Jason F. Shepherd

A user study of visualization effectiveness using EEG and cognitive load

Effectively evaluating visualization techniques is a difficult task often assessed through feedback from user studies and expert evaluations. This work presents an alternative approach to visualization evaluation in which brain activity is passively recorded using electroencephalography (EEG). These measurements are used to compare different visualization techniques in terms of the burden they place on a viewers cognitive resources. In this paper, EEG signals and response times are recorded while users interpret different representations of data distributions. This information is processed to provide insight into the cognitive load imposed on the viewer. This paper describes the design of the user study performed, the extraction of cognitive load measures from EEG data, and how those measures are used to quantitatively evaluate the effectiveness of visualizations.

Quadrilateral mesh simplification

We introduce a simplification algorithm for meshes composed of quadrilateral elements. It is reminiscent of edge-collapse based methods for triangle meshes, but takes a novel approach to the challenging problem of maintaining the quadrilateral connectivity during level-of-detail creation. The method consists of a set of unit operations applied to the dual of the mesh, each designed to improve mesh structure and maintain topological genus. Geometric shape is maintained by an extension of a quadric error metric to quad meshes. The technique is straightforward to implement and efficient enough to be applied to real-world models. Our technique can handle models with sharp features, and can be used to re-mesh general polygonal, i.e. tri- and quad-dominant, meshes into quadonly meshes.

Feature-Based Statistical Analysis of Combustion Simulation Data

We present a new framework for feature-based statistical analysis of large-scale scientific data and demonstrate its effectiveness by analyzing features from Direct Numerical Simulations (DNS) of turbulent combustion. Turbulent flows are ubiquitous and account for transport and mixing processes in combustion, astrophysics, fusion, and climate modeling among other disciplines. They are also characterized by coherent structure or organized motion, i.e. nonlocal entities whose geometrical features can directly impact molecular mixing and reactive processes. While traditional multi-point statistics provide correlative information, they lack nonlocal structural information, and hence, fail to provide mechanistic causality information between organized fluid motion and mixing and reactive processes. Hence, it is of great interest to capture and track flow features and their statistics together with their correlation with relevant scalar quantities, e.g. temperature or species concentrations. In our approach we encode the set of all possible flow features by pre-computing merge trees augmented with attributes, such as statistical moments of various scalar fields, e.g. temperature, as well as length-scales computed via spectral analysis. The computation is performed in an efficient streaming manner in a pre-processing step and results in a collection of meta-data that is orders of magnitude smaller than the original simulation data. This meta-data is sufficient to support a fully flexible and interactive analysis of the features, allowing for arbitrary thresholds, providing per-feature statistics, and creating various global diagnostics such as Cumulative Density Functions (CDFs), histograms, or time-series. We combine the analysis with a rendering of the features in a linked-view browser that enables scientists to interactively explore, visualize, and analyze the equivalent of one terabyte of simulation data. We highlight the utility of this new framework for combustion science; however, it is applicable to many other science domains.

Methods and Applications of Generalized Sheet Insertion for Hexahedral Meshing

This paper presents methods and applications of sheet insertion in a hexahedral mesh. A hexahedral sheet is dual to a layer of hexahedra in a hexahedral mesh. Because of symmetries within a hexahedral element, every hexahedral mesh can be viewed as a collection of these sheets. It is possible to insert new sheets into an existing mesh, and these new sheets can be used to define new mesh boundaries, refine the mesh, or in some cases can be used to improve quality in an existing mesh. Sheet insertion has a broad range of possible applications including mesh generation, boundary refinement, R-adaptivity and joining existing meshes. Examples of each of these applications are demonstrated.

Topological and geometrical properties of hexahedral meshes

Over the years, there have been a number of practical studies with working definitions of ‘mesh’ as related to computational simulation, however, there are only a few theoretical papers with formal definitions of mesh. Algebraic topology papers are available that define tetrahedral meshes in terms of simplices. Algebraic topology and polytope theory has also been utilized to define hexahedral meshes. Additional literature is also available describing particular properties of the dual of a mesh. In this paper, we give several formal definitions in relation to hexahedral meshes and the dual of hexahedral meshes. Our main goal is to provide useful, understandable and minimal definitions specifically for computer scientists or mathematicians working in hexahedral meshing. We also extend these definitions to some useful classifications of hexahedral meshes, including definitions for ‘fundamental’ hexahedral meshes and ‘minimal’ hexahedral meshes.

