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We present a visual approach for the exploration of stress tensor fields. Therefore, we introduce the idea of multiple linked views to tensor visualization. In contrast to common tensor visualization methods that only provide a single view to the tensor field, we pursue the idea of providing various perspectives onto the data in attribute and object space. Especially in the context of stress tensors, advanced tensor visualization methods have a young tradition. Thus, we propose a combination of visualization techniques domain experts are used to with statistical views of tensor attributes. The application of this concept to tensor fields was achieved by extending the notion of shape space. It provides an intuitive way of finding tensor invariants that represent relevant physical properties. Using brushing techniques, the user can select features in attribute space, which are mapped to displayable entities in a three-dimensional hybrid visualization in object space. Volume rendering serves as context, while glyphs encode the whole tensor information in focus regions. Tensorlines can be included to emphasize directionally coherent features in the tensor field. We show that the benefit of such a multi-perspective approach is manifold. Foremost, it provides easy access to the complexity of tensor data. Moreover, including wellknown analysis tools, such as Mohr diagrams, users can familiarize themselves gradually with novel visualization methods. Finally, by employing a focus-driven hybrid rendering, we significantly reduce clutter, which was a major problem of other three-dimensional tensor visualization methods.
The mitotic spindle ensures the faithful segregation of chromosomes. Here we combine the first large-scale serial electron tomography of whole mitotic spindles in early C. elegans embryos with live-cell imaging to reconstruct all microtubules in 3D and identify their plus- and minus-ends. We classify them as kinetochore (KMTs), spindle (SMTs) or astral microtubules (AMTs) according to their positions, and quantify distinct properties of each class. While our light microscopy and mutant studies show that microtubules are nucleated from the centrosomes, we find only a few KMTs directly connected to the centrosomes. Indeed, by quantitatively analysing several models of microtubule growth, we conclude that minus-ends of KMTs have selectively detached and depolymerized from the centrosome. In toto, our results show that the connection between centrosomes and chromosomes is mediated by an anchoring into the entire spindle network and that any direct connections through KMTs are few and likely very transient.
This work is concerned with adaptive screen-space sampling for volume ray-casting. The goal is to reduce the
number of rays being cast into the scene and, thus, the overall number of sampling points. We guarantee reliable
images through explicit error control using an error estimator that is founded in the field of finite element methods
(FEM). FEM theory further provides a well-founded theory to prove the efficiency of the presented algorithm via
convergence analysis. We, therefore, compare the convergence behavior of our method against uniform subdivisions
and a refinement scheme that was presented in the context of CPU volume ray-casting. Minimizing
the number of sampling points is of interest for rendering large datasets where each evaluation might need an expensive
decompression. Furthermore, with increasing screen resolutions high-resolution images are created more
efficiently with our method.
Three-Dimensional Second-Order Tensor Fields: Exploratory Visualization and Anisotropic Sampling
(2013)
Tensors provide a powerful mathematical language to describe physical phenomena. Consequently, they have a long tradition in physics and appear in various application areas, either as intermediate product or as output of simulations or measurements. The potential of tensors to describe complex anisotropic behavior, however, concurrently complicates their interpretation. The central research question of this thesis is how three-dimensional tensor fields of second order are visualized effectively so that, as a long term goal, their interpretation becomes easier. The focus of this thesis lies on the class of indefinite tensors. The methods that are proposed in this thesis fall into two main categories: (1.) the interactive exploration of the three-dimensional tensor data, and (2.) the geometric reduction of the data to two-dimensional planes or triangulated surfaces. In both cases, possible visualization approaches are presented. For interactive exploration of the data, we propose to combine diagram views with three-dimensional hybrid visualizations. We show that this facilitates familiarizing with the data and leads to exciting analytic queries. If a geometric data reduction is possible, we focus on glyph- and texture-based methods. In this context, the thesis is concerned with methods to improve their quality. Therefore, we propose two algorithms for the efficient creation of anisotropic sample distributions. Moreover, we present a novel visualization method that works on planar slices as well as on triangulated surfaces. The basic idea of this method is to use anisotropic sample distributions for the efficient computation of anisotropic Voronoi cells, which then are used as base elements for texture mapping. Hence, the usage of textures to encode the tensor’s various degrees of freedom becomes possible. We evaluate our methods for the interactive exploration on stress tensor fields from structure simulations. To show the ffectiveness of novel visualization methods, various datasets are presented.