14 Search Results for "Hamann, Bernd"

Document
DOI: 10.4230/LIPIcs.SoCG.2026.57
Singular Arrange and Traverse Algorithm for Computing Reeb Spaces of Bivariate PL Maps

Authors: Petar Hristov, Ingrid Hotz, and Talha Bin Masood

Published in: LIPIcs, Volume 367, 42nd International Symposium on Computational Geometry (SoCG 2026)

Abstract
We present an exact and efficient algorithm for computing the Reeb space of a bivariate PL map. The Reeb space is a topological structure that generalizes the Reeb graph to the setting of multiple scalar-valued functions defined over a shared domain, a situation that frequently arises in practical applications. While the Reeb graph has become a standard tool in computer graphics, shape analysis, and scientific visualization, the Reeb space is still in the early stages of adoption. Although several algorithms for computing the Reeb space have been proposed, none offer an implementation that is both exact and efficient, which has substantially limited its practical use. To address this gap, we introduce singular arrange and traverse, a new algorithm built upon the arrange and traverse framework [Hristov et al., 2025]. Our method exploits the fact that, in the bivariate case, only singular edges contribute to the structure of Reeb space, allowing us to ignore many regular edges [Tierny and Carr, 2017]. This observation results in substantial efficiency gains on datasets where most edges are regular, which is common in many numerical simulations of physical systems. We provide an implementation of our method and benchmark it against the original arrange and traverse algorithm, showing performance gains of up to four orders of magnitude on real-world datasets.
Cite as

Petar Hristov, Ingrid Hotz, and Talha Bin Masood. Singular Arrange and Traverse Algorithm for Computing Reeb Spaces of Bivariate PL Maps. In 42nd International Symposium on Computational Geometry (SoCG 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 367, pp. 57:1-57:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{hristov_et_al:LIPIcs.SoCG.2026.57,
  author =	{Hristov, Petar and Hotz, Ingrid and Masood, Talha Bin},
  title =	{{Singular Arrange and Traverse Algorithm for Computing Reeb Spaces of Bivariate PL Maps}},
  booktitle =	{42nd International Symposium on Computational Geometry (SoCG 2026)},
  pages =	{57:1--57:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-418-5},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{367},
  editor =	{Ahn, Hee-Kap and Hoffmann, Michael and Nayyeri, Amir},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2026.57},
  URN =		{urn:nbn:de:0030-drops-258644},
  doi =		{10.4230/LIPIcs.SoCG.2026.57},
  annote =	{Keywords: Computational topology, Reeb graph, Reeb space, Multivariate data, Multifield, Geometric arrangement}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2026.72
Topological Simplification Guided by Forbidden Regions

Authors: Jakub Leśkiewicz, Bartosz Furmanek, Michał Lipiński, and Dmitriy Morozov

Published in: LIPIcs, Volume 367, 42nd International Symposium on Computational Geometry (SoCG 2026)

Abstract
Topological simplification is the process of reducing complexity of a function while maintaining its essential features. Its goal is to find a new filter function, which reorders cells of the input complex in a way which eliminates some persistent homological features, without affecting the rest. We present a new approach to simplification based on the concept of forbidden regions and combinatorial dynamics. It allows us to reorder and cancel critical values, whose cancellation is not possible using existing methods because they are not consecutive in the total order. Each such cancellation takes O(c⋅n) time in the worst case, where c is the number of birth-death pairs and n is the size of the input complex.
Cite as

Jakub Leśkiewicz, Bartosz Furmanek, Michał Lipiński, and Dmitriy Morozov. Topological Simplification Guided by Forbidden Regions. In 42nd International Symposium on Computational Geometry (SoCG 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 367, pp. 72:1-72:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{leskiewicz_et_al:LIPIcs.SoCG.2026.72,
  author =	{Le\'{s}kiewicz, Jakub and Furmanek, Bartosz and Lipi\'{n}ski, Micha{\l} and Morozov, Dmitriy},
  title =	{{Topological Simplification Guided by Forbidden Regions}},
  booktitle =	{42nd International Symposium on Computational Geometry (SoCG 2026)},
  pages =	{72:1--72:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-418-5},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{367},
  editor =	{Ahn, Hee-Kap and Hoffmann, Michael and Nayyeri, Amir},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2026.72},
  URN =		{urn:nbn:de:0030-drops-258797},
  doi =		{10.4230/LIPIcs.SoCG.2026.72},
  annote =	{Keywords: persistent homology, topological simplification, depth posets}
}
Document
DOI: 10.4230/LITES.7.1.1
Randomization as Mitigation of Directed Timing Inference Based Attacks on Time-Triggered Real-Time Systems with Task Replication