Localized coarsening of conforming all-hexahedral meshes

Finite element mesh adaptation methods can be used to improve the efficiency and accuracy of solutions to computational modeling problems. In many applications involving hexahedral meshes, localized modifications which preserve a conforming all-hexahedral mesh are desired. Effective hexahedral refinement methods that satisfy these criteria have recently become available; however, due to hexahedral mesh topology constraints, little progress has been made in the area of hexahedral coarsening. This paper presents a new method to locally coarsen conforming all-hexahedral meshes. The method works on both structured and unstructured meshes and is not based on undoing previous refinement. Building upon recent developments in quadrilateral coarsening, the method utilizes hexahedral sheet and column operations, including pillowing, column collapsing, and sheet extraction. A general algorithm for automated coarsening is presented and examples of models that have been coarsened with this new algorithm are shown. While results are promising, further work is needed to improve the automated process.

New Applications of the Verdict Library for Standardized Mesh Verification Pre, Post, and End-to-End Processing

verdict is a collection of subroutines for evaluating the geometric qualities of triangles, quadrilaterals, tetrahedra, and hexahedra using a variety of functions. A quality is a real number assigned to one of these shapes depending on its particular vertex coordinates. These functions are used to evaluate the input to finite element, finite volume, boundary element, and other types of solvers that approximate the solution to partial differential equations defined over regions of space. This article describes the most recent version of verdict and provides a summary of the main properties of the quality functions offered by the library. It finally demonstrates the versatility and applicability of verdict by illustrating its use in several scientific applications that pertain to pre, post, and end-to-end processing.

Interval Assignment for Volumes with Holes

This paper presents a new technique for automatically detecting interval constraints for swept volumes with holes. The technique finds true volume constraints that are not necessarily imposed by the surfaces of the volume. A graphing algorithm finds independent, parallel paths of edges from source surfaces to target surfaces. The number of intervals on two paths between a given source and target surface must be equal; in general, the collection of paths determine a set of linear constraints. Linear programming techniques solve the interval assignment problem for the surface and volume constraints simultaneously.

Embedding Features in a Cartesian Grid.

Grid-based mesh generation methods have been available for many years and can provide a reliable method for meshing arbitrary geometries with hexahedral elements. The principal use for these methods has mostly been limited to biological-type models where topology that may incorporate sharp edges and curve definitions are not critical. While these applications have been effective, robust generation of hexahedral meshes on mechanical models, where the topology is typically of prime importance, impose difficulties that existing grid-based methods have not yet effectively addressed. This work introduces a set of procedures that can be used in resolving the features of a geometric model for grid-based hexahedral mesh generation for mechanical or topology-rich models.

An Immersive Topology Environment for Meshing.

The Immersive Topology Environment for Meshing (ITEM) is a wizard-like environment, built on top of the CUBIT Geometry and Meshing Toolkit. ITEM is focused on three main objectives: 1) guiding the user through the simulation model preparation workflow; 2) providing the user with intelligent options based upon the current state of the model; and 3) where appropriate, automating as much of the process as possible. To accomplish this, a diagnostic-solution approach is taken. Based upon diagnostics of the current state of the model, specific solutions for a variety of common tasks are provided to the user. Some of these tasks include geometry simplification, small feature suppression, resolution of misaligned assembly parts, decomposition for hex meshing, and source and target selection for sweeping. The user may scroll through a list of intelligent solutions for a specific diagnostic and entity, view a graphical preview of each solution and quickly perform the solution to resolve the problem. In many cases, automatic solutions for these tasks can be generated and executed if the user chooses. This paper will discuss the various diagnostics and geometric reasoning algorithms and approaches taken by ITEM to determine solutions for preparing an analysis model.