A Visualization System for Hexahedral Mesh Quality Study

In this paper, we introduce a new 3D hex mesh visual analysis system that emphasizes poor-quality areas with an aggregated glyph, highlights overlapping elements, and provides detailed boundary error inspection in three forms. By supporting multi-level analysis through multiple views, our system effectively evaluates various mesh models and compares the performance of mesh generation and optimization algorithms for hexahedral meshes.Comment: Accepted by IEEE VIS 2023 Short Papers and will be published on IEEE Xplore. Paper contains 4 pages, and 1 reference page. Supplemental includes 4 page

Design of 2D time-varying vector fields

pre-printDesign of time-varying vector fields, i.e., vector fields that can change over time, has a wide variety of important applications in computer graphics. Existing vector field design techniques do not address time-varying vector fields. In this paper, we present a framework for the design of time-varying vector fields, both for planar domains as well as manifold surfaces. Our system supports the creation and modification of various time-varying vector fields with desired spatial and temporal characteristics through several design metaphors, including streamlines, pathlines, singularity paths, and bifurcations. These design metaphors are integrated into an element-based design to generate the time-varying vector fields via a sequence of basis field summations or spatial constrained optimizations at the sampled times. The key-frame design and field deformation are also introduced to support other user design scenarios. Accordingly, a spatial-temporal constrained optimization and the time-varying transformation are employed to generate the desired fields for these two design scenarios, respectively. We apply the time-varying vector fields generated using our design system to a number of important computer graphics applications that require controllable dynamic effects, such as evolving surface appearance, dynamic scene design, steerable crowd movement, and painterly animation. Many of these are difficult or impossible to achieve via prior simulation-based methods. In these applications, the time-varying vector fields have been applied as either orientation fields or advection fields to control the instantaneous appearance or evolving trajectories of the dynamic effects

Linear arboricity of degenerate graphs

A linear forest is a union of vertex-disjoint paths, and the linear arboricity of a graph $G$, denoted by $\operatorname{la}(G)$, is the minimum number of linear forests needed to partition the edge set of $G$. Clearly, $\operatorname{la}(G) \ge \lceil\Delta(G)/2\rceil$ for a graph $G$ with maximum degree $\Delta(G)$. On the other hand, the Linear Arboricity Conjecture due to Akiyama, Exoo, and Harary from 1981 asserts that $\operatorname{la}(G) \leq \lceil(\Delta(G)+1) / 2\rceil$ for every graph $G$. This conjecture has been verified for planar graphs and graphs whose maximum degree is at most $6$, or is equal to $8$ or $10$. Given a positive integer $k$, a graph $G$ is $k$-degenerate if it can be reduced to a trivial graph by successive removal of vertices with degree at most $k$. We prove that for any $k$-degenerate graph $G$, $\operatorname{la}(G) = \lceil\Delta(G)/2 \rceil$ provided $\Delta(G) \ge 2k^2 -k$.Comment: 15 pages, 1 figur

Hybrid Base Complex: Extract and Visualize Structure of Hex-dominant Meshes

Hex-dominant mesh generation has received significant attention in recent research due to its superior robustness compared to pure hex-mesh generation techniques. In this work, we introduce the first structure for analyzing hex-dominant meshes. This structure builds on the base complex of pure hex-meshes but incorporates the non-hex elements for a more comprehensive and complete representation. We provide its definition and describe its construction steps. Based on this structure, we present an extraction and categorization of sheets using advanced graph matching techniques to handle the non-hex elements. This enables us to develop an enhanced visual analysis of the structure for any hex-dominant meshes.We apply this structure-based visual analysis to compare hex-dominant meshes generated by different methods to study their advantages and disadvantages. This complements the standard quality metric based on the non-hex element percentage for hex-dominant meshes. Moreover, we propose a strategy to extract a cleaned (optimized) valence-based singularity graph wireframe to analyze the structure for both mesh and sheets. Our results demonstrate that the proposed hybrid base complex provides a coarse representation for mesh element, and the proposed valence singularity graph wireframe provides a better internal visualization of hex-dominant meshes.Comment: accepted by IEEE Transactions on Visualization and Computer Graphic

Extract and Characterize Hairpin Vortices in Turbulent Flows

Hairpin vortices are one of the most important vortical structures in turbulent flows. Extracting and characterizing hairpin vortices provides useful insight into many behaviors in turbulent flows. However, hairpin vortices have complex configurations and might be entangled with other vortices, making their extraction difficult. In this work, we introduce a framework to extract and separate hairpin vortices in shear driven turbulent flows for their study. Our method first extracts general vortical regions with a region-growing strategy based on certain vortex criteria (e.g., $\lambda_2$) and then separates those vortices with the help of progressive extraction of ($\lambda_2$) iso-surfaces in a top-down fashion. This leads to a hierarchical tree representing the spatial proximity and merging relation of vortices. After separating individual vortices, their shape and orientation information is extracted. Candidate hairpin vortices are identified based on their shape and orientation information as well as their physical characteristics. An interactive visualization system is developed to aid the exploration, classification, and analysis of hairpin vortices based on their geometric and physical attributes. We also present additional use cases of the proposed system for the analysis and study of general vortices in other types of flows.Comment: Accepted for presentation at IEEE VIS 2023. The paper will appear in IEEE Transactions on Visualization and Computer Graphic