Authors: Kristin Krüger, Nils Vreman, Richard Pates, Martina Maggio, Marcus Völp, and Gerhard Fohler

Published in: LITES, Volume 7, Issue 1 (2021): Special Issue on Embedded System Security. Leibniz Transactions on Embedded Systems, Volume 7, Issue 1

Abstract
Time-triggered real-time systems achieve deterministic behavior using schedules that are constructed offline, based on scheduling constraints. Their deterministic behavior makes time-triggered systems suitable for usage in safety-critical environments, like avionics. However, this determinism also allows attackers to fine-tune attacks that can be carried out after studying the behavior of the system through side channels, targeting safety-critical victim tasks. Replication -- i.e., the execution of task variants across different cores -- is inherently able to tolerate both accidental and malicious faults (i.e. attacks) as long as these faults are independent of one another. Yet, targeted attacks on the timing behavior of tasks which utilize information gained about the system behavior violate the fault independence assumption fault tolerance is based on. This violation may give attackers the opportunity to compromise all replicas simultaneously, in particular if they can mount the attack from already compromised components. In this paper, we analyze vulnerabilities of time-triggered systems, focusing on safety-certified multicore real-time systems. We introduce two runtime mitigation strategies to withstand directed timing inference based attacks: (i) schedule randomization at slot level, and (ii) randomization within a set of offline constructed schedules. We evaluate these mitigation strategies with synthetic experiments and a real case study to show their effectiveness and practicality.
Cite as

Kristin Krüger, Nils Vreman, Richard Pates, Martina Maggio, Marcus Völp, and Gerhard Fohler. Randomization as Mitigation of Directed Timing Inference Based Attacks on Time-Triggered Real-Time Systems with Task Replication. In LITES, Volume 7, Issue 1 (2021): Special Issue on Embedded System Security. Leibniz Transactions on Embedded Systems, Volume 7, Issue 1, pp. 01:1-01:29, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@Article{kruger_et_al:LITES.7.1.1,
  author =	{Kr\"{u}ger, Kristin and Vreman, Nils and Pates, Richard and Maggio, Martina and V\"{o}lp, Marcus and Fohler, Gerhard},
  title =	{{Randomization as Mitigation of Directed Timing Inference Based Attacks on Time-Triggered Real-Time Systems with Task Replication}},
  journal =	{Leibniz Transactions on Embedded Systems},
  pages =	{01:1--01:29},
  ISSN =	{2199-2002},
  year =	{2021},
  volume =	{7},
  number =	{1},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LITES.7.1.1},
  URN =		{urn:nbn:de:0030-drops-192847},
  doi =		{10.4230/LITES.7.1.1},
  annote =	{Keywords: real-time systems, time-triggered systems, security}
}
Document
DOI: 10.4230/OASIcs.iPMVM.2020.6
Interactive Quality Inspection of Measured Deviations in Sheet Metal Assemblies

Authors: Felix Claus, Hans Hagen, Viktor Leonhardt, Heike Leitte, and Bernd Hamann

Published in: OASIcs, Volume 89, 2nd International Conference of the DFG International Research Training Group 2057 – Physical Modeling for Virtual Manufacturing (iPMVM 2020)

Abstract
We present an exploratory data analysis approach for finite element (FE) simulations to interactively inspect measured deviations in sheet metals arising in automotive applications. Exterior car body parts consist of large visible surfaces, and strict tolerances must be met by them to satisfy both aesthetic requirements and quality performance requirements. To fulfill quality requirements like gap and flushness, exterior vehicle components have adjustable mechanical boundaries. These boundaries are used to influence the shape and position of a sheet metal part relative to its chassis. We introduce a method that supports an inspection engineer with an interactive framework that makes possible a detailed analysis of measured sheet metal deviation fields generated from 3D scans. An engineer can interactively change boundary conditions and obtains the resulting deviation field in real-time. Thus, it is possible to determine viable and desirable adjustments efficiently, leading to time and cost savings in the assembly process.
Cite as

Felix Claus, Hans Hagen, Viktor Leonhardt, Heike Leitte, and Bernd Hamann. Interactive Quality Inspection of Measured Deviations in Sheet Metal Assemblies. In 2nd International Conference of the DFG International Research Training Group 2057 – Physical Modeling for Virtual Manufacturing (iPMVM 2020). Open Access Series in Informatics (OASIcs), Volume 89, pp. 6:1-6:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{claus_et_al:OASIcs.iPMVM.2020.6,
  author =	{Claus, Felix and Hagen, Hans and Leonhardt, Viktor and Leitte, Heike and Hamann, Bernd},
  title =	{{Interactive Quality Inspection of Measured Deviations in Sheet Metal Assemblies}},
  booktitle =	{2nd International Conference of the DFG International Research Training Group 2057 – Physical Modeling for Virtual Manufacturing (iPMVM 2020)},
  pages =	{6:1--6:18},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-95977-183-2},
  ISSN =	{2190-6807},
  year =	{2021},
  volume =	{89},
  editor =	{Garth, Christoph and Aurich, Jan C. and Linke, Barbara and M\"{u}ller, Ralf and Ravani, Bahram and Weber, Gunther H. and Kirsch, Benjamin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.iPMVM.2020.6},
  URN =		{urn:nbn:de:0030-drops-137554},
  doi =		{10.4230/OASIcs.iPMVM.2020.6},
  annote =	{Keywords: Data Analysis, Interactive Inspection, 3D-Metrology, Finite Element Simulation}
}
Document
DOI: 10.4230/OASIcs.iPMVM.2020.18
The Discrete Morse Complex of Images: Algorithms, Modeling and Applications

Authors: Ricardo Dutra da Silva, Helio Pedrini, and Bernd Hamann

Published in: OASIcs, Volume 89, 2nd International Conference of the DFG International Research Training Group 2057 – Physical Modeling for Virtual Manufacturing (iPMVM 2020)

Abstract
The Morse complex can be used for studying the topology of a function, e.g., an image or terrain height field when understood as bivariate functions. We present an algorithm for the computation of the discrete Morse complex of two-dimensional images using an edge-based data structure. By using this data structure, it is possible to perform local operations efficiently, which is important to construct the complex and make the structure useful for areas like visualization, persistent homology computation, or construction of a topological hierarchy. We present theoretical and applied results to demonstrate benefits and use of our method.
Cite as

Ricardo Dutra da Silva, Helio Pedrini, and Bernd Hamann. The Discrete Morse Complex of Images: Algorithms, Modeling and Applications. In 2nd International Conference of the DFG International Research Training Group 2057 – Physical Modeling for Virtual Manufacturing (iPMVM 2020). Open Access Series in Informatics (OASIcs), Volume 89, pp. 18:1-18:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{dasilva_et_al:OASIcs.iPMVM.2020.18,
  author =	{da Silva, Ricardo Dutra and Pedrini, Helio and Hamann, Bernd},
  title =	{{The Discrete Morse Complex of Images: Algorithms, Modeling and Applications}},
  booktitle =	{2nd International Conference of the DFG International Research Training Group 2057 – Physical Modeling for Virtual Manufacturing (iPMVM 2020)},
  pages =	{18:1--18:19},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-95977-183-2},
  ISSN =	{2190-6807},
  year =	{2021},
  volume =	{89},
  editor =	{Garth, Christoph and Aurich, Jan C. and Linke, Barbara and M\"{u}ller, Ralf and Ravani, Bahram and Weber, Gunther H. and Kirsch, Benjamin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.iPMVM.2020.18},
  URN =		{urn:nbn:de:0030-drops-137679},
  doi =		{10.4230/OASIcs.iPMVM.2020.18},
  annote =	{Keywords: Discrete Morse Complex, Image Topology, Cell Complexes}
}
Document
DOI: 10.4230/OASIcs.VLUDS.2011.1
Virtual Reality supported Visualization and Evaluation of Noise Levels in Manufacturing Environments

Authors: Xiang Yang, Bernd Hamann, and Jan C. Aurich

Published in: OASIcs, Volume 27, Visualization of Large and Unstructured Data Sets: Applications in Geospatial Planning, Modeling and Engineering - Proceedings of IRTG 1131 Workshop 2011

Abstract
Virtual Reality (VR) provides users advanced visualization and interaction technology for designing, analyzing and exploring complex data. To address the issue of noise in manufacturing environments, we developed a VR-supported method allowing users to explore noise behavior. This method consists of an implementation of acoustic simulation and visualization for both desktop and Cave Automatic Virtual Environment (CAVE) based VR systems. It enables user-oriented, interactive analysis of simulated data, where there capability to immerse oneself in the data is especially valuable. In a real-world factory, the acoustic measurements obtained essential input data for simulation settings and validation data for simulation results. Furthermore, some political and legal aspects are addressed to enhance the evaluation of results and the visualization. By using the implemented software tool, users are able to understand and investigate the noise issue in manufacturing straightforwardly.
Cite as

Xiang Yang, Bernd Hamann, and Jan C. Aurich. Virtual Reality supported Visualization and Evaluation of Noise Levels in Manufacturing Environments. In Visualization of Large and Unstructured Data Sets: Applications in Geospatial Planning, Modeling and Engineering - Proceedings of IRTG 1131 Workshop 2011. Open Access Series in Informatics (OASIcs), Volume 27, pp. 1-12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2012)

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@InProceedings{yang_et_al:OASIcs.VLUDS.2011.1,
  author =	{Yang, Xiang and Hamann, Bernd and Aurich, Jan C.},
  title =	{{Virtual Reality supported Visualization and Evaluation of Noise Levels in Manufacturing Environments}},
  booktitle =	{Visualization of Large and Unstructured Data Sets: Applications in Geospatial Planning, Modeling and Engineering - Proceedings of IRTG 1131 Workshop 2011},
  pages =	{1--12},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-939897-46-0},
  ISSN =	{2190-6807},
  year =	{2012},
  volume =	{27},
  editor =	{Garth, Christoph and Middel, Ariane and Hagen, Hans},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.VLUDS.2011.1},
  URN =		{urn:nbn:de:0030-drops-37370},
  doi =		{10.4230/OASIcs.VLUDS.2011.1},
  annote =	{Keywords: virtual reality, acoustic simulation, visualization, manufacturing}
}
Document
DOI: 10.4230/OASIcs.VLUDS.2011.13
Spherical Terrain Rendering using the hierarchical HEALPix grid

Authors: Rolf Westerteiger, Andreas Gerndt, and Bernd Hamann

Published in: OASIcs, Volume 27, Visualization of Large and Unstructured Data Sets: Applications in Geospatial Planning, Modeling and Engineering - Proceedings of IRTG 1131 Workshop 2011

Abstract
We present an interactive spherical terrain rendering system employing a hierarchical subdivision of the HEALPix coordinate system using quadtrees. Compared to other parameterizations, the scheme avoids singularities and allows for efficient fusion of mixed-resolution digital elevation models and imagery. A Level-of-Detail heuristic is used to guarantee both high performance and visual fidelity. Unified treatment of DEM and imagery data is achieved by performing the HEALPix projection within a GPU shader. The system is applied to the exploration of Mars, using both MOLA (NASA) and HRSC (German Aerospace Center) data sets.
Cite as

Rolf Westerteiger, Andreas Gerndt, and Bernd Hamann. Spherical Terrain Rendering using the hierarchical HEALPix grid. In Visualization of Large and Unstructured Data Sets: Applications in Geospatial Planning, Modeling and Engineering - Proceedings of IRTG 1131 Workshop 2011. Open Access Series in Informatics (OASIcs), Volume 27, pp. 13-23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2012)

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@InProceedings{westerteiger_et_al:OASIcs.VLUDS.2011.13,
  author =	{Westerteiger, Rolf and Gerndt, Andreas and Hamann, Bernd},
  title =	{{Spherical Terrain Rendering using the hierarchical HEALPix grid}},
  booktitle =	{Visualization of Large and Unstructured Data Sets: Applications in Geospatial Planning, Modeling and Engineering - Proceedings of IRTG 1131 Workshop 2011},
  pages =	{13--23},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-939897-46-0},
  ISSN =	{2190-6807},
  year =	{2012},
  volume =	{27},
  editor =	{Garth, Christoph and Middel, Ariane and Hagen, Hans},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.VLUDS.2011.13},
  URN =		{urn:nbn:de:0030-drops-37389},
  doi =		{10.4230/OASIcs.VLUDS.2011.13},
  annote =	{Keywords: terrain rendering}
}
Document
DOI: 10.4230/OASIcs.VLUDS.2011.59
CFD Simulation of Liquid-Liquid Extraction Columns and Visualization of Eulerian Datasets

