**2013**

Artikel |

2013 |

Nadia Magnenat Thalmann, Nicholas Patrikalakis, Franz-Erich Wolter, Qunsheng Peng Editorial Visual Computer 29 469-471 2013 Beschreibungstext anzeigen Editorial of the special edition of The Visual Computer, which contains the best 35 papers of the Computer Graphics International 2013 (CGI 2013) held in Hanover, at the Leibniz University of Hanover in Germany. Beschreibungstext verbergen |

Christian Gerstenberger, Franz-Erich Wolter Numerical simulation of acoustic streaming within the cochlea Journal of Computational Acoustics 21 2013 Beschreibungstext anzeigen This paper is concerned with the numerical examination of acoustically driven flows within the inner ear on the basis of a computational model. For this purpose, a comprehensive system of differential equations and boundary conditions is deduced, which takes, to a satisfactory extent, the complexity of the main biophysical mechanisms of the cochlea into account. Beside an appropriate representation of the fluid dynamics, also the biomechanical properties of the basilar membrane as well as the internal amplification mechanism caused by the outer hair cell motility are considered in order to get realistic estimates of the structure and magnitude of the mean flow field. The present paper introduces a two-stage approach for the numerical evaluation of the solutions on the basis of the finite element method. The first step deals with the calculation of the linear acoustic reaction whereas the second step is associated with the determination of a first-order approximation of the acoustic streaming field. It is shown that the results are essentially consistent with measurements as well as analytical and experimental considerations. In addition, the numerical estimates of the acoustically driven flows provide an instrument for a more profound discussion on their physiological impact.
Keywords: Acoustic streaming; cochlea; fluid-structure interaction. Beschreibungstext verbergen |

Alexander Kuenz, Gunnar Schwoch, Franz-Erich Wolter Individualism in Global Airspace - User-Preferred Trajectories in Future ATM 2013 Beschreibungstext anzeigen Both future air traffic management programs SESAR and NextGen foresee trajectory based operations as one of the major enablers for more efficient handling of air traffic. Furthermore, both initiatives claim to support user preferred trajectories. Using a common airspace it is unlikely to get a conflict-free scenario from independently optimized preferred trajectories. This paper investigates if the concept of user preferred trajectories is feasible, and what constraints are necessary to reach a conflict-free global scenario. Restricting aircraft’s trajectories a priori by forcing them to fly on pre-defined en-route segments, respect semi-circular routes, or apply given departure and arrival times reduces the achievable efficiency, but helps to avoid conflicts and keep the concept simple. On the other hand, trying to combine independently optimized trajectories to a full traffic scenario needs a lot of adaptations to achieve conflict-free operations. Even though the good answer to a problem lies often in-between the extreme solutions, this paper investigates the second approach. Based on a real day of actual traffic over Europe, an optimized sample is generated applying user’s preferred trajectory for each flight. Based on an individually optimized traffic scenario yielding nearly 29,000 conflicts, strategic resolution is performed generating least possible penalties for involved aircraft. The main technique of solving conflicts applied is shifting whole flights in time by a few minutes. Direct and recursive algorithms are presented; a focus is put on solving airport-related conflicts first. The efficiency of the original optimized scenario stays untouched, as lateral, vertical, and speed profiles remain identical; flights are only rescheduled to a slightly earlier or later departure (and arrival) slot in order to minimize conflicts. More than 94% of all conflicts can be solved by shifting whole flights in time respecting a maximum offset of 10 minutes. In a subsequent step, lateral and vertical maneuvers are facilitated; resulting in a resolution for more than 97% of all conflicts. |

Alexander Vais, Benjamin Berger, Franz-Erich Wolter Complex line bundle Laplacians THE VISUAL COMPUTER Springer 2013 Beschreibungstext anzeigen In the present work, we extend the theoretical and numerical discussion of the well-known Laplace–Beltrami operator by equipping the underlying manifolds with additional structure provided by vector bundles. Focusing on the particular class of flat complex line bundles, we examine a whole family of Laplacians including the Laplace–Beltrami operator as a special case. To demonstrate that our proposed approach is numerically feasible, we describe a robust and efficient finite-element discretization, supplementing the theoretical discussion with first numerical spectral decompositions of those Laplacians. Our method is based on the concept of introducing complex phase discontinuities into the finite element basis functions across a set of homology generators of the given manifold. More precisely, given an n phase shifts, one for each generator, resulting in a n-dimensional family of Laplacians with associated spectra and eigenfunctions. The spectra and absolute magnitudes of the eigenfunctions are not influenced by the exact location of the paths, depending only on their corresponding homology classes.Employing our discretization technique, we provide and discuss several interesting computational examples highlighting special properties of the resulting spectral decompositions. We examine the spectrum, the eigenfunctions and their zero sets which depend continuously on the choice of phase shifts. |

Roman Vlasov, Karl-Ingo Friese, Franz-Erich Wolter Haptic Rendering of Volume Data with Collision Detection Guarantee Using Path Finding. Transactions on Computational Science 18 Lecture Notes in Computer Science 7848 212-231 2013 Beschreibungstext anzeigen In this paper we present a novel haptic rendering method for exploration of volumetric data. It addresses a recurring flaw in almost all related approaches, where the manipulated object, when moved too quickly, can go through or inside an obstacle. Additionally, either a specific topological structure for the collision objects is needed, or extra speed-up data structures should be prepared. These issues could make it difficult to use a method in practice. Our approach was designed to be free of such drawbacks. An improved version of the method presented here does not have the issues of the original method – oscillations of the interaction point and wrong friction force in some cases. It uses the ray casting technique for collision detection and a path finding approach for rigid collision response. The method operates directly on voxel data and does not use any precalculated structures, but uses an implicit surface representation being generated on the fly. This means that a virtual scene may be both dynamic or static. Additionally, the presented approach has a nearly constant time complexity independent of data resolution. Beschreibungstext verbergen |

