Visualization of Particle‐based Data with Transparency and Ambient Occlusion

Particle‐based simulation techniques, like the discrete element method or molecular dynamics, are widely used in many research fields. In real‐time explorative visualization it is common to render the resulting data using opaque spherical glyphs with local lighting only. Due to massive overlaps, however, inner structures of the data are often occluded rendering visual analysis impossible. Furthermore, local lighting is not sufficient as several important features like complex shapes, holes, rifts or filaments cannot be perceived well. To address both problems we present a new technique that jointly supports transparency and ambient occlusion in a consistent illumination model. Our approach is based on the emission‐absorption model of volume rendering. We provide analytic solutions to the volume rendering integral for several density distributions within a spherical glyph. Compared to constant transparency our approach preserves the three‐dimensional impression of the glyphs much better. We approximate ambient illumination with a fast hierarchical voxel cone‐tracing approach, which builds on a new real‐time voxelization of the particle data. Our implementation achieves interactive frame rates for millions of static or dynamic particles without any preprocessing. We illustrate the merits of our method on real‐world data sets gaining several new insights.     

An Evaluation of Glyph Perception for Real Symmetric Traceless Tensor Properties

A perceptual study of four tensor glyphs for symmetric, real, traceless tensors was performed. Each glyph encodes three properties of the system: Orientation, uniaxiality (alignment along the direction of orientation), and biaxiality (alignment along a vector orthogonal to the orientation). Thirty users over two studies were asked to identify these three properties for each glyph type under a variety of permutations in order to evaluate the effectiveness of visually communicating the properties; response time was also measured. We discuss the significant differences found between the methods as guidance to the use of these glyphs for traceless tensor visualization.     

Exploratory Visualization of Animal Kinematics Using Instantaneous Helical Axes

We present novel visual and interactive techniques for exploratory visualization of animal kinematics using instantaneous helical axes (IHAs). The helical axis has been used in orthopedics, biomechanics, and structural mechanics as a construct for describing rigid body motion. Within biomechanics, recent imaging advances have made possible accurate high‐speed measurements of individual bone positions and orientations during experiments. From this high‐speed data, instantaneous helical axes of motion may be calculated. We address questions of effective interactive, exploratory visualization of this high‐speed 3D motion data. A 3D glyph that encodes all parameters of the IHA in visual form is presented. Interactive controls are used to examine the change in the IHA over time and relate the IHA to anatomical features of interest selected by a user. The techniques developed are applied to a stereoscopic, interactive visualization of the mechanics of pig mastication and assessed by a team of evolutionary biologists who found interactive IHA‐based analysis a useful addition to more traditional motion analysis techniques.     

FlexyFont: Learning Transferring Rules for Flexible Typeface Synthesis

Maintaining consistent styles across glyphs is an arduous task in typeface design. In this work we introduce FlexyFont, a flexible tool for synthesizing a complete typeface that has a consistent style with a given small set of glyphs. Motivated by a key fact that typeface designers often maintain a library of glyph parts to achieve a consistent typeface, we intend to learn part consistency between glyphs of different characters across typefaces. We take a part assembling approach by firstly decomposing the given glyphs into semantic parts and then assembling them according to learned sets of transferring rules to reconstruct the missing glyphs. To maintain style consistency, we represent the style of a font as a vector of pairwise part similarities. By learning a distribution over these feature vectors, we are able to predict the style of a novel typeface given only a few examples. We utilize a popular machine learning method as well as retrieval‐based methods to quantitatively assess the performance of our feature vector, resulting in favorable results. We also present an intuitive interface that allows users to interactively create novel typefaces with ease. The synthesized fonts can be directly used in real‐world design.     