Authors: Mark W. Hlawitschka, Fang Chen, Hans-Jörg Bart, and Bernd Hamann

Published in: OASIcs, Volume 27, Visualization of Large and Unstructured Data Sets: Applications in Geospatial Planning, Modeling and Engineering - Proceedings of IRTG 1131 Workshop 2011

Abstract
In this joint work, a complete framework for modeling, simulating and visualizing multiphase fluid flow within an extraction column is presented. We first present a volume-of-fluid simulation, which is able to predict the surface of the droplets during coalescence. However, a fast and efficient model is needed for the simulation of a liquid-liquid extraction column due to the high number of occurring droplets. To simulate the velocity and droplet size in a DN32 extraction column, a coupled computational fluid dynamic-population balance model solver is used. The simulation is analyzed using path-line based visualization techniques. A novel semi-automatic re-seeding technique for droplet path-line integration is proposed. With our technique, path-lines of fluid droplets can be re-initialized after contact with the stirring devices. The droplet breakage is captured, allowing the engineer to improve the design of liquid-liquid columns layout.
Cite as

Mark W. Hlawitschka, Fang Chen, Hans-Jörg Bart, and Bernd Hamann. CFD Simulation of Liquid-Liquid Extraction Columns and Visualization of Eulerian Datasets. In Visualization of Large and Unstructured Data Sets: Applications in Geospatial Planning, Modeling and Engineering - Proceedings of IRTG 1131 Workshop 2011. Open Access Series in Informatics (OASIcs), Volume 27, pp. 59-70, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2012)

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@InProceedings{hlawitschka_et_al:OASIcs.VLUDS.2011.59,
  author =	{Hlawitschka, Mark W. and Chen, Fang and Bart, Hans-J\"{o}rg and Hamann, Bernd},
  title =	{{CFD Simulation of Liquid-Liquid Extraction Columns and Visualization of Eulerian Datasets}},
  booktitle =	{Visualization of Large and Unstructured Data Sets: Applications in Geospatial Planning, Modeling and Engineering - Proceedings of IRTG 1131 Workshop 2011},
  pages =	{59--70},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-939897-46-0},
  ISSN =	{2190-6807},
  year =	{2012},
  volume =	{27},
  editor =	{Garth, Christoph and Middel, Ariane and Hagen, Hans},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.VLUDS.2011.59},
  URN =		{urn:nbn:de:0030-drops-37410},
  doi =		{10.4230/OASIcs.VLUDS.2011.59},
  annote =	{Keywords: computational fluid dynamics, multiphase fluid, droplet collision, Eule- rian, path-line}
}
Document
DOI: 10.4230/OASIcs.VLUDS.2011.135
A Survey of Dimension Reduction Methods for High-dimensional Data Analysis and Visualization

Authors: Daniel Engel, Lars Hüttenberger, and Bernd Hamann

Published in: OASIcs, Volume 27, Visualization of Large and Unstructured Data Sets: Applications in Geospatial Planning, Modeling and Engineering - Proceedings of IRTG 1131 Workshop 2011

Abstract
Dimension reduction is commonly defined as the process of mapping high-dimensional data to a lower-dimensional embedding. Applications of dimension reduction include, but are not limited to, filtering, compression, regression, classification, feature analysis, and visualization. We review methods that compute a point-based visual representation of high-dimensional data sets to aid in exploratory data analysis. The aim is not to be exhaustive but to provide an overview of basic approaches, as well as to review select state-of-the-art methods. Our survey paper is an introduction to dimension reduction from a visualization point of view. Subsequently, a comparison of state-of-the-art methods outlines relations and shared research foci.
Cite as