Alexander Vais, Daniel Brandes, Hannes Thielhelm, Franz-Erich Wolter Laplacians on flat line bundles over 3-manifolds Computers and Graphics (Pergamon) 37 718-729 2013 Beschreibungstext anzeigen The well-known Laplace-Beltrami operator, established as a basic tool in shape processing, builds on a long history of mathematical investigations that have induced several numerical models for computational purposes. However, the Laplace-Beltrami operator is only one special case of many possible generalizations that have been researched theoretically. Thereby it is natural to supplement some of those extensions with concrete computational frameworks. In this work we study a particularly interesting class of extended Laplacians acting on sections of flat line bundles over compact Riemannian manifolds. Numerical computations for these operators have recently been accomplished on two-dimensional surfaces. Using the notions of line bundles and differential forms, we follow up on that work giving a more general theoretical and computational account of the underlying ideas and their relationships. Building on this we describe how the modified Laplacians and the corresponding computations can be extended to three-dimensional Riemannian manifolds, yielding a method that is able to deal robustly with volumetric objects of intricate shape and topology. We investigate and visualize the two-dimensional zero sets of the first eigenfunctions of the modified Laplacians, yielding an approach for constructing characteristic well-behaving, particularly robust homology generators invariant under isometric deformation. The latter include nicely embedded Seifert surfaces and their non-orientable counterparts for knot complements. |

Karl-Ingo Friese, Sarah Cichy, Franz-Erich Wolter, Roman Botcharnikov Analysis of tomographic mineralogical data using YaDiV-Overview and practical case study Computers and Geosciences 56 92-103 2013 Beschreibungstext anzeigen We introduce the 3D-segmentation and -visualization software YaDiV to the mineralogical application of rock texture analysis. YaDiV has been originally designed to process medical DICOM datasets. But due to software advancements and additional plugins, this open-source software can now be easily used for the fast quantitative morphological characterization of geological objects from tomographic datasets.In this paper, we give a summary of YaDiV's features and demonstrate the advantages of 3D-stereographic visualization and the accuracy of 3D-segmentation for the analysis of geological samples. For this purpose, we present a virtual and a real use case (here: experimentally crystallized and vesiculated magmatic rocks, corresponding to the composition of the 1991-1995 Unzen eruption, Japan). Especially the spacial representation of structures in YaDiV allows an immediate, intuitive understanding of the 3D-structures, which may not become clear by only looking on 2D-images. We compare our results of object number density calculations with the established classical stereological 3D-correction methods for 2D-images and show that it was possible to achieve a seriously higher quality and accuracy.The methods described in this paper are not dependent on the nature of the object. The fact, that YaDiV is open-source and users with programming skills can create new plugins themselves, may allow this platform to become applicable to a variety of geological scenarios from the analysis of textures in tiny rock samples to the interpretation of global geophysical data, as long as the data are provided in tomographic form. Beschreibungstext verbergen |

Adrian Santangelo, Philipp Blanke, Tarik Hadifi, Franz-Erich Wolter, Bernd Arno Behrens Fast 3D inverse simulation of hot forging processes via Medial Axis Transformation: An approach for preform estimation in hot die forging Production Engineering 7 409-416 2013 Beschreibungstext anzeigen In hot die forging processes, the selection of an ideal preform is of great importance with respect to cavity filling and mechanical load. The common procedure in order to define an adequate preform is the usage of Finite-Element-Analysis (FEA), usually as an iterative process in which various preforms are tested with regard to their suitability. An approach that aims at reducing the number of trials by proposing a first estimation of a suitable preform is presented in this paper. It is conjectured that the material flow paths and resistance can be described by the cavity shape using the Medial Axis Transformation. Based on this, a local inverse material flow for time discrete steps is calculated. The result is a first estimation of an adequate preform shape within a few minutes as an input for further FEA. FE-based parametric design optimization procedure is then presented and compared to the inverse approach, which is identified as a useful complement for the forward simulation technique. Beschreibungstext verbergen |

Beiträge in Tagungsbänden |

2013 |

Martin Gutschke, Alexander Vais and Franz-Erich Wolter A Geometrical Framework to Capture the Dynamical Evolution of Slow-Fast Vector Fields 2013 Beschreibungstext anzeigen This paper was presented within the NASAGEM Workshop of CGI 2013, see Table of Contents CGI. In this work we present computational meth- ods dealing with dynamical systems. We focus on those systems being characterized by slow-fast vector fields or corresponding differential algebraic equations that commonly occur in physical applications. In the latter one usually considers a manifold of admissible physi- cal states and a vector field describing the evolution of the physical system over time. The manifold is embed- ded within a higher-dimensional space and is implicitly defined by a system of equations. Certain physical sys- tems, such as so-called relaxation oscillators, perform sudden jumps in their state evolution which are diffi- cult to model. The main contribution of the present work is to approach this problem from a geometric per- spective which provