This article presents a well-scaling parallel algorithm for the computation of Morse-Smale (MS) segmentations, including the region separators and region boundaries. The segmentation of the domain into ascending and descending manifolds, solely defined on the vertices, improves the computational time using path compression and fully segments the border region. Region boundaries and region separators are generated using a multi-label marching tetrahedra algorithm. This enables a fast and simple solution to find optimal parameter settings in preliminary exploration steps by generating an MS complex preview. It also poses a rapid option to generate a fast visual representation of the region geometries for immediate utilization. Two experiments demonstrate the performance of our approach with speedups of over an order of magnitude in comparison to two publicly available implementations. The example section shows the similarity to the MS complex, the useability of the approach, and the benefits of this method with respect to the presented datasets. We provide our implementation with the paper.

Abstract In many applications, visual analytics (VA) has developed into a standard tool to ease data access and knowledge generation. VA describes a holistic cycle transforming data into hypothesis and visualization to generate insights that enhance the data. Unfortunately, many data sources used in the VA process are affected by uncertainty. In addition, the VA cycle itself can introduce uncertainty to the knowledge generation process but does not provide a mechanism to handle these sources of uncertainty. In this manuscript, we aim to provide an extended VA cycle that is capable of handling uncertainty by quantification, propagation, and visualization, defined as uncertainty-aware visual analytics (UAVA). Here, a recap of uncertainty definition and description is used as a starting point to insert novel components in the visual analytics cycle. These components assist in capturing uncertainty throughout the VA cycle. Further, different data types, hypothesis generation approaches, and uncertainty-aware visualization approaches are discussed that fit in the defined UAVA cycle. In addition, application scenarios that can be handled by such a cycle, examples, and a list of open challenges in the area of UAVA are provided.

Abstract Inspection planning approaches so far have focused on automatically obtaining an optimal set of viewpoints required to cover a given object. While research has provided interesting results, the automatic inspection planning has still not been made a part of the everyday inspection system development process. This is mostly because the plans are difficult to verify and it is impossible to compare them to laboratory-developed plans. In this work, we give an overview of available generate-and-test approaches, evaluate their results for various objects and finally compare them to plans created by inspection system development experts. The comparison emphasizes both benefits and downsides of automated approaches and highlights problems which need to be tackled in the future in order to make the automated inspection planning more applicable.

Abstract The goal of visual surface inspection is to analyze an object’s surface and detect defects by looking at it from different angles. Developments over the past years have made it possible to partially automate this process. Inspection systems use robots to move cameras and obtain pictures that are evaluated by image processing algorithms. Setting up these systems or adapting them to new models is primarily done manually. A key challenge is to define camera viewpoints from which the images are taken. The number of viewpoints should be as low as possible while still guaranteeing an inspection of the desired quality. System engineers define and evaluate configurations that are improved based on a time-consuming trial-and-error process leading to a sufficient, but not necessarily optimal, configuration. With the availability of 3D surface models defined by triangular meshes, this step can be done virtually. This paper presents a new scalable approach to determine a small number of well-placed camera viewpoints for optical surface inspection planning. The initial model is approximated by B-spline surfaces. A set of geometric feature functionals is defined and used for an adaptive, non-uniform surface sampling that is sparse in geometrically low-complexity areas and dense in regions of higher complexity. The presented approach is applicable to solid objects with a given 3D surface model. It makes camera viewpoint generation independent of the resolution of the triangle mesh, and it improves previous results considering number of viewpoints and their relevance.

As of today, data analysis focuses primarily on the findings to be made inside the data and concentrates less on how those findings relate to the domain of investigation. Contemporary visualization as a field of research shows a strong tendency to adopt this data-centrism. Despite their decisive influence on the analysis result, qualitative aspects of the analysis process such as the structure, soundness, and complexity of the applied reasoning strategy are rarely discussed explicitly. We argue that if the purpose of visualization is the provision of domain insight rather than the depiction of data analysis results, a holistic perspective requires a qualitative component to to be added to the discussion of quantitative and human factors. To support this point, we demonstrate how considerations of qualitative factors in visual analysis can be applied to obtain explanations and possible solutions for a number of practical limitations inherent to the data-centric perspective on analysis. Based on this discussion of what we call qualitative visual analysis, we develop an inside-outside principle of nested levels of context that can serve as a conceptual basis for the development of visualization systems that optimally support the emergence of insight during analysis.

Abstract In order to discuss the kinds of reasoning a visualization supports and the conclusions that can be drawn within the analysis context, a theoretical framework is needed that enables a formal treatment of the reasoning process. Such a model needs to encompass three stages of the visualization pipeline: encoding, decoding and interpretation. The encoding details how data are transformed into a visualization and what can be seen in the visualization. The decoding explains how humans construct graphical contexts inside the depicted visualization and how they interpret them assigning meaning to displayed structures according to a formal reasoning strategy. In the presented model, we adapt and combine theories for the different steps into a unified formal framework such that the analysis process is modelled as an assignment of meaning to displayed structures according to a formal reasoning strategy. Additionally, we propose the ConceptGraph, a combined graph‐based representation of the finite‐state transducers resulting from the three stages, that can be used to formalize and understand the reasoning process. We apply the new model to several visualization types and investigate reasoning strategies for various tasks.

Ramachandran Plots are an important tool for researchers in bio-chemistry to examine the stability of a molecule. In these plots, dihedral (torsion) angles of the protein's backbone are visualized ona plane, where different areas are known to be stable configurations. Unfortunately, the underlying atom positions are affected by uncer-tainty, which is usually captured and expressed using the b-value. For classic Ramachandran Plots, this uncertainty is not propagatedwhen computing the dihedral angles and neglected when visualizinga Ramachandran Plot. To solve this problem, this paper presentsan extended version of the Ramachandran Plot, which allows tocommunicate the uncertainty of atom positions along the compu-tation of dihedral angles and an intuitive visualization. We showthe effectiveness of the presented approach by examining differentRamachandran Plots for molecules and show how the inclusion ofuncertainty helps biochemistry researchers to determine the stabilityof a protein with higher accuracy.

In the development of graphical algorithms, choosing an appropriate data representation plays a pivotal role. Hence, there is a need for studies that support corresponding decision making. Here, we investigate curvature estimation based on two discrete representations-volume images and triangle meshes-and present a comprehensive cross-comparison. For doing so, four carefully selected geometries, represented as implicit functions, have been discretized to volume images and triangle meshes in different resolutions on a comparable scale. Afterwards, implementations available in open-source libraries (CGAL, DIPimage, libigl, trimesh2, VTK) and our own implementation of a relevant paper [1] were applied to them and the resulting estimations of mean and Gaussian curvature were compared in terms of quality and runtime. Independent of the underlying discrete representation, all estimators generated similar errors, but overall, mesh-based methods allowed for more accurate estimations. We measured a maximum normalized mean absolute error difference of 6.36 percent between the most precise mesh-based method compared to corresponding image-based methods when considering only discretizations of sufficient resolution. In terms of runtime, methods working on triangle meshes were faster when geometries had a small surface density. For geometries with larger surface densities, which is fairly common when considering real data, e.g., in material or medical science, the runtimes for both representations were similar.

Keyhole surgeries become increasingly important in clinical daily routine as they help minimizing the damage of a patient’s healthy tissue. The planning of keyhole surgeries is based on medical imaging and an important factor that influences the surgeries’ success. Due to the image reconstruction process, medical image data contains uncertainty that exacerbates the planning of a keyhole surgery. In this paper we present a visual workflow that helps clinicians to examine and compare different surgery paths as well as visualizing the patients’ affected tissue. The analysis is based on the concept of hierarchical image semantics, that segment the underlying image data with respect to the input images’ uncertainty and the users understanding of tissue composition. Users can define arbitrary surgery paths that they need to investigate further. The defined paths can be queried by a rating function to identify paths that fulfill user-defined properties. The workflow allows a visual inspection of the affected tissues and its substructures. Therefore, the workflow includes a linked view system indicating the three-dimensional location of selected surgery paths as well as how these paths affect the patients tissue. To show the effectiveness of the presented approach, we applied it to the planning of a keyhole surgery of a brain tumor removal and a kneecap surgery.

Software-defined network/ing (SDN) is a novel configuration technique that has the potential to become the future backbone of computer networking. In contrast to conventional networking techniques, SDN utilizes controller elements to configure groups of networking nodes, resulting in a hierarchy. SDNs have to be simulated and analyzed to identify applicable configuration settings for real world applications. To determine the quality of a SDN configuration, its packet flow is an important indicator for the analysis. This work presents an interactive system for the analysis of SDN data. An intuitive overview of the SDN hierarchy and the underlying packet flow is provided. The ability to track packets through the SDN and to interlink multiple views of the SDN forms an interactive analysis tool that is successfully applied to a simulated SDN dataset.

Abstract This paper presents the state of the art in the area of topology‐based visualization. It describes the process and results of an extensive annotation for generating a definition and terminology for the field. The terminology enabled a typology for topological models which is used to organize research results and the state of the art. Our report discusses relations among topological models and for each model describes research results for the computation, simplification, visualization, and application. The paper identifies themes common to subfields, current frontiers, and unexplored territory in this research area.

An eddy is a feature associated with a rotating body of fluid, surrounded by a ring of shearing fluid. In the ocean, eddies are 10 to 150 km in diameter, are spawned by boundary currents and baroclinic instabilities, may live for hundreds of days, and travel for hundreds of kilometers. Eddies are important in climate studies because they transport heat, salt, and nutrients through the world's oceans and are vessels of biological productivity. The study of eddies in global ocean-climate models requires large-scale, high-resolution simulations. This poses a problem for feasible (timely) eddy analysis, as ocean simulations generate massive amounts of data, causing a bottleneck for traditional analysis workflows. To enable eddy studies, we have developed an in situ workflow for the quantitative and qualitative analysis of MPAS-Ocean, a high-resolution ocean climate model, in collaboration with the ocean model research and development process. Planned eddy analysis at high spatial and temporal resolutions will not be possible with a postprocessing workflow due to various constraints, such as storage size and I/O time, but the in situ workflow enables it and scales well to ten-thousand processing elements.

Time surfaces are a versatile tool to visualise advection and deformation in flow fields. Due to complex flow behaviours involving stretching, shearing, and folding, straightforward mesh-based representations of these surfaces can develop artefacts and degenerate quickly. Common counter-measures rely on refinement and adaptive insertion of new particles which lead to an unpredictable increase in memory requirements. We propose a novel time surface extraction technique that keeps the number of required flow particles constant, while providing a high level of fidelity and enabling straightforward load balancing. Our solution implements a 2D particle relaxation procedure that makes use of local surface metric tensors to model surface deformations. We combine this with an accurate bicubic surface representation to provide an artefact-free surface visualisation. We demonstrate and evaluate benefits of the proposed method with respect to surface accuracy and computational efficiency.

In urban microclimate research, mobile transects are utilized to observe the relationship between atmospheric variables and the urban environment. However, the data sets resulting from mobile measurements are complex: They are spatially dependent, multivariate, and often-times multitemporal. At the same time, the spatial context of each observation - its field of view and area represented - is physically complex and dynamic. These properties make analysis and visualization challenging. We present a prototype visualization framework that assists researchers in the analysis of mobile transect measurements. The system enables users to visualize and explore observations as walls that delineate the transect route on a map. The observed attributes are stacked upon each other within these walls as ribbons to facilitate the qualitative analysis of spatial variability and multivariate correlations. The relationship between observations and spatial context can interactively be explored by moving a slider along the transect route. For each observation on the track, the spatially contextual source area is displayed and linked to a view of the fraction of land cover classes contained within the source area. These qualitative analysis capabilities are complemented by an interactive clustering interface, which allows for the classification of transect segments according to a coherent pattern of multivariate relationships between a user-defined set of observations. The framework was developed by a team comprising both visualization and urban microclimate researchers, and a case study shows its utility for this specialized application.

Analysis of spatio-temporal event data is of central importance in many domains of science and policy making. Current visualization methods rely on animation, small multiples, and space-time cubes to enable spatio-temporal data exploration. These methods require the user to remember state spaces or deal with layout occlusions when exploring their data. To overcome such issues, we propose a novel visualization technique for such data that applies the topological notion of Reeb graphs to identify hotspots as areas of relatively high event density within kernel density estimates. We illustrate that the topological identification of hotspots proposed in this paper is able to elucidate lifetime, properties, and relationships of hotspots by visualizing their temporal evolution based on the spatio-temporal Reeb graph. To validate our approach, we demonstrate our method on an epidemiological and a crime dataset. The resulting visualizations assist users in quickly identifying and comprehending important dates, events, hotspot properties, and relationships between hotspots.

The papers in this special section present extended versions of four selected papers from the 2014 IEEE Pacific Visualization Symposium (PacificVis’14).

Providing sustainable urban water distribution systems is a complex process involving decision makers and authorities as well as the public opinion. In this process, a successful visualization should support analyzing and comparing different scenarios. Therefore, in this study, several visualization techniques are combined to provide an effective representation of a water distribution system. The main parameter to visualize is nodal pressure. First, the nodal pressure values for the study area are obtained as a function of operation time using the U.S. Environmental Protection Agency EPANET model. Then, the time steps are represented as small multiple maps. In order to improve the visibility of each node, all the nodes along the edges are aggregated and represented as a single node. The circle view representation is used to visualize two values of a nodal pressure variable. Finally, the water network is mapped onto a grid, which allows a user to see every node individually without overlaps. Results show that this combination of visualization techniques to illustrate the water network scenarios is beneficial for decision makers to provide sustainable urban water services.