Daniel Engel, Lars Hüttenberger, and Bernd Hamann. A Survey of Dimension Reduction Methods for High-dimensional Data Analysis and Visualization. In Visualization of Large and Unstructured Data Sets: Applications in Geospatial Planning, Modeling and Engineering - Proceedings of IRTG 1131 Workshop 2011. Open Access Series in Informatics (OASIcs), Volume 27, pp. 135-149, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2012)

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@InProceedings{engel_et_al:OASIcs.VLUDS.2011.135,
  author =	{Engel, Daniel and H\"{u}ttenberger, Lars and Hamann, Bernd},
  title =	{{A Survey of Dimension Reduction Methods for High-dimensional Data Analysis and Visualization}},
  booktitle =	{Visualization of Large and Unstructured Data Sets: Applications in Geospatial Planning, Modeling and Engineering - Proceedings of IRTG 1131 Workshop 2011},
  pages =	{135--149},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-939897-46-0},
  ISSN =	{2190-6807},
  year =	{2012},
  volume =	{27},
  editor =	{Garth, Christoph and Middel, Ariane and Hagen, Hans},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.VLUDS.2011.135},
  URN =		{urn:nbn:de:0030-drops-37475},
  doi =		{10.4230/OASIcs.VLUDS.2011.135},
  annote =	{Keywords: high-dimensional, multivariate data, dimension reduction, manifold learning}
}
Document
DOI: 10.4230/OASIcs.VLUDS.2010.1
Finite Element Analysis for Linear Elastic Solids Based on Subdivision Schemes

Authors: Daniel Burkhart, Bernd Hamann, and Georg Umlauf

Published in: OASIcs, Volume 19, Visualization of Large and Unstructured Data Sets - Applications in Geospatial Planning, Modeling and Engineering (IRTG 1131 Workshop) (2011)

Abstract
Finite element methods are used in various areas ranging from mechanical engineering to computer graphics and bio-medical applications. In engineering, a critical point is the gap between CAD and CAE. This gap results from different representations used for geometric design and physical simulation. We present two different approaches for using subdivision solids as the only representation for modeling, simulation and visualization. This has the advantage that no data must be converted between the CAD and CAE phases. The first approach is based on an adaptive and feature-preserving tetrahedral subdivision scheme. The second approach is based on Catmull-Clark subdivision solids.
Cite as

Daniel Burkhart, Bernd Hamann, and Georg Umlauf. Finite Element Analysis for Linear Elastic Solids Based on Subdivision Schemes. In Visualization of Large and Unstructured Data Sets - Applications in Geospatial Planning, Modeling and Engineering (IRTG 1131 Workshop). Open Access Series in Informatics (OASIcs), Volume 19, pp. 1-10, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2011)

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@InProceedings{burkhart_et_al:OASIcs.VLUDS.2010.1,
  author =	{Burkhart, Daniel and Hamann, Bernd and Umlauf, Georg},
  title =	{{Finite Element Analysis for Linear Elastic Solids Based on Subdivision Schemes}},
  booktitle =	{Visualization of Large and Unstructured Data Sets - Applications in Geospatial Planning, Modeling and Engineering (IRTG 1131 Workshop)},
  pages =	{1--10},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-939897-29-3},
  ISSN =	{2190-6807},
  year =	{2011},
  volume =	{19},
  editor =	{Middel, Ariane and Scheler, Inga and Hagen, Hans},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.VLUDS.2010.1},
  URN =		{urn:nbn:de:0030-drops-30928},
  doi =		{10.4230/OASIcs.VLUDS.2010.1},
  annote =	{Keywords: Subdivision solids, Finite element method, Isogeometric analysis}
}
Document
DOI: 10.4230/DFU.SciViz.2010.275
Real-time Terrain Mapping

Authors: Tony Bernardin, Eric Cowgil, Ryan Gold, Bernd Hamann, and Oliver Kreylos

Published in: Dagstuhl Follow-Ups, Volume 1, Scientific Visualization: Advanced Concepts (2010)

