerical diffusion. Due to its physically based formulation, this approach is capable of conveying intricate flow structures not shown in the traditional dye advection schemes while avoiding visual artifacts.

Current unsteady multi-field simulation data-sets consist of millions of data-points. To efficiently reduce this enormous amount of information, local statistical complexity was recently introduced as a method that identifies distinctive structures using concepts from information theory. Due to high computational costs this method was so far limited to 2D data. In this paper we propose a new strategy for the computation that is substantially faster and allows for a more precise analysis. The bottleneck of the original method is the division of spatio-temporal configurations in the field (light-cones) into different classes of behavior. The new algorithm uses a density-driven Voronoi tessellation for this task that more accurately captures the distribution of configurations in the sparsely sampled high-dimensional space. The efficient computation is achieved using structures and algorithms from graph theory. The ability of the method to detect distinctive regions in 3D is illustrated using flow and weather simulations.

Flow visualization is a classic sub-field of scientific visualization. The task of flow visualization algorithms is to depict vector data, i.e., data with magnitude and direction. An important cate ...

Geometric models of white matter architecture play an increasing role in neuroscientific applications of diffusion tensor imaging, and the most popular method for building them is fiber tractography. For some analysis tasks, however, a compelling alternative may be found in the first and second derivatives of diffusion anisotropy. We extend to tensor fields the notion from classical computer vision of ridges and valleys, and define anisotropy creases as features of locally extremal values of tensor anisotropy. Mathematically, these are the loci where the gradient of anisotropy is orthogonal to one or more eigenvectors of its Hessian. We propose that anisotropy creases provide a basis for extracting a skeleton of the major white matter pathways, in that ridges of anisotropy coincide with interiors of fiber tracts, and valleys of anisotropy coincide with the interfaces between adjacent but distinctly oriented tracts. The crease extraction algorithm we present generates high-quality polygonal models of crease surfaces, which are further simplified by connected-component analysis. We demonstrate anisotropy creases on measured diffusion MRI data, and visualize them in combination with tractography to confirm their anatomic relevance.

Background There are no published data showing the three-dimensional sequence of repolarization and the associated potential fields in the ventricles. Knowledge of the sequence of repolarization has medical relevance because high spatial dispersion of recovery times and action potential durations favors cardiac arrhythmias. In this study we describe measured and simulated 3-D excitation and recovery sequences and activation-recovery intervals (ARIs) (measured) or action potential durations (APDs) (simulated) in the ventricular walls. Methods We recorded from 600 to 1400 unipolar electrograms from canine ventricular walls during atrial and ventricular pacing at 350-450 ms cycle length. Measured excitation and recovery times and ARIs were displayed as 2-D maps in transmural planes or 3-D maps in the volume explored, using specially developed software. Excitation and recovery sequences and APD distributions were also simulated in parallelepipedal slabs using anisotropic monodomain or bidomain models based on the Lou-Rudy version 1 model with homogeneous membrane properties. Results Simulations showed that in the presence of homogeneous membrane properties, the sequence of repolarization was similar but not identical to the excitation sequence. In a transmural plane perpendicular to epicardial fiber direction, both activation and recovery pathways starting from an epicardial pacing site returned toward the epicardium at a few cm distance from the pacing site. However, APDs were not constant, but had a dispersion of ∼14 ms in the simulated domain. The maximum APD value was near the pacing site and two minima appeared along a line perpendicular to fiber directions, passing through the pacing site. Electrical measurements in dog ventricles showed that, for short cycle lengths, both excitation and recovery pathways, starting from an epicardial pacing site, returned toward the epicardium. For slower pacing rates, pathways of recovery departed from the pathway of excitation. Highest ARI values were observed near the pacing site in part of the experiments. In addition, maps of activation-recovery intervals showed mid-myocardial clusters with activation-recovery intervals that were slightly longer than ARIs closer to the epi- or endocardium, suggesting the presence of M cells in those areas. Transmural dispersion of measured ARIs was on the order of 20-25 ms. Potential distributions during recovery were less affected by myocardial anisotropy than were excitation potentials.

The paper presents a topology-based visualization method for time-dependent two-dimensional vector elds. A time interpolation enables the accurate tracking of critical points and closed orbits as well as the detection and identication of structural changes. This completely characterizes the topology of the unsteady ow. Bifurcation theory provides the theoretical framework. The results are conveyed by surfaces that separate subvolumes of uniform ow behavior in a three-dimensional space-time domain.

Topological methods produce simple and meaningful depicti ons of symmetric, second order two-dimensional tensor fields. Extending previous work dealing with vector fields, we propose here a scheme for the visualization of time-dependent tensor fields. Basic notions of unsteady t topology are discussed. Topological changes known as bifurcations - are precisely detected and identifie d by our method which permits an accurate tracking of degenerate points and related structures.

We present an approximate dynamical systems model for the mass center trajectory of a tapped column of N uniform, inelastic, spheres (diameter d), in which collisional energy loss is governed by the Walton-Braun linear loading-unloading soft interaction. Rigorous analysis of the model, akin to the equations for the motion of a single bouncing ball on a vibrating plate, reveals a parameter γ≔2aω2(1+e)/g that gauges the dynamical regimes and their transitions. In particular, we find bifurcations from periodic to chaotic dynamics that depend on frequency ω, amplitude a/d of the tap. Dynamics predicted by the model are also qualitatively observed in discrete element simulations carried out over a broad range of the tap parameters.

Peak finding provides more accurate classification for direct volume rendering by sampling directly at local maxima in a transfer function, allowing for better reproduction of high-frequency features. However, the 1D peak finding technique does not extend to higherdimensional classification. In this work, we develop a new method for peak finding with multidimensional transfer functions, which looks for peaks along the image of the ray. We use piecewise approximations to dynamically sample in transfer function space between world-space samples. As with unidimensional peak finding, this approach is useful for specifying transfer functions with greater precision, and for accurately rendering noisy volume data at lower sampling rates. Multidimensional peak finding produces comparable image quality with order-of-magnitude better performance, and can reproduce features omitted entirely by standard classification. With no precomputation or storage requirements, it is an attractive alternative to preintegration for multidimensional transfer functions.

Topology was introduced in the visualization literature some 15 years ago as a mathematical language to describe and capture the salient structures of symmetric second-order tensor fields. Yet, despite significant theoretical and algorithmic advances, this approach has failed to gain wide acceptance in visualization practice over the last decade. In fact, the very idea of a versatile visualization methodology for tensor fields that could transcend application domains has been virtually abandoned in favor of problem-specific feature definitions and visual representations. We propose to revisit the basic idea underlying topology from a different perspective. To do so, we introduce a Lagrangian metaphor that transposes to the structural analysis of eigenvector fields a perspective that is commonly used in the study of fluid flows. Indeed, one can view eigenvector fields as the local superimposition of two vector fields, from which a bidirectional flow field can be defined. This allows us to analyze the structure of a tensor field through the behavior of fictitious particles advected by this flow. Specifically, we show that the separatrices of 3D tensor field topology can in fact be captured in a fuzzy and numerically more robust setting as ridges of a trajectory coherence measure. As a result, we propose an alternative structure characterization strategy for the visual analysis of practical 3D tensor fields, which we demonstrate on several synthetic and computational datasets.

In the study of a magnetic confinement fusion device such as a tokamak, physicists need to understand the topology of the flux (or magnetic) surfaces that form within the magnetic field. Among the two distinct topological structures, we are particularly interested in the magnetic island chains which correspond to the break up of the ideal rational surfaces. Different from our previous method [13], in this work we resort to the periodicity analysis of two distinct functions to identify and characterize flux surfaces and island chains. These two functions are derived from the computation of the fieldlines and puncture points on a Poincare section, respectively. They are the distance measure plot and the ridgeline plot. We show that the periods of these two functions are directly related to the topology of the surface via a resonance detection (i.e., period estimation and the common denominators computation). In addition, we show that for an island chain the two functions possess resonance components which do not occur for a flux surface. Furthermore, by combining the periodicity analysis of these two functions, we are able to devise a heuristic yet robust and reliable approach for classifying and characterizing different magnetic surfaces in the toroidal magnetic fields.

Area-preserving maps arise in the study of conservative dynamical systems describing a wide variety of physical phenomena, from the rotation of planets to the dynamics of a fluid. The visual inspection of these maps reveals a remarkable topological picture in which invariant manifolds form the fractal geometric scaffold of both quasi-periodic and chaotic regions. We discuss in this paper the visualization of such maps built upon these invariant manifolds. This approach is in stark contrast with the discrete Poincare plots that are typically used for the visual inspection of maps. We propose to that end several modified definitions of the finite-time Lyapunov exponents that we apply to reveal the underlying structure of the dynamics. We examine the impact of various parameters and the numerical aspects that pertain to the implementation of this method. We apply our technique to a standard analytical example and to a numerical simulation of magnetic confinement in a fusion reactor. In both cases our simple method is able to reveal salient structures across spatial scales and to yield expressive images across application domains.

Area-preserving maps are found across a wide range of scientific and engineering problems. Their study is made challenging by the significant computational effort typically required for their inspection but more fundamentally by the fractal complexity of salient structures. The visual inspection of these maps reveals a remarkable topological picture consisting of fixed (or periodic) points embedded in so-called island chains, invariant manifolds, and regions of ergodic behavior. This paper is concerned with the effective visualization and precise topological analysis of area-preserving maps with two degrees of freedom from numerical or analytical data. Specifically, a method is presented for the automatic extraction and characterization of fixed points and the computation of their invariant manifolds, also known as separatrices, to yield a complete picture of the structures present within the scale and complexity bounds selected by the user. This general approach offers a significant improvement over the visual representations that are so far available for area-preserving maps. The technique is demonstrated on a numerical simulation of magnetic confinement in a fusion reactor.

We introduce the general pinhole camera (GPC), defined by a center of projection (i.e., the pinhole), an image plane, and a set of sampling locations in the image plane. We demonstrate the advantages of the GPC in the contexts of remote visualization, focus-plus-context visualization, and extreme antialiasing, which benefit from the GPC sampling flexibility. For remote visualization, we describe a GPC that allows zooming-in at the client without the need for transferring additional data from the server. For focus-plus-context visualization, we describe a GPC with multiple regions of interest with sampling rate continuity to the surrounding areas. For extreme antialiasing, we describe a GPC variant that allows supersampling locally with a very high number of color samples per output pixel (e.g., 1,024{\times}), supersampling levels that are out of reach for conventional approaches that supersample the entire image. The GPC supports many types of data, including surface geometry, volumetric, and image data, as well as many rendering modes, including highly view-dependent effects such as volume rendering. Finally, GPC visualization is efficient-GPC images are rendered and resampled with the help of graphics hardware at interactive rates.