Glyphs for Asymmetric Second‐Order 2D Tensors

Tensors model a wide range of physical phenomena. While symmetric tensors are sufficient for some applications (such as diffusion), asymmetric tensors are required, for example, to describe differential properties of fluid flow. Glyphs permit inspecting individual tensor values, but existing tensor glyphs are fully defined only for symmetric tensors. We propose a glyph to visualize asymmetric second‐order two‐dimensional tensors. The glyph includes visual encoding for physically significant attributes of the tensor, including rotation, anisotropic stretching, and isotropic dilation. Our glyph design conserves the symmetry and continuity properties of the underlying tensor, in that transformations of a tensor (such as rotation or negation) correspond to analogous transformations of the glyph. We show results with synthetic data from computational fluid dynamics.     

Pathline glyphs

Visualization of pathlines is common and highly relevant for the analysis of unsteady flow. However, pathlines can intersect, leading to visual clutter and perceptual issues. This makes it intrinsically difficult to provide expressive visualizations of the entire domain by an arrangement of multiple pathlines, in contrast to well‐established streamline placement techniques. We present an approach to reduce these problems. It is inspired by glyph‐based visualization and small multiples: we partition the domain into cells, each corresponding to a downscaled version of the entire domain. Inside these cells, a single downscaled pathline is drawn. On the overview scale, our pathline glyphs lead to emergent visual patterns that provide insight into time‐dependent flow behavior. Zooming‐in allows us to analyze individual pathlines in detail and compare neighboring lines. The overall approach is complemented with a context‐preserving zoom lens and interactive pathline‐based exploration. While we primarily target the visualization of 2D flow, we also address the extension to 3D. Our evaluation includes several examples, comparison to other flow visualization techniques, and a user study with domain experts.     

Coherent Culling and Shading for Large Molecular Dynamics Visualization

Molecular dynamics simulations are a principal tool for studying molecular systems. Such simulations are used to investigate molecular structure, dynamics, and thermodynamical properties, as well as a replacement for, or complement to, costly and dangerous experiments. With the increasing availability of computational power the resulting data sets are becoming increasingly larger, and benchmarks indicate that the interactive visualization on desktop computers poses a challenge when rendering substantially more than millions of glyphs. Trading visual quality for rendering performance is a common approach when interactivity has to be guaranteed. In this paper we address both problems and present a method for high‐quality visualization of massive molecular dynamics data sets. We employ several optimization strategies on different levels of granularity, such as data quantization, data caching in video memory, and a two‐level occlusion culling strategy: coarse culling via hardware occlusion queries and a vertex‐level culling using maximum depth mipmaps. To ensure optimal image quality we employ GPU raycasting and deferred shading with smooth normal vector generation. We demonstrate that our method allows us to interactively render data sets containing tens of millions of high‐quality glyphs.     

Effective Techniques to Visualize Filament‐Surface Relationships

Combined visualizations of filamentous structures and surrounding volumetric objects are common in biological and medical applications. Often, the structures' spatial relationships remain unclear to the viewer. In this paper, we discuss and evaluate techniques to emphasize spatial relationships. We concentrate on the visualization of transparent objects and intersecting lines. Among various techniques, participants of an exploratory user study preferred coloring of lines, marking of line‐surface intersections by glyphs, and the combination of both. These techniques were additionally evaluated in a confirmatory study in which participants were asked to judge whether a filament runs through a transparent structure. We found that the evaluated techniques significantly improve the participants' performance in terms of the number of correct responses and response time. The best performance was found for the combination of line coloring and intersection glyph display.     

Flow‐Induced Inertial Steady Vector Field Topology

Traditionally, vector field visualization is concerned with 2D and 3D flows. Yet, many concepts can be extended to general dynamical systems, including the higher‐dimensional problem of modeling the motion of finite‐sized objects in fluids. In the steady case, the trajectories of these so‐called inertial particles appear as tangent curves of a 4D or 6D vector field. These higher‐dimensional flows are difficult to map to lower‐dimensional spaces, which makes their visualization a challenging problem. We focus on vector field topology, which allows scientists to study asymptotic particle behavior. As recent work on the 2D case has shown, both extraction and classification of isolated critical points depend on the underlying particle model. In this paper, we aim for a model‐independent classification technique, which we apply to two different particle models in not only 2D, but also 3D cases. We show that the classification can be done by performing an eigenanalysis of the spatial derivatives' velocity subspace of the higher‐dimensional 4D or 6D flow. We construct glyphs that depict not only the types of critical points, but also encode the directional information given by the eigenvectors. We show that the eigenvalues and eigenvectors of the inertial phase space have sufficient symmetries and structure so that they can be depicted in 2D or 3D, instead of 4D or 6D.     