Abstract
We present an interactive, real-time mapping system for digital elevation maps (DEMs), which allows Earth scientists to map and therefore understand the deformation of the continental crust at length scales of 10m to 1000km. Our system visualizes the surface of the Earth as a 3D~surface generated from a DEM, with a color texture generated from a registered multispectral image and vector-based mapping elements draped over it. We use a quadtree-based multiresolution method to be able to render high-resolution terrain mapping data sets of large spatial regions in real time. The main strength of our system is the combination of interactive rendering and interactive mapping directly onto the 3D~surface, with the ability to navigate the terrain and to change viewpoints arbitrarily during mapping. User studies and comparisons with commercially available mapping software show that our system improves mapping accuracy and efficiency, and also enables qualitatively different observations that are not possible to make with existing systems.
Cite as

Tony Bernardin, Eric Cowgil, Ryan Gold, Bernd Hamann, and Oliver Kreylos. Real-time Terrain Mapping. In Scientific Visualization: Advanced Concepts. Dagstuhl Follow-Ups, Volume 1, pp. 275-288, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2010)

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@InCollection{bernardin_et_al:DFU.SciViz.2010.275,
  author =	{Bernardin, Tony and Cowgil, Eric and Gold, Ryan and Hamann, Bernd and Kreylos, Oliver},
  title =	{{Real-time Terrain Mapping}},
  booktitle =	{Scientific Visualization: Advanced Concepts},
  pages =	{275--288},
  series =	{Dagstuhl Follow-Ups},
  ISBN =	{978-3-939897-19-4},
  ISSN =	{1868-8977},
  year =	{2010},
  volume =	{1},
  editor =	{Hagen, Hans},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DFU.SciViz.2010.275},
  URN =		{urn:nbn:de:0030-drops-27106},
  doi =		{10.4230/DFU.SciViz.2010.275},
  annote =	{Keywords: Earth, Space, and Environmental Sciences Visualization, Interaction, Terrain Visualization, Multiresolution Visualization}
}
Document
DOI: 10.4230/DFU.SciViz.2010.30
Generalized Swap Operation for Tetrahedrizations

Authors: Burkhard Lehner, Bernd Hamann, and Georg Umlauf

Published in: Dagstuhl Follow-Ups, Volume 1, Scientific Visualization: Advanced Concepts (2010)

Abstract
Mesh optimization of 2D and 3D triangulations is used in multiple applications extensively. For example, mesh optimization is crucial in the context of adaptively discretizing geometry, typically representing the geometrical boundary conditions of a numerical simulation, or adaptively discretizing the entire space over which various dependent variables of a numerical simulation must be approximated. Together with operations applied to the vertices the so-called edge or face swap operations are the building block of all optimization approaches. To speed up the optimization or to avoid local minima of the function measuring overall mesh quality these swaps are combined to generalized swap operations with a less local impact on the triangulation. Despite the fact that these swap operations change only the connectivity of a triangulation, it depends on the geometry of the triangulation whether the generalized swap will generate inconsistently oriented or degenerate simplices. Because these are undesirable for numerical reasons, this paper is concerned with geometric criteria that guarantee the generalized swaps for a 3D triangulation to yield only valid, non-degenerate triangulations.
Cite as

Burkhard Lehner, Bernd Hamann, and Georg Umlauf. Generalized Swap Operation for Tetrahedrizations. In Scientific Visualization: Advanced Concepts. Dagstuhl Follow-Ups, Volume 1, pp. 30-44, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2010)

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@InCollection{lehner_et_al:DFU.SciViz.2010.30,
  author =	{Lehner, Burkhard and Hamann, Bernd and Umlauf, Georg},
  title =	{{Generalized Swap Operation for Tetrahedrizations}},
  booktitle =	{Scientific Visualization: Advanced Concepts},
  pages =	{30--44},
  series =	{Dagstuhl Follow-Ups},
  ISBN =	{978-3-939897-19-4},
  ISSN =	{1868-8977},
  year =	{2010},
  volume =	{1},
  editor =	{Hagen, Hans},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DFU.SciViz.2010.30},
  URN =		{urn:nbn:de:0030-drops-26956},
  doi =		{10.4230/DFU.SciViz.2010.30},
  annote =	{Keywords: 3D Triangulation, Geometric Conditions, Swap Operations}
}
Document
DOI: 10.4230/DFU.SciViz.2010.45
On Curved Simplicial Elements and Best Quadratic Spline Approximation for Hierarchical Data Representation

Authors: Bernd Hamann

Published in: Dagstuhl Follow-Ups, Volume 1, Scientific Visualization: Advanced Concepts (2010)