Topological analysis, visualization, and design of vector fields on surfaces

Analysis, visualization, and design of vector fields on surfaces have a wide variety of major applications in both scientific visualization and computer graphics. On the one hand, analysis and visualization of vector fields provide critical insights to the flow data produced from simulation or experiments of various engineering processes. On the other hand, many graphics applications require vector fields as input to drive certain graphical processes. This thesis addresses vector field analysis and design for both visualization and graphics applications. Topological analysis of vector fields provides the qualitative (or structural) information of the underlying dynamics of the given vector data, which helps the domain experts identify the critical features and behaviors efficiently. In this dissertaion, I introduce a more complete vector field topology called Entity Connection Graph (ECG) by including periodic orbits, an essential component in vector field topology. An efficient technique for periodic orbit extraction is introduced and incorporated into the algorithm for ECG construction. The analysis results are visualized using the improved evenly-spaced streamline placement with all separation features being highlighted. This is the first time that periodic orbits have been extracted from surface flows. Through applications to engine simulation datasets, I demonstrate how the extracted topology helps engineers interpret the flow data that contains certain desirable behaviors which indicate the ideal engineering process. Accuracy is typically of paramount importance for visualization and analysis tasks. However, the trajectory-based vector field topology approaches are sensitive to small perturbations such as error and noise which are contained in the given data and introduced during data acquisition and processing. This makes rigorous interpretation of vector field topology and flow dynamics difficult. To overcome that, I advocate the use of Morse decomposition to define a more reliable vector field topology called Morse Connection Graph (MCG). In particular, I present the pipeline of Morse decomposition of an input vector field. A technique based on the idea of [tau]-map is introduced to produce desirably fine Morse decompositions of vector fields. To address the issue of slow performance of the global [tau]-map framework, I describe a hierarchical MCG refinement framework. It enables the [tau]-map approach to be conducted within a Morse set of interest which greatly reduces the computation cost and leads to faster analysis. It is my hope that the work on Morse decomposition will invoke the investigation of other similar data analysis problems such as scalar field and tensor field analysis. The techniques of time-independent vector field design have been well-studied. However, there is little attention on the systematic design of time-varying vector fields on surfaces. This dissertation addresses this by developing a design system that allows the creation and modification of time-varying vector fields on surfaces. More specifically, I present a number of novel techniques to enable efficient design over important characteristics in the vector field such as singularity paths, pathlines, and bifurcations. These vector field features are used to generate a vector field by either blending basis vector fields or performing a constrained optimization process. Unwanted singularities and bifurcations can lead to visual artifacts, and I address them through singularity and bifurcation editing. I demonstrate the capabilities of the design system by applying it to the design of two types of vector fields: the orientation field and the advection field for the application of texture synthesis and animation

Potential immune evasion of the severe acute respiratory syndrome coronavirus 2 Omicron variants

Coronavirus disease 2019 (COVID-19), which is caused by the novel severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), has caused a global pandemic. The Omicron variant (B.1.1.529) was first discovered in November 2021 in specimens collected from Botswana, South Africa. Omicron has become the dominant variant worldwide, and several sublineages or subvariants have been identified recently. Compared to those of other mutants, the Omicron variant has the most highly expressed amino acid mutations, with almost 60 mutations throughout the genome, most of which are in the spike (S) protein, especially in the receptor-binding domain (RBD). These mutations increase the binding affinity of Omicron variants for the ACE2 receptor, and Omicron variants may also lead to immune escape. Despite causing milder symptoms, epidemiological evidence suggests that Omicron variants have exceptionally higher transmissibility, higher rates of reinfection and greater spread than the prototype strain as well as other preceding variants. Additionally, overwhelming amounts of data suggest that the levels of specific neutralization antibodies against Omicron variants decrease in most vaccinated populations, although CD4+ and CD8+ T-cell responses are maintained. Therefore, the mechanisms underlying Omicron variant evasion are still unclear. In this review, we surveyed the current epidemic status and potential immune escape mechanisms of Omicron variants. Especially, we focused on the potential roles of viral epitope mutations, antigenic drift, hybrid immunity, and “original antigenic sin” in mediating immune evasion. These insights might supply more valuable concise information for us to understand the spreading of Omicron variants