Quantile and median filters are usually implemented by accumulating a histogram in a mask with side length 2r + 1, and then selecting the desired quantile from the histogram. Fully updating the histogram for every pixel in a d-dimensional image leads to an O(rd) algorithm per pixel. Huang et al. proposed to shift the histogram pixel-by-pixel to reduce the complexity to O(rd-1) per pixel. We also show how to transfer their algorithm to higher dimensions, in this contribution. Perreault and Hébert extended this idea to reach O(1) runtime per pixel in arbitrary dimension. Thus, from an algorithmic point of view, quantile filtering of d-dimensional data is a solved problem. But the memory requirements of that algorithm grow with a power of D - 1. In this contribution, we therefore propose a novel hybrid quantile filter algorithm which is situated between the two aforementioned methods in terms of memory requirements, and which is faster for a wide range of mask sizes due to reduced overhead.

Abstract Analysis of chemical constituents from mass spectrometry of aerosols involves non‐negative matrix factorization, an approximation of high‐dimensional data in lower‐dimensional space. The associated optimization problem is non‐convex, resulting in crude approximation errors that are not accessible to scientists. To address this shortcoming, we introduce a new methodology for user‐guided error‐aware data factorization that entails an assessment of the amount of information contributed by each dimension of the approximation, an effective combination of visualization techniques to highlight, filter, and analyze error features, as well as a novel means to interactively refine factorizations. A case study and the domain‐expert feedback provided by the collaborating atmospheric scientists illustrate that our method effectively communicates errors of such numerical optimization results and facilitates the computation of high‐quality data factorizations in a simple and intuitive manner.

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.

Material interfaces and free surfaces are a topic of increasing interest in the field of computational fluid dynamics. In parts, reconstructed interfaces from such multi-fluid simulations behave like classic integral surfaces as known in the visualization community, while other regions of the surface undergo topological changes or behave orthogonally to what is expected by the underlying flow field. Thus, the analysis of the flow field in connection with material interface shape and topology is a challenging task. We develop a technique that facilitates visualization and analysis of such complex material interface behavior over time. For this matter, we track a surface parametrization of time-varying material interfaces and identify locations of interaction between material interfaces and fluid particles. Splatting and surface visualization techniques produce an intuitive representation of the derived interface stability. Our results demonstrate, how the interaction of the flow field with the material interface can be highlighted by appropriate extraction and visualization techniques and how the developed techniques can aid analysis of mixing and material interface consistency.

The study of aerosol composition for air quality research involves the analysis of high-dimensional single particle mass spectrometry data. We describe, apply, and evaluate a novel interactive visual framework for dimensionality reduction of such data. Our framework is based on non-negative matrix factorization with specifically defined regularization terms that aid in resolving mass spectrum ambiguity. Thereby, visualization assumes a key role in providing insight into and allowing to actively control a heretofore elusive data processing step, and thus enabling rapid analysis meaningful to domain scientists. In extending existing black box schemes, we explore design choices for visualizing, interacting with, and steering the factorization process to produce physically meaningful results. A domain-expert evaluation of our system performed by the air quality research experts involved in this effort has shown that our method and prototype admits the finding of unambiguous and physically correct lower-dimensional basis transformations of mass spectrometry data at significantly increased speed and a higher degree of ease.

In this paper, we characterize the range of features that can be extracted from an Morse-Smale complex and describe a unified query language to extract them. We provide a visual dictionary to guide users when defining features in terms of these queries. We demonstrate our topology-rich visualization pipeline in a tool that interactively queries the MS complex to extract features at multiple resolutions, assigns rendering attributes, and combines traditional volume visualization with the extracted features. The flexibility and power of this approach is illustrated with examples showing novel features.

Crease surfaces describe extremal structures of 3D scalar fields. We present a new region-growing-based approach to the meshless extraction of adaptive nonmanifold valley and ridge surfaces that overcomes limitations of previous approaches by decoupling point seeding and triangulation of the surface. Our method is capable of extracting valley surface skeletons as connected minimum structures. As our algorithm is inherently mesh-free and curvature adaptive, it is suitable for surface construction in fields with an arbitrary neighborhood structure. As an application for insightful visualization with valley surfaces, we choose a low frequency acoustics simulation. We use our valley surface construction approach to visualize the resulting complex-valued scalar pressure field for arbitrary frequencies to identify regions of sound cancellation. This provides an expressive visualization of the topology of wave node and antinode structures in simulated acoustics.

A fundamental characteristic of fluid flow is that it causes mixing: introduce a dye into a flow, and it will disperse. Mixing can be used as a method to visualize and characterize flow. Because mixing is a process that occurs over time, it is a 4D problem that presents a challenge for computation, visualization, and analysis. Motivated by a mixing problem in geophysics, we introduce a combination of methods to analyze, transform, and finally visualize mixing in simulations of convection in a self-gravitating 3D spherical shell representing convection in the Earth's mantle. Geophysicists use tools such as the finite element model CitcomS to simulate convection, and introduce massless, passive tracers to model mixing. The output of geophysical flow simulation is hard to analyze for domain experts because of overall data size and complexity. In addition, information overload and occlusion are problems when visualizing a whole-earth model. To address the large size of the data, we rearrange the simulation data using intelligent indexing for fast file access and efficient caching. To address information overload and interpret mixing, we compute tracer concentration statistics, which are used to characterize mixing in mantle convection models. Our visualization uses a specially tailored version of Direct Volume Rendering. The most important adjustment is the use of constant opacity. Because of this special area of application, i. e. the rendering of a spherical shell, many computations for volume rendering can be optimized. These optimizations are essential to a smooth animation of the time-dependent simulation data. Our results show how our system can be used to quickly assess the simulation output and test hypotheses regarding Earth's mantle convection. The integrated processing pipeline helps geoscientists to focus on their main task of analyzing mantle homogenization.

Planetary topography is the result of complex interactions between geological processes, of which faulting is a prominent component. Surface-rupturing earthquakes cut and move landforms which develop across active faults, producing characteristic surface displacements across the fault. Geometric models of faults and their associated surface displacements are commonly applied to reconstruct these offsets to enable interpretation of the observed topography. However, current 2D techniques are limited in their capability to convey both the three-dimensional kinematics of faulting and the incremental sequence of events required by a given reconstruction. Here we present a real-time system for interactive retro-deformation of faulted topography to enable reconstruction of fault displacement within a high-resolution (sub 1m/pixel) 3D terrain visualization. We employ geometry shaders on the GPU to intersect the surface mesh with fault-segments interactively specified by the user and transform the resulting surface blocks in realtime according to a kinematic model of fault motion. Our method facilitates a human-in-the-loop approach to reconstruction of fault displacements by providing instant visual feedback while exploring the parameter space. Thus, scientists can evaluate the validity of traditional point-to-point reconstructions by visually examining a smooth interpolation of the displacement in 3D. We show the efficacy of our approach by using it to reconstruct segments of the San Andreas fault, California as well as a graben structure in the Noctis Labyrinthus region on Mars.