Non‐iterative Second‐order Approximation of Signed Distance Functions for Any Isosurface Representation

Signed distance functions (SDF) to explicit or implicit surface representations are intensively used in various computer graphics and visualization algorithms. Among others, they are applied to optimize collision detection, are used to reconstruct data fields or surfaces, and, in particular, are an obligatory ingredient for most level set methods. Level set methods are common in scientific visualization to extract surfaces from scalar or vector fields. Usual approaches for the construction of an SDF to a surface are either based on iterative solutions of a special partial differential equation or on marching algorithms involving a polygonization of the surface. We propose a novel method for a non‐iterative approximation of an SDF and its derivatives in a vicinity of a manifold. We use a second‐order algebraic fitting scheme to ensure high accuracy of the approximation. The manifold is defined (explicitly or implicitly) as an isosurface of a given volumetric scalar field. The field may be given at a set of irregular and unstructured samples. Stability and reliability of the SDF generation is achieved by a proper scaling of weights for the Moving Least Squares approximation, accurate choice of neighbors, and appropriate handling of degenerate cases. We obtain the solution in an explicit form, such that no iterative solving is necessary, which makes our approach fast.     

An Illustrative Visualization Framework for 3D Vector Fields

Most 3D vector field visualization techniques suffer from the problem of visual clutter, and it remains a challenging task to effectively convey both directional and structural information of 3D vector fields. In this paper, we present a novel visualization framework that combines the advantages of clustering methods and illustrative rendering techniques to generate a concise and informative depiction of complex flow structures. Given a 3D vector field, we first generate a number of streamlines covering the important regions based on an entropy measurement. Then we decompose the streamlines into different groups based on a categorization of vector information, wherein the streamline pattern in each group is ensured to be coherent or nearly coherent. For each group, we select a set of representative streamlines and render them in an illustrative fashion to enhance depth cues and succinctly show local flow characteristics. The results demonstrate that our approach can generate a visualization that is relatively free of visual clutter while facilitating perception of salient information of complex vector fields.     

InSpectr: Multi‐Modal Exploration,Visualization, and Analysis of Spectral Data

This paper addresses the increasing demand in industry for methods to analyze and visualize multimodal data involving a spectral modality. Two data modalities are used: high‐resolution X‐ray computed tomography (XCT) for structural characterization and low‐resolution X‐ray fluorescence (XRF) spectral data for elemental decomposition. We present InSpectr, an integrated tool for the interactive exploration and visual analysis of multimodal, multiscalar data. The tool has been designed around a set of tasks identified by domain experts in the fields of XCT and XRF. It supports registered single scalar and spectral datasets optionally coupled with element maps and reference spectra. InSpectr is instantiating various linked views for the integration of spatial and non‐spatial information to provide insight into an industrial component's structural and material composition: views with volume renderings of composite and individual 3D element maps visualize global material composition; transfer functions defined directly on the spectral data and overlaid pie‐chart glyphs show elemental composition in 2D slice‐views; a representative aggregated spectrum and spectra density histograms are introduced to provide a global overview in the spectral view. Spectral magic lenses, spectrum probing and elemental composition probing of points using a pie‐chart view and a periodic table view aid the local material composition analysis. Two datasets are investigated to outline the usefulness of the presented techniques: a 3D virtually created phantom with a brass metal alloy and a real‐world 2D water phantom with insertions of gold, barium, and gadolinium. Additionally a detailed user evaluation of the results is provided.     

