We introduce the Stress-Guided Lightweight Design Benchmark (SGLDBench), a comprehensive benchmark suite for applying and evaluating material layout strategies to generate stiff, lightweight designs in 3D domains. SGLDBench provides a seamlessly integrated simulation and analysis framework, including six reference strategies and a scalable multigrid elasticity solver to efficiently execute these strategies and validate the stiffness of their results. This facilitates the systematic analysis and comparison of design strategies based on the mechanical properties they achieve. SGLDBench enables the evaluation of diverse load conditions and, through the tight integration of the solver, supports high-resolution designs and stiffness analysis. Additionally, SGLDBench emphasizes visual analysis to explore the relationship between the geometric structure of a design and the distribution of stresses, offering insights into the specific properties and behaviors of different design strategies. SGLDBench's specific features are highlighted through several experiments, comparing the results of reference strategies with respect to geometric and mechanical properties.

Database systems face challenges when using mutual information (MI) for analyzing non-linear relationships between large timeseries, due to computational and memory requirements. Interactive workflows are especially hindered by long response times. To address these challenges, we present timeseries neural MI fields (TNMIFs), a compact data structure that has been trained to reconstruct MI efficiently across various time-windows and window positions in large timeseries. We demonstrate learning and reconstruction with a large timeseries dataset comprising 1420 timeseries, each storing data at 1639 timesteps. While the learned data structure consumes only 45 megabytes, it answers queries for the MI estimates between the windows in a selected timeseries and the corresponding windows in all other timeseries within 44 milliseconds. Given a measure of similarity between timeseries based on windowed MI estimates, even the matrix showing all mutual timeseries similarities can be computed in less than 32 seconds. To support measuring dependence between lagged timeseries, an extended data structure learns to reconstruct MI to positively (future) and negatively (past) lagged windows. Using a maximum lag of 64 in both directions decreases query times by about a factor of 10.

Visualizing spatial correlations in 3D ensembles is challenging due to the vast amounts of information that need to be conveyed. Memory and time constraints make it unfeasible to pre-compute and store the correlations between all pairs of domain points. We propose the embedding of adaptive correlation sampling into chord diagrams with hierarchical edge bundling to alleviate these constraints. Entities representing spatial regions are arranged along the circular chord layout via a space-filling curve, and Bayesian optimal sampling is used to efficiently estimate the maximum occurring correlation between any two points from different regions. Hierarchical edge bundling reduces visual clutter and emphasizes the major correlation structures. By selecting an edge, the user triggers a focus diagram in which only the two regions connected via this edge are refined and arranged in a specific way in a second chord layout. For visualizing correlations between two different variables, which are not symmetric anymore, we switch to showing a full correlation matrix. This avoids drawing the same edges twice with different correlation values. We introduce GPU implementations of both linear and non-linear correlation measures to further reduce the time that is required to generate the context and focus views, and to even enable the analysis of correlations in a 1000-member ensemble.

This article presents a comprehensive study of rendering techniques for 3D line sets with transparency. The rendering of transparent lines is widely used for visualizing trajectories of tracer particles in flow fields. Transparency is then used to fade out lines deemed unimportant, based on, for instance, geometric properties or attributes defined along with them. Accurate blending of transparent lines requires rendering the lines in back-to-front or front-to-back order, yet enforcing this order for space-filling 3D line sets with extremely high-depth complexity becomes challenging. In this article, we study CPU and GPU rendering techniques for transparent 3D line sets. We compare accurate and approximate techniques using optimized implementations and several benchmark data sets. We discuss the effects of data size and transparency on quality, performance, and memory consumption. Based on our study, we propose two improvements to per-pixel fragment lists and multi-layer alpha blending. The first improves the rendering speed via an improved GPU sorting operation, and the second improves rendering quality via transparency-based bucketing.

The visual inspection of a hexahedral mesh with respect to element quality is difficult due to clutter and occlusions that are produced when rendering all element faces or their edges simultaneously. Current approaches overcome this problem by using focus on specific elements that are then rendered opaque, and carving away all elements occluding their view. In this work, we make use of advanced GPU shader functionality to generate a focus+context rendering that highlights the elements in a selected region and simultaneously conveys the global mesh structure and deformation field. To achieve this, we propose a gradual transition from edge-based focus rendering to volumetric context rendering, by combining fragment shader-based edge and face rendering with per-pixel fragment lists. A fragment shader smoothly transitions between wireframe and face-based rendering, including focus-dependent rendering style and depth-dependent edge thickness and halos, and per-pixel fragment lists are used to blend fragments in correct visibility order. To maintain the global mesh structure in the context regions, we propose a new method to construct a sheet-based level-of-detail hierarchy and smoothly blend it with volumetric information. The user guides the exploration process by moving a lens-like hotspot. Since all operations are performed on the GPU, interactive frame rates are achieved even for large meshes.