We present an efficient method for volume rendering by ray casting on the CPU. We employ coherent packet traversal of an implicit bounding volume hierarchy, heuristically pruned using preintegrated transfer functions, to exploit empty or homogeneous space. We also detail SIMD optimizations for volumetric integration, trilinear interpolation, and gradient lighting. The resulting system performs well on low-end and laptop hardware, and can outperform out-of-core GPU methods by orders of magnitude when rendering large volumes without level-of-detail (LOD) on a workstation. We show that, while slower than GPU methods for low-resolution volumes, an optimized CPU renderer does not require LOD to achieve interactive performance on large data sets.

Abstract Researchers and analysts in modern industrial and academic environments are faced with a daunting amount of multi‐dimensional data. While there has been significant development in the areas of data mining and knowledge discovery, there is still the need for improved visualizations and generic solutions. The state‐of‐the‐art in visual analytics and exploratory data visualization is to incorporate more profound analysis methods while focusing on fast interactive abilities. The common trend in these scenarios is to either visualize an abstraction of the data set or to better utilize screen‐space. This paper presents a novel technique that combines clustering, dimension reduction and multi‐dimensional data representation to form a multivariate data visualization that incorporates both detail and overview. This amalgamation counters the individual drawbacks of common projection and multi‐dimensional data visualization techniques, namely ambiguity and clutter. A specific clustering criterion is used to decompose a multi‐dimensional data set into a hierarchical tree structure. This decomposition is embedded in a novel Dimensional Anchor visualization through the use of a weighted linear dimension reduction technique. The resulting Structural Decomposition Tree (SDT) provides not only an insight of the data set's inherent structure, but also conveys detailed coordinate value information. Further, fast and intuitive interaction techniques are explored in order to guide the user in highlighting, brushing, and filtering of the data.

Abstract The evolution of strain and development of material anisotropy in models of the Earth’s mantle flow convey important information about how to interpret the geometric relationship between observation of seismic anisotropy and the actual mantle flow field. By combining feature extraction techniques such as path line integration and tensor accumulation, we compute time‐varying strain vector fields that build the foundation for a number of feature extraction and visualization techniques. The proposed field segmentation, clustering, histograms and multi‐volume visualization techniques facilitate an intuitive understanding of three‐dimensional strain in such flow fields, overcoming limitations of previous methods such as 2‐D line plots and slicing. We present applications of our approach to an artificial time varying flow data set and a real world example of stationary flow in a subduction zone and discuss the challenges of processing these geophysical data sets as well as the insights gained.

This paper introduces a novel importance measure for critical points in 2D scalar fields. This measure is based on a combination of the deep structure of the scale space with the well-known concept of homological persistence. We enhance the noise robust persistence measure by implicitly taking the hill-, ridge- and outlier-like spatial extent of maxima and minima into account. This allows for the distinction between different types of extrema based on their persistence at multiple scales. Our importance measure can be computed efficiently in an out-of-core setting. To demonstrate the practical relevance of our method we apply it to a synthetic and a real-world data set and evaluate its performance and scalability.

This paper presents a new technique for detecting sharp features on point-sampled geometry. Sharp features of different nature and possessing angles varying from obtuse to acute can be identified without any user interaction. The algorithm works directly on the point cloud, no surface reconstruction is needed. Given an unstructured point cloud, our method first computes a Gauss map clustering on local neighborhoods in order to discard all points which are unlikely to belong to a sharp feature. As usual, a global sensitivity parameter is used in this stage. In a second stage, the remaining feature candidates undergo a more precise iterative selection process. Central to our method is the automatic computation of an adaptive sensitivity parameter, increasing significantly the reliability and making the identification more robust in the presence of obtuse and acute angles. The algorithm is fast and does not depend on the sampling resolution, since it is based on a local neighbor graph computation.

The recent development of methods for extracting precise measurements of spatial gene expression patterns from three-dimensional (3D) image data opens the way for new analyses of the complex gene regulatory networks controlling animal development. We present an integrated visualization and analysis framework that supports user-guided data clustering to aid exploration of these new complex data sets. The interplay of data visualization and clustering-based data classification leads to improved visualization and enables a more detailed analysis than previously possible. We discuss 1) the integration of data clustering and visualization into one framework, 2) the application of data clustering to 3D gene expression data, 3) the evaluation of the number of clusters k in the context of 3D gene expression clustering, and 4) the improvement of overall analysis quality via dedicated postprocessing of clustering results based on visualization. We discuss the use of this framework to objectively define spatial pattern boundaries and temporal profiles of genes and to analyze how mRNA patterns are controlled by their regulatory transcription factors.

The Double Insertion, Nonuniform, Stationary subdivision surface (DINUS) generalizes both the nonuniform, bicubic spline surface and the Catmull-Clark subdivision surface. DINUS allows arbitrary knot intervals on the edges, allows incorporation of special features, and provides limit point as well as limit normal rules. It is the first subdivision scheme that gives the user all this flexibility and at the same time all essential limit information, which is important for applications in modeling and adaptive rendering. DINUS is also amenable to analysis techniques for stationary schemes. We implemented DINUS as an Autodesk Maya plugin to show several modeling and rendering examples.

In recent years, high-resolution displays have become increasingly important to decision makers and scientists because large screens combined with a high pixel count facilitate content rich, simultaneous display of computer-generated imagery and high-definition video data from multiple sources. Tiled displays are attractive due to their extended screen real estate, scalability, and low cost. LCD panels are usually preferred over projectors because of their superior resolution. One of the drawbacks of LCD-based tiled displays is the fact that users sometimes get distracted by the screens' bezels, which cause discontinuities in rendered images, animations, or videos. Most conventional solutions either ignore the bezels and display all pixels, causing objects to become distorted, or eliminate the pixels that would normally fall under the bezels, causing pixels to be missing in the display of static images. In animations, the missing pixels will eventually reappear when the object moves, providing an experience that is similar to looking through a French window. In this paper, we present a new scalable approach that leads neither to discontinuities nor to significant loss of information. By projecting onto the bezels, we demonstrate that a combination of LCD-based tiled displays and projection significantly reduces the bezel problem. Our technique eliminates ambiguities that commonly occur on tiled displays in the fields of information visualization, visual data analysis, human-computer interaction, and scientific data display. It improves the usability of multimonitor systems by virtually eliminating the bezels. We describe a setup and provide results from an evaluation experiment conducted on a 3 x 3 and on a 10 x 5 tiled display wall.

Integral surfaces are ideal tools to illustrate vector fields and fluid flow structures. However, these surfaces can be visually complex and exhibit difficult geometric properties, owing to strong stretching, shearing and folding of the flow from which they are derived. Many techniques for non-photorealistic rendering have been presented previously. It is, however, unclear how these techniques can be applied to integral surfaces. In this paper, we examine how transparency and texturing techniques can be used with integral surfaces to convey both shape and directional information. We present a rendering pipeline that combines these techniques aimed at faithfully and accurately representing integral surfaces while improving visualization insight. The presented pipeline is implemented directly on the GPU, providing real-time interaction for all rendering modes, and does not require expensive preprocessing of integral surfaces after computation.