Approximate on‐Surface Distance Computation using Quasi‐Developable Charts

There is a vast number of applications that require distance field computation over triangular meshes. State‐of‐the‐art algorithms have quadratic or sub‐quadratic worst‐case complexity, making them impractical for interactive applications. While most of the research on this subject has been focused on reducing the computation complexity of the algorithms, in this work we propose an approximate algorithm that achieves similar results working in lower resolutions of the input meshes. The creation of lower resolution meshes is the essence of our proposal. The idea is to identify regions on the input mesh that can be unfolded into planar regions with minimal area distortion (i.e. quasi‐developable charts). Once charts are computed, their interior is re‐triangulated to reduce the number of triangles, which results in a collection of simplified charts that we call a base mesh. Due to the properties of quasi‐developable regions, we are able to compute distance fields over the base mesh instead of over the input mesh. This reduces the memory footprint and data processed for distance computations, which is the bottleneck of these algorithms. We present results that are one order of magnitude faster than current exact solutions, with low approximation errors.     

A Dynamic Noise Primitive for Coherent Stylization

We present a new solution for temporal coherence in non‐photorealistic rendering (NPR) of animations. Given the conflicting goals of preserving the 2D aspect of the style and the 3D scene motion, any such solution is a tradeoff. We observe that primitive‐based methods in NPR can be seen as texture‐based methods when using large numbers of primitives, leading to our key insight, namely that this process is similar to sparse convolution noise in procedural texturing. Consequently, we present a new primitive for NPR based on Gabor noise, that preserves the 2D aspect of noise, conveys the 3D motion of the scene, and is temporally continuous. We can thus use standard techniques from procedural texturing to create various styles, which we show for interactive NPR applications. We also present a user study to evaluate this and existing solutions, and to provide more insight in the trade‐off implied by temporal coherence. The results of the study indicate that maintaining coherent motion is important, but also that our new solution provides a good compromise between the 2D aspect of the style and 3D motion.     

An Interactive Design System of Free‐Formed Bamboo‐Copters

We present an interactive design system for designing free‐formed bamboo‐copters, where novices can easily design free‐formed, even asymmetric bamboo‐copters that successfully fly. The designed bamboo‐copters can be fabricated using digital fabrication equipment, such as a laser cutter. Our system provides two useful functions for facilitating this design activity. First, it visualizes a simulated flight trajectory of the current bamboo‐copter design, which is updated in real time during the user's editing. Second, it provides an optimization function that automatically tweaks the current bamboo‐copter design such that the spin quality—how stably it spins—and the flight quality—how high and long it flies—are enhanced. To enable these functions, we present non‐trivial extensions over existing techniques for designing free‐formed model airplanes [ UKSI14 ], including a wing discretization method tailored to free‐formed bamboo‐copters and an optimization scheme for achieving stable bamboo‐copters considering both spin and flight qualities.     

An Operator Approach to Tangent Vector Field Processing

In this paper, we introduce a novel coordinate‐free method for manipulating and analyzing vector fields on discrete surfaces. Unlike the commonly used representations of a vector field as an assignment of vectors to the faces of the mesh, or as real values on edges, we argue that vector fields can also be naturally viewed as operators whose domain and range are functions defined on the mesh. Although this point of view is common in differential geometry it has so far not been adopted in geometry processing applications. We recall the theoretical properties of vector fields represented as operators, and show that composition of vector fields with other functional operators is natural in this setup. This leads to the characterization of vector field properties through commutativity with other operators such as the Laplace‐Beltrami and symmetry operators, as well as to a straight‐forward definition of differential properties such as the Lie derivative. Finally, we demonstrate a range of applications, such as Killing vector field design, symmetric vector field estimation and joint design on multiple surfaces.     

Practical Path Guiding for Efficient Light‐Transport Simulation

We present a robust, unbiased technique for intelligent light‐path construction in path‐tracing algorithms. Inspired by existing path‐guiding algorithms, our method learns an approximate representation of the scene's spatio‐directional radiance field in an unbiased and iterative manner. To that end, we propose an adaptive spatio‐directional hybrid data structure, referred to as SD‐tree, for storing and sampling incident radiance. The SD‐tree consists of an upper part—a binary tree that partitions the 3D spatial domain of the light field—and a lower part—a quadtree that partitions the 2D directional domain. We further present a principled way to automatically budget training and rendering computations to minimize the variance of the final image. Our method does not require tuning hyperparameters, although we allow limiting the memory footprint of the SD‐tree. The aforementioned properties, its ease of implementation, and its stable performance make our method compatible with production environments. We demonstrate the merits of our method on scenes with difficult visibility, detailed geometry, and complex specular‐glossy light transport, achieving better performance than previous state‐of‐the‐art algorithms.     

