On the Role of Topology in Focus+Context Visualization

Viola, Ivan; Gröller, M. Eduard

doi:10.1007/978-3-540-70823-0_12

Cited by 4 publications

(2 citation statements)

References 10 publications

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“…In this section we describe the families of models used to implement the interaction procedures, visual elements, slicing interface, and the automatic algorithm to compute the longitudinal axis and to extract representative cross‐sectional images for generating the flip‐book. Our fundamental techniques are based on a wide variety of prior art, including the use of exploded view in surface, flow, and volume visualization [WT10, KLMA10, VG07,ZWR14], algorithms for 3D triangle mesh slicing [MVS∗17, Kos03], and other variants on computer graphics and visual interfaces for mathematical visualization including, e.g., the work of [LZ21] and [Sch98].…”

Section: Implementation Methodsmentioning

confidence: 99%

A Flip‐book of Knot Diagrams for Visualizing Surfaces in 4‐Space

Liu

Zhang

2022

Computer Graphics Forum

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Just as 2D shadows of 3D curves lose structure where lines cross, 3D graphics projections of smooth 4D topological surfaces are interrupted where one surface intersects itself. They twist, turn, and fold back on themselves, leaving important but hidden features behind the surface sheets. In this paper, we propose a smart slicing tool that can read the 4D surface in its entropy map and suggest the optimal way to generate cross‐sectional images — or “slices” — of the surface to visualize its underlying 4D structure. Our visualization thinks of a 4D‐embedded surface as a collection of 3D curves stacked in time, very much like a flip‐book animation, where successive terms in the sequence differ at most by a critical change. This novel method can generate topologically meaningful visualization to depict complex and unfamiliar 4D surfaces, with the minimum number of cross‐sectional diagrams. Our approach has been successfully used to create flip‐books of diagrams to visualize a range of known 4D surfaces. In this preliminary study, our results show that the new visualization and slicing tool can help the viewers to understand and describe the complex spatial relationships and overall structures of 4D surfaces.

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Section: Implementation Methodsmentioning

confidence: 99%

A Flip‐book of Knot Diagrams for Visualizing Surfaces in 4‐Space

Liu

Zhang

2022

Computer Graphics Forum

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“…As DoF is so widely used in photography, it has also received attention within scientific visualization for Focus+Context (F&C) [8,23,22] purposes. F&C is a general concept for directing the viewers attention onto certain parts of picture, and in scientific visualization its usage is motivated by exploration of large complex structures.…”

Section: Introductionmentioning

confidence: 99%

Coverage-based opacity estimation for interactive Depth of Field in molecular visualization

Kottravel

Falk

Sundén

et al. 2015

2015 IEEE Pacific Visualization Symposium (PacificVis)

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Figure 1: Thermus thermophilus 70S ribosome (PDB ID: 2WDK) rendered with no Depth of Field effect (left) and using our approach focusing on near structures (center) and far away structures (right). ABSTRACTIn this paper, we introduce coverage-based opacity estimation to achieve Depth of Field (DoF) effects when visualizing molecular dynamics (MD) data. The proposed algorithm is a novel object-based approach which eliminates many of the shortcomings of state-of-the-art image-based DoF algorithms. Based on observations derived from a physically-correct reference renderer, coverage-based opacity estimation exploits semi-transparency to simulate the blur inherent to DoF effects. It achieves high quality DoF effects, by augmenting each atom with a semi-transparent shell, which has a radius proportional to the distance from the focal plane of the camera. Thus, each shell represents an additional coverage area whose opacity varies radially, based on our observations derived from the results of multi-sampling DoF algorithms. By using the proposed technique, it becomes possible to generate high quality visual results, comparable to those achieved through ground-truth multi-sampling algorithms. At the same time, we obtain a significant speedup which is essential for visualizing MD data as it enables interactive rendering. In this paper, we derive the underlying theory, introduce coverage-based opacity estimation and demonstrate how it can be applied to real world MD data in order to achieve DoF effects. We further analyze the achieved results with respect to performance as well as quality and show that they are comparable to images generated with modern distributed ray tracing engines.

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Visualizing and Slicing Topological Surfaces in Four Dimensions

Huan¹,

Zhang²

2021

jist

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Smooth topological surfaces embedded in 4D create complex internal structures in their projected 3D figures. Often these 3D figures twist, turn, and fold back on themselves, leaving important properties behind the surface sheets. Triangle meshes are not well suited for illustrating such internal structures and their topological features. In this paper, we propose a new approach to visualize these internal structures by slicing the 4D surfaces in our dimensions and revealing the underlying 4D structures using their cross-sectional diagrams. We think of a 4D-embedded surface as a collection of 3D curves stacked and evolved in time, very much like a 3D movie in a time-elapse form; and our new approach is to translate a surface in 4-space into such a movie — a sequence of time-lapse frames where successive terms in the sequence differ at most by a critical change. The visualization interface presented in this paper allows us to interactively define the longitudinal axis, and the automatic algorithms can partition the 4D surface into parallel slices and expose its internal structure by generating a time-lapse movie consisting of topologically meaningful cross-sectional diagrams from the representative slices. We have extracted movies from a range of known 4D mathematical surfaces with our approach. The results of the usability study show that the proposed slicing interface allows a mathematically true user experience with surfaces in four dimensions.

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On the Role of Topology in Focus+Context Visualization

Cited by 4 publications

References 10 publications

A Flip‐book of Knot Diagrams for Visualizing Surfaces in 4‐Space

A Flip‐book of Knot Diagrams for Visualizing Surfaces in 4‐Space

Coverage-based opacity estimation for interactive Depth of Field in molecular visualization

Visualizing and Slicing Topological Surfaces in Four Dimensions

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