Abstract Existing techniques for rendering arbitrary‐form implicit surfaces are limited, either in performance, correctness or flexibility. Ray tracing algorithms employing interval arithmetic (IA) or affine arithmetic (AA) for root‐funding are robust and general in the class of surfaces they support, but traditionally slow. Nonetheless, implemented efficiently using a stack‐driven iterative algorithm and SIMD vector instructions, these methods can achieve interactive performance for common algebraic surfaces on the CPU. A similar algorithm can also be implemented stacklessly, allowing for efficient ray tracing on the GPU. This paper presents these algorithms, as well as an inclusion‐preserving reduced affine arithmetic (RAA) for faster ray‐surface intersection. Shader metaprogramming allows for immediate and automatic generation of symbolic expressions and their interval or affine extensions. Moreover, we are able to render even complex forms robustly, in real‐time at high resolution.

Abstract This paper presents a novel method for the extraction and visualization of volume deformations in grid‐less point based flow simulations. Our primary goals are the segmentation of different paths through a mixing device and the visualization of ellipsoidal particle deformations. The main challenges are the numerically efficient processing of deformation tensors and the robust integration of stream‐ and streaklines at boundaries of the dataset such that closed segments are obtained. Our results show two‐ and three‐dimensional particle deformations as well as the segmentation of volumes in stationary fields and areas in time‐dependent datasets taking consistent paths through a mixing device.

During animal development, complex patterns of gene expression provide positional information within the embryo. To better understand the underlying gene regulatory networks, the Berkeley Drosophila Transcription Network Project (BDTNP) has developed methods that support quantitative computational analysis of three-dimensional (3D) gene expression in early Drosophila embryos at cellular resolution. We introduce PointCloudXplore (PCX), an interactive visualization tool that supports visual exploration of relationships between different genes' expression using a combination of established visualization techniques. Two aspects of gene expression are of particular interest: 1) gene expression patterns defined by the spatial locations of cells expressing a gene and 2) relationships between the expression levels of multiple genes. PCX provides users with two corresponding classes of data views: 1) Physical Views based on the spatial relationships of cells in the embryo and 2) Abstract Views that discard spatial information and plot expression levels of multiple genes with respect to each other. Cell Selectors highlight data associated with subsets of embryo cells within a View. Using linking, these selected cells can be viewed in multiple representations. We describe PCX as a 3D gene expression visualization tool and provide examples of how it has been used by BDTNP biologists to generate new hypotheses.

An editorail on the 15th Anniversary of the IEEE Transactions on Visualization and Computer Graphics.

Direct volume rendering and isosurfacing are ubiquitous rendering techniques in scientific visualization, commonly employed in imaging 3D data from simulation and scan sources. Conventionally, these methods have been treated as separate modalities, necessitating different sampling strategies and rendering algorithms. In reality, an isosurface is a special case of a transfer function, namely a Dirac impulse at a given isovalue. However, artifact-free rendering of discrete isosurfaces in a volume rendering framework is an elusive goal, requiring either infinite sampling or smoothing of the transfer function. While preintegration approaches solve the most obvious deficiencies in handling sharp transfer functions, artifacts can still result, limiting classification. In this paper, we introduce a method for rendering such features by explicitly solving for isovalues within the volume rendering integral. In addition, we present a sampling strategy inspired by ray differentials that automatically matches the frequency of the image plane, resulting in fewer artifacts near the eye and better overall performance. These techniques exhibit clear advantages over standard uniform ray casting with and without preintegration, and allow for high-quality interactive volume rendering with sharp C0 transfer functions.

Laser wakefield particle accelerators have shown the potential to generate electric fields thousands of times higher than those of conventional accelerators. The resulting extremely short particle acceleration distance could yield a potential new compact source of energetic electrons and radiation, with wide applications from medicine to physics. Physicists investigate laser-plasma internal dynamics by running particle-in-cell simulations; however, this generates a large dataset that requires time-consuming, manual inspection by experts in order to detect key features such as beam formation. This paper describes a framework to automate the data analysis and classification of simulation data. First, we propose a new method to identify locations with high density of particles in the space-time domain, based on maximum extremum point detection on the particle distribution. We analyze high density electron regions using a lifetime diagram by organizing and pruning the maximum extrema as nodes in a minimum spanning tree. Second, we partition the multivariate data using fuzzy clustering to detect time steps in a experiment that may contain a high quality electron beam. Finally, we combine results from fuzzy clustering and bunch lifetime analysis to estimate spatially confined beams. We demonstrate our algorithms successfully on four different simulation datasets.

We present a novel user interface in the form of a complementary virtual environment for managing personal document archives, i.e., for document filing and retrieval. Our implementation of a spatial medium for document interaction, exploratory search and active navigation plays to the strengths of human visual information processing and further stimulates it.

One of the central challenges in modern science is the need to quickly derive knowledge and understanding from large, complex collections of data. We present a new approach that deals with this challenge by combining and extending techniques from high performance visual data analysis and scientific data management. This approach is demonstrated within the context of gaining insight from complex, time-varying datasets produced by a laser wakefield accelerator simulation. Our approach leverages histogram-based parallel coordinates for both visual information display as well as a vehicle for guiding a data mining operation. Data extraction and subsetting are implemented with state-of-the-art index/query technology. This approach, while applied here to accelerator science, is generally applicable to a broad set of science applications, and is implemented in a production-quality visual data analysis infrastructure. We conduct a detailed performance analysis and demonstrate good scalability on a distributed memory Cray XT4 system.

Abstract We present an acoustic rendering approach visualizing the listener‐specific contribution of frequency‐dependent pressure fields on a scene geometry with acoustic reflection and scattering properties. Our method facilitates the evaluation of simulated acoustics showing the effect of simulation parameters like absorption and scattering. The image‐based spatial localization of acoustic properties is complementary to the auditive evaluation by means of auralization. Our core contribution is a pressure‐based acoustic rendering equation and a corresponding raytracing method applying techniques from photorealistic rendering to the field of simulated room acoustics. Applications are directed at the visualization of interference patterns and analyzing the impact of acoustic reflection parameters.

Interaction between particles in so-called granular media, such as soil and sand, plays an important role in the context of geomechanical phenomena and numerous industrial applications. A two scale homogenization approach based on a micro and a macro scale level is briefly introduced in this paper. Computation of granular material in such a way gives a deeper insight into the context of discontinuous materials and at the same time reduces the computational costs. However, the description and the understanding of the phenomena in granular materials are not yet satisfactory. A sophisticated problem-specific visualization technique would significantly help to illustrate failure phenomena on the microscopic level. As main contribution, we present a novel 2D approach for the visualization of simulation data, based on the above outlined homogenization technique. Our visualization tool supports visualization on micro scale level as well as on macro scale level. The tool shows both aspects closely arranged in form of multiple coordinated views to give users the possibility to analyze the particle behavior effectively. A novel type of interactive rose diagrams was developed to represent the dynamic contact networks on the micro scale level in a condensed and efficient way.