Still‐Frame Simulation for Fire Effects of Images

We propose various simulation strategies to generate single‐frame fire effects for images, as opposed to multi‐frame fire effects for animations. To accelerate 3D simulation and to provide a user with early hints on the final effect, we propose a 2D‐guided 3D simulation approach, which runs a faster 2D simulation first, and then guides 3D simulation using the 2D simulation result. To achieve this, we explore various boundary conditions and develop a constrained projection method. Since only the final frame will be used while intermediate frames are abandoned, earlier intermediate frames can take larger time steps and have large noise applied, quickly generating turbulent flow structures. As the final frame approaches, we increase the flow quality by reducing the time step and not adding any noise. This adaptive time stepping allows us to use more computational resource near or at the final frame. We also develop divergence and buoyancy modification methods to guide flames along arbitrary, even physically implausible, directions. Our simulation methods can effectively and efficiently generate a variety of fire effects useful for image decoration.     

As‐Killing‐As‐Possible Vector Fields for Planar Deformation

Cartoon animation, image warping, and several other tasks in two‐dimensional computer graphics reduce to the formulation of a reasonable model for planar deformation. A deformation is a map from a given shape to a new one, and its quality is determined by the type of distortion it introduces. In many applications, a desirable map is as isometric as possible. Finding such deformations, however, is a nonlinear problem, and most of the existing solutions approach it by minimizing a nonlinear energy. Such methods are not guaranteed to converge to a global optimum and often suffer from robustness issues. We propose a new approach based on approximate Killing vector fields (AKVFs), first introduced in shape processing. AKVFs generate near‐isometric deformations, which can be motivated as direction fields minimizing an “as‐rigid‐as‐possible” (ARAP) energy to first order. We first solve for an AKVF on the domain given user constraints via a linear optimization problem and then use this AKVF as the initial velocity field of the deformation. In this way, we transfer the inherent nonlinearity of the deformation problem to finding trajectories for each point of the domain having the given initial velocities. We show that a specific class of trajectories — the set of logarithmic spirals — is especially suited for this task both in practice and through its relationship to linear holomorphic vector fields. We demonstrate the effectiveness of our method for planar deformation by comparing it with existing state‐of‐the‐art deformation methods.     

Dynamic Multi‐View Exploration of Shape Spaces

Statistical shape modeling is a widely used technique for the representation and analysis of the shapes and shape variations present in a population. A statistical shape model models the distribution in a high dimensional shape space, where each shape is represented by a single point. We present a design study on the intuitive exploration and visualization of shape spaces and shape models. Our approach focuses on the dual‐space nature of these spaces. The high‐dimensional shape space represents the population, whereas object space represents the shape of the 3D object associated with a point in shape space. A 3D object view provides local details for a single shape. The high dimensional points in shape space are visualized using a 2D scatter plot projection, the axes of which can be manipulated interactively. This results in a dynamic scatter plot, with the further extension that each point is visualized as a small version of the object shape that it represents. We further enhance the population‐object duality with a new type of view aimed at shape comparison. This new “shape evolution view” visualizes shape variability along a single trajectory in shape space, and serves as a link between the two spaces described above. Our three‐view exploration concept strongly emphasizes linked interaction between all spaces. Moving the cursor over the scatter plot or evolution views, shapes are dynamically interpolated and shown in the object view. Conversely, camera manipulation in the object view affects the object visualizations in the other views. We present a GPU‐accelerated implementation, and show the effectiveness of the three‐view approach using a number of real‐world cases. In these, we demonstrate how this multi‐view approach can be used to visually explore important aspects of a statistical shape model, including specificity, compactness and reconstruction error.