Abstract
We present a method for hierarchical data approximation using curved quadratic simplicial elements for domain decomposition. Scientific data defined over two- or three-dimensional domains typically contain boundaries and discontinuities that are to be preserved and approximated well for data analysis and visualization. Curved simplicial elements make possible a better representation of curved geometry, domain boundaries, and discontinuities than simplicial elements with non-curved edges and faces. We use quadratic basis functions and compute best quadratic simplicial spline approximations that are $C^0$-continuous everywhere except where field discontinuities occur whose locations we assume to be given. We adaptively refine a simplicial approximation by identifying and bisecting simplicial elements with largest errors. It is possible to store multiple approximation levels of increasing quality. Our method can be used for hierarchical data processing and visualization.
Cite as

Bernd Hamann. On Curved Simplicial Elements and Best Quadratic Spline Approximation for Hierarchical Data Representation. In Scientific Visualization: Advanced Concepts. Dagstuhl Follow-Ups, Volume 1, pp. 45-61, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2010)

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@InCollection{hamann:DFU.SciViz.2010.45,
  author =	{Hamann, Bernd},
  title =	{{On Curved Simplicial Elements and Best Quadratic Spline Approximation for Hierarchical Data Representation}},
  booktitle =	{Scientific Visualization: Advanced Concepts},
  pages =	{45--61},
  series =	{Dagstuhl Follow-Ups},
  ISBN =	{978-3-939897-19-4},
  ISSN =	{1868-8977},
  year =	{2010},
  volume =	{1},
  editor =	{Hagen, Hans},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DFU.SciViz.2010.45},
  URN =		{urn:nbn:de:0030-drops-26960},
  doi =		{10.4230/DFU.SciViz.2010.45},
  annote =	{Keywords: Approximation, Bisection, Grid Generation, Finite Elements, Hierarchical Approximation, Simplicial Decomposition, Spline}
}
Document
DOI: 10.4230/DFU.SciViz.2010.110
Tensor Field Reconstruction Based on Eigenvector and Eigenvalue Interpolation

Authors: Ingrid Hotz, Jaya Sreevalsan-Nair, Hans Hagen, and Bernd Hamann

Published in: Dagstuhl Follow-Ups, Volume 1, Scientific Visualization: Advanced Concepts (2010)

Abstract
Interpolation is an essential step in the visualization process. While most data from simulations or experiments are discrete many visualization methods are based on smooth, continuous data approximation or interpolation methods. We introduce a new interpolation method for symmetrical tensor fields given on a triangulated domain. Differently from standard tensor field interpolation, which is based on the tensor components, we use tensor invariants, eigenvectors and eigenvalues, for the interpolation. This interpolation minimizes the number of eigenvectors and eigenvalues computations by restricting it to mesh vertices and makes an exact integration of the tensor lines possible. The tensor field topology is qualitatively the same as for the component wise-interpolation. Since the interpolation decouples the ``shape'' and ``direction'' interpolation it is shape-preserving, what is especially important for tracing fibers in diffusion MRI data.
Cite as

Ingrid Hotz, Jaya Sreevalsan-Nair, Hans Hagen, and Bernd Hamann. Tensor Field Reconstruction Based on Eigenvector and Eigenvalue Interpolation. In Scientific Visualization: Advanced Concepts. Dagstuhl Follow-Ups, Volume 1, pp. 110-123, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2010)

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@InCollection{hotz_et_al:DFU.SciViz.2010.110,
  author =	{Hotz, Ingrid and Sreevalsan-Nair, Jaya and Hagen, Hans and Hamann, Bernd},
  title =	{{Tensor Field Reconstruction Based on Eigenvector and Eigenvalue Interpolation}},
  booktitle =	{Scientific Visualization: Advanced Concepts},
  pages =	{110--123},
  series =	{Dagstuhl Follow-Ups},
  ISBN =	{978-3-939897-19-4},
  ISSN =	{1868-8977},
  year =	{2010},
  volume =	{1},
  editor =	{Hagen, Hans},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DFU.SciViz.2010.110},
  URN =		{urn:nbn:de:0030-drops-27003},
  doi =		{10.4230/DFU.SciViz.2010.110},
  annote =	{Keywords: Tensor Field, Eigenvector, Eigenvalue, Interpolation}
}
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