We present a novel GPU-based algorithm for high-quality rendering of bivariate spline surfaces. An essential difference to the known methods for rendering graph surfaces is that we use quartic smooth splines on triangulations rather than triangular meshes. Our rendering approach is direct in the sense that since we do not use an intermediate tessellation but rather compute ray-surface intersections (by solving quartic equations numerically) as well as surface normals (by using Bernstein-Bézier techniques) for Phong illumination on the GPU. Inaccurate shading and artifacts appearing for triangular tesselated surfaces are completely avoided. Level of detail is automatic since all computations are done on a per fragment basis. We compare three different (quasi-) interpolating schemes for uniformly sampled gridded data, which differ in the smoothness and the approximation properties of the splines. The results show that our hardware based renderer leads to visualizations (including texturing, multiple light sources, environment mapping, etc.) of highest quality.

Flow vector fields contain a wealth of information that needs to be visualized. As an extension of the well-known streamline technique, we have developed a context-based method for visualizing steady flow vector fields in two and three dimensions. We call our method "Priority Streamlines". In our approach, the density of the streamlines is controlled by a scalar function that can be user-defined, or be given by additional information (e.g., temperature, pressure, vorticity, velocity) considering the underlying flow vector field. In regions, which are interesting the streamlines are drawn with increased density, while less interesting regions are drawn sparsely. Since streamlines in the most important regions are drawn first, we can use thresholding to obtain a streamline representation highlighting essential features. Color-mapping and transparency can be used for visualizing other information hidden in the flow vector field.

Interactive virtual reality applications commonly require two key technologies: multiple degree-of-freedom input devices, and 2D or 3D displays. The industry has developed a vast variety of devices for a growing consumer market. Consumer magazines regularly publish test reports for new devices. These reports are often focused on the gaming community, which is typically the driving force behind new product development. Although many lessons can be learned from the gaming industry, the scientific community is generally focused on other criteria, such as precision, degrees of freedom, and user tracking. It is expected that some of these criteria, which are currently in the state of research, will eventually be incorporated into products for a mass market, just like consumer graphics cards and certain input devices did in the past.

The recently introduced notion of Finite-Time Lyapunov Exponent to characterize Coherent Lagrangian Structures provides a powerful framework for the visualization and analysis of complex technical flows. Its definition is simple and intuitive, and it has a deep theoretical foundation. While the application of this approach seems straightforward in theory, the associated computational cost is essentially prohibitive. Due to the Lagrangian nature of this technique, a huge number of particle paths must be computed to fill the space-time flow domain. In this paper, we propose a novel scheme for the adaptive computation of FTLE fields in two and three dimensions that significantly reduces the number of required particle paths. Furthermore, for three-dimensional flows, we show on several examples that meaningful results can be obtained by restricting the analysis to a well-chosen plane intersecting the flow domain. Finally, we examine some of the visualization aspects of FTLE-based methods and introduce several new variations that help in the analysis of specific aspects of a flow.

Acoustic quality in room acoustics is measured by well defined quantities, like definition, which can be derived from simulated impulse response filters or measured values. These take into account the intensity and phase shift of multiple reflections due to a wave front emanating from a sound source. Definition (D50) and clarity (C50) for example correspond to the fraction of the energy received in total to the energy received in the first 50 ms at a certain listener position. Unfortunately, the impulse response measured at a single point does not provide any information about the direction of reflections, and about the reflection surfaces which contribute to this measure. For the visualization of room acoustics, however, this information is very useful since it allows to discover regions with high contribution and provides insight into the influence of all reflecting surfaces to the quality measure. We use the phonon tracing method to calculate the contribution of the reflection surfaces to the impulse response for different listener positions. This data is used to compute importance values for the geometry taking a certain acoustic metric into account. To get a visual insight into the directional aspect, we map the importance to the reflecting surfaces of the geometry. This visualization indicates which parts of the surfaces need to be changed to enhance the chosen acoustic quality measure. We apply our method to the acoustic improvement of a lecture hall by means of enhancing the overall speech comprehensibility (clarity) and evaluate the results using glyphs to visualize the clarity (C50) values at listener positions throughout the room.

We present a novel approach for analyzing two-dimensional (2D) flow field data based on the idea of invariant moments. Moment invariants have traditionally been used in computer vision applications, and we have adapted them for the purpose of interactive exploration of flow field data. The new class of moment invariants we have developed allows us to extract and visualize 2D flow patterns, invariant under translation, scaling, and rotation. With our approach one can study arbitrary flow patterns by searching a given 2D flow data set for any type of pattern as specified by a user. Further, our approach supports the computation of moments at multiple scales, facilitating fast pattern extraction and recognition. This can be done for critical point classification, but also for patterns with greater complexity. This multi-scale moment representation is also valuable for the comparative visualization of flow field data. The specific novel contributions of the work presented are the mathematical derivation of the new class of moment invariants, their analysis regarding critical point features, the efficient computation of a novel feature space representation, and based upon this the development of a fast pattern recognition algorithm for complex flow structures.

With powerful graphics hardware becoming affordable for everyone, there is an increasing tendency towards a new generation of user interfaces, with the focus shifting from traditional two-dimensional desktops to three-dimensional virtual environments. Therefore, there is a growing need for applicable immersive interaction metaphors to manipulate these environments. In our paper we propose a gesture recognition engine using an inexpensive data glove with integrated 6 DOF tracking. Despite of noisy input data from the glove, we are able to achieve reliable and flexible gesture recognition. New gestures can be trained easily and existing gestures can be individually adapted for different users

In this work we present several visualization approaches for analyzing acoustic behavior inside a room. Our methods are based on the results of the phonon tracing algorithm. For a simulated phonon map we examine the influence of the room surfaces on the wave fronts during their propagation from the sound source. Our visualization is based on individual phonon and surface representations as well as scattered data interpolation. Additionally, an observation of acoustic behavior at different positions inside the room using colored and deformed spheres is possible.

To allow a more rigorous understanding of animal gene regulatory networks, the Berkeley Drosophila Transcription Network Project (BDTNP) has developed a suite of methods that support quantitative, computational analysis of three-dimensional (3D) gene expression patterns with cellular resolution in early Drosophila embryos. Here we report the first components of a visualization tool, PointCloudXplore, that allows the relationships between different gene’s expression to be analyzed using the BDTNP’s datasets. PointCloudXplore uses the established visualization techniques of multiple views, brushing, and linking to support the analysis of high-dimensional datasets that describe many genes’ expression. Each of the views in PointCloud- Xplore shows a different gene expression data property. Brushing is used to select and emphasize data associated with defined subsets of embryo cells within a view. Linking is used to show in additional views the expression data for a group of cells that have first been highlighted as a brush in a single view, allowing further data subset properties to be determined. In PointCloudXplore, physical views of the data are linked to parallel coordinates. Physical views show the spatial relationships between different genes’ expression patterns within the embryo. Parallel coordinates, on the other hand, show only some features of each gene’s expression, but allow simultaneous analysis of data for many more genes than would be possible in a physical view. We have developed several extensions to standard parallel coordinates to facilitate brushing the visualization of 3D gene expression data.

We present a comparative visualization of the acoustic simulation results obtained by two different approaches that were combined into a single simulation algorithm. The first method solves the wave equation on a volume grid based on finite elements. The second method, phonon tracing, is a geometric approach that we have previously developed for interactive simulation, visualization and modeling of room acoustics. Geometric approaches of this kind are more efficient than FEM in the high and medium frequency range. For low frequencies they fail to represent diffraction, which on the other hand can be simulated properly by means of FEM. When combining both methods we need to calibrate them properly and estimate in which frequency range they provide comparable results. For this purpose we use an acoustic metric called gain and display the resulting error. Furthermore we visualize interference patterns, since these depend not only on diffraction, but also exhibit phase-dependent amplification and neutralization effects.

We present a new algorithm extracting and fairing surfaces from segmented volumes composed of multiple materials. In a first pass, the material boundaries in the volume are smoothed considering signed distance functions for the individual materials. Second, we apply a marching-cubes-like contouring method providing initial meshes defining material boundaries. Non-manifold features emerge along lines where more than two materials encounter. Finally, the mesh geometry is relaxed in a constrained fairing process. We use our algorithm to construct a heart model from segmented time-varying magnetic resonance images. Information concerning the heart ontology is used to merge certain structures to functional units.

We present a new particle tracing approach for the simulation of mid- and high-frequency sound. Inspired by the photorealism obtained by methods like photon mapping, we develop a similar method for the physical simulation of sound within rooms. For given source and listener positions, our method computes a finite-response filter accounting for the different reflections at various surfaces with frequency-dependent absorption coefficients. Convoluting this filter with an anechoic input signal reproduces a realistic aural impression of the simulated room. We do not consider diffraction effects due to low frequencies, since these can be better computed by finite elements. Our method allows the visualization of a wave front propagation using color-coded blobs traversing the paths of individual phonons.

We present a visual analysis and exploration of fluid flow through a cooling jacket. Engineers invest a large amount of time and serious effort to optimize the flow through this engine component because of its important role in transferring heat away from the engine block. In this study we examine the design goals that engineers apply in order to construct an ideal-as-possible cooling jacket geometry and use a broad range of visualization tools in order to analyze, explore, and present the results. We systematically employ direct, geometric, and texture-based flow visualization techniques as well as automatic feature extraction and interactive feature-based methodology. And we discuss the relative advantages and disadvantages of these approaches as well as the challenges, both technical and perceptual with this application. The result is a feature-rich state-of-the-art flow visualization analysis applied to an important and complex data set from real-world computational fluid dynamics simulations.

This poster abstract presents a scalable information visualization system for mobile devices and desktop systems. It is designed to support the operation and the workflow of wastewater systems. The regarded information data includes general information about buildings and units, process data, occupational safety regulations, work directions and first aid instructions in case of an accident. Technically, the presented framework combines visualization with agent technology in order to automatically scale various visualization types to fit on different platforms like PDAs (Personal Digital Assistants) or Tablet PCs. The implementation is based on but not limited to SQL, JSP, HTML and VRML.

The automotive industry demands visual support for the verification of the quality of their products from the design phase to the manufacturing phase. This implies the need of tools for measurement planning, programming measuring devices, managing measurement data, and the visual exploration of the measurement results. To improve the quality control throughout the whole process chain an integration of such tools in a platform independent framework is crucial. We present eMMA (enhanced Measure Management Application), a client/server system integrating measurement planning, data management, and straightforward as well as sophisticated visual exploration tools in a single framework.

This paper describes a Data Management System for Multimedial Information Visualization called DaMI. It is possible to create 2D or 3D model based on data out of standard databases and additional metainformation. DaMI is a generic system guaranteeing an optimal reusability and compatibility.

The physical interpretation of mathematical features of tensor fields is highly application-specific. Existing visualization methods for tensor fields only cover a fraction of the broad application areas. We present a visualization method tailored specifically to the class of tensor field exhibiting properties similar to stress and strain tensors, which are commonly encountered in geomechanics. Our technique is a global method that represents the physical meaning of these tensor fields with their central features: regions of compression or expansion. The method is based on two steps: first, we define a positive definite metric, with the same topological structure as the tensor field; second, we visualize the resulting metric. The eigenvector fields are represented using a texture-based approach resembling line integral convolution (LIC) methods. The eigenvalues of the metric are encoded in free parameters of the texture definition. Our method supports an intuitive distinction between positive and negative eigenvalues. We have applied our method to synthetic and some standard data sets, and "real" data from earth science and mechanical engineering application.

We present a method to represent unstructured scalar fields at multiple levels of detail. Using a parallelizable classification algorithm to build a cluster hierarchy, we generate a multiresolution representation of a given volumetric scalar data set. The method uses principal component analysis (PCA) for cluster generation and a fitting technique based on radial basis functions (RBFs). Once the cluster hierarchy has been generated, we utilize a variety of techniques for extracting different levels of detail. The main strength of this work is its generality. Regardless of grid type, this method can be applied to any discrete scalar field representation, even one given as a "point cloud".

Isosurfaces are commonly used to visualize scalar fields. Critical isovalues indicate isosurface topology changes: the creation of new surface components, merging of surface components or the formation of holes in a surface component. Therefore, they highlight interesting isosurface behavior and are helpful in exploration of large trivariate data sets. We present a method that detects critical isovalues in a scalar field defined by piecewise trilinear interpolation over a rectilinear grid and describe how to use them when examining volume data. We further review varieties of the marching cubes (MC) algorithm, with the intention of preserving topology of the trilinear interpolant when extracting an isosurface. We combine and extend two approaches in such a way that it is possible to extract meaningful isosurfaces even when a critical value is chosen as the isovalue.

This paper presents a new algorithm for the calculation of stream surfaces for tetrahedral grids. It propagates the surface through the tetrahedra, one at a time, calculating the intersections with the tetrahedral faces. The method allows us to incorporate topological information from the cells, e.g. critical points. The calculations are based on barycentric coordinates, since this simplifies the theory and the algorithm. The stream surfaces are ruled surfaces inside each cell, and their construction starts with line segments on the faces. Our method supports the analysis of velocity fields resulting from computational fluid dynamics (CFD) simulations.

Vector fields can present complex structural behavior, especially in turbulent computational fluid dynamics. The topological analysis of these data sets reduces the information, but one is usually still left with too many details for interpretation. In this paper, we present a simplification approach that removes pairs of critical points from the data set, based on relevance measures. In contrast to earlier methods, no grid changes are necessary, since the whole method uses small local changes of the vector values defining the vector field. An interpretation in terms of bifurcations underlines the continuous, natural flavor of the algorithm.

Topological methods produce simple and meaningful depictions 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 tensor topology are discussed. Topological changes - known as bifurcations - are precisely detected and identified by our method which permits an accurate tracking of degenerate points and related structures.

One of the main research topics in scientific visualization is to "visualize the appropriate features" of a certain structure or data set. Geodesics are very important in geometry and physics, but there is one major problem which prevents scientists from using them as a visualization tool: the differential equations for geodesics are very complicated and in most cases numerical algorithms must be used. There is always a certain approximation error involved. How can you be sure to visualize the features and not only the approximation quality. The paper presents an algorithm to overcome this problem. It consists of two parts. In the first, a geometric method for the construction of geodesics of arbitrary surfaces is introduced. This method is based on the fundamental property that geodesics are a generalization of straight lines on plains. In the second part these geodesics are used to generate local nets on the surfaces.

Topology analysis of plane, turbulent vector fields results in visual clutter caused by critical points indicating vortices of finer and finer scales. A simplification can be achieved by merging critical points within a prescribed radius into higher order critical points. After building clusters containing the singularities to merge, the method generates a piecewise linear representation of the vector field in each cluster containing only one (higher order) singularity. Any visualization method can be applied to the result after this process. Using different maximal distances for the critical points to be merged results in a hierarchy of simplified vector fields that can be used for analysis on different scales.

We present a method for visualizing three dimensional vector fields which are defined on a two dimensional manifold only. These vector fields do exist in real application, as we show by an example of an optical measuring instrument which can gauge the displacement at the surface of a mechanical part. The general idea is to compute LIC textures in the manifold's tangent space and to deform the manifold according to the normal information. The resulting LIC texture is mapped onto the deformed manifold and is rendered as a three dimensional scene. Due to the light's reflection on the deformed manifold, one can interactively explore the result of the deformation.

An application of C/sup 1/ scalar interpolation for 2D vector field topology visualization is presented. Powell-Sabin and Nielson interpolants are considered which both make use of Nielson's Minimum Norm Network for the precomputation of the derivatives in our implementation. A comparison of their results to the commonly used linear interpolant underlines their significant improvement of singularity location and topological skeleton depiction. Evaluation is based upon the processing of polynomial vector fields with known topology containing higher order singularities.

In CAD/CAM technology, the design of free form surfaces is the beginning of a chain of operations, which ends with the numerically controlled (NC) production of the designed object. An important part of this chain is shape analysis. We present a stability concept for surfaces based on infinitesimal bendings. The infinitesimal rigidity is enforced by certain boundary conditions.

Glial cells express a large variety of bio-electric and bio-chemical phenomena. A quantitative analysis shows that the brain consists of about 10 to 50 times more glial cells than neurons. Similar to neurons, glial cells implement voltage-dependent and ligand-gated membrane channels. Neurotransmitter receptors associated with ion-selective membrane channels have been described in several types of macroglial cells. Leech giant glial cells provide a good example for studying structural and physiological properties of this cell type. Confocal laser-scanning microscopy generates images from cutting (i.e. focus) planes of the object, in a way that, by varying the focus plane, the object can be resolved and scanned serially at several levels. Artifacts, such as transparent, low contrast, and blurred or fuzzy structures from neighboring slices must be filtered in order to reveal the capillary structure of the cell. With the microscope, the object cannot be rotated by ninety degrees, perpendicular to the viewing direction. Once scanned, the viewing direction cannot be altered any more. Computer graphics allows projections from any perspective angle, so that the cell can be studied in full detail. A visualization system should provide a flexible environment for interactively exploring the cell. Therefore, we have extended our InVIS (Interactive Visualization) system, which has been originally designed for medical applications (CT and MRI), to confocal microscopy. We describe the structure of our system and the addition of new features.

The article deals with dependencies of a piecewise linear vector field and the triangulation of the domain. It shows that the topology of the field may depend on the triangulation and gives a suitable choice to obtain a simple topology by changes of the triangulation. The main point is the appearance of pairs of critical points with positive and negative Poincare index. Many of these occurrences can be avoided by changing the grid. This is proved in the article. An algorithm is presented which uses these results to extract simpler topological skeletons than usual methods. Finally there are several examples comparing these algorithms to demonstrate the effects of the data dependent triangulation.

Presents an algorithm for the visualization of vector field topology based on Clifford algebra. It allows the detection of higher-order singularities. This is accomplished by first analysing the possible critical points and then choosing a suitable polynomial approximation, because conventional methods based on piecewise linear or bilinear approximation do not allow higher-order critical points and destroy the topology in such cases. The algorithm is still very fast, because of using linear approximation outside the areas with several critical points.

We introduce the concept of streamballs for flow visualization. Streamballs are based upon implicit surface generation techniques adopted from the well-known metaballs. Their property to split or merge automatically in areas of significant divergence or convergence makes them an ideal tool for the visualization of arbitrary complex fields. Using convolution surfaces generated by continuous skeletons for streamball construction offers the possibility to visualize even tensor fields.>

Abstract The generation of technical smooth surfaces from a mesh of three‐dimensional data points is an important problem in geometric modelling. In this publication we give a survey of some new techniques based on a calculus of variation approach. Apart from the pure construction of these surfaces, the analysis of their quality is equally important in the design and manufacturing process. Generalized focal surfaces are presented here as a new surface interrogation tool.

In view of the fundamental role that functional composition plays in mathematics, it is not surprising that a variety of problems in geometric modeling can be viewed as instances of the following composition problem: given representations for two functions F and G , compute a representation of the function H = F o G . We examine this problem in detail for the case when F and G are given in either Be´zier or B-spline form. Blossoming techniques are used to gain theoretical insight into the structure of the solution which is then used to develop efficient, tightly codable algorithms. From a practical point of view, if the composition algorithms are implemented as library routines, a number of geometric-modeling problems can be solved with a small amount of additional software.

The generation of smooth surfaces from a mesh of three-dimensional data points is an important problem in geometric modeling. Apart from the pure construction of these curves and surfaces, the analysis of their quality is equally important in the design and manufacturing process. Generalized focal surfaces are presented as a new surface interrogation tool.>

Abstract We describe techniques for the visualization of a scalar‐valued function defined over a surface. The main interest focuses on a 4D graph of such a function and projections of this graph into 3‐space. The paper also contains methods for testing the smoothness of interpolants over surfaces and a short tutorial on fundamental ideas of multidimensional descriptive geometry which can be helpful in several areas of scientific visualization.

The authors discuss various visualization techniques that have the goal of identifying unwanted curvature regions interactively on screen. The authors give a critical survey of surface interrogation methods. Several isoline and contouring techniques are presented, and the reflection line method, which simulates the so-called light cage by computer graphics, is presented. The isophote method analyzes surfaces by determining lines of equal light intensity. Silhouettes are special isophotes. A different approach to these problems is the mapping-technique. The mapping methods recognize unwanted curvature regions by detecting singularities of a special mapping of the curve or surface investigated. Curvature plots are a practical means of analyzing free-form surfaces. All these methods are effective, but generally need a lot of computational effort. The free-form surface visualization by ray tracing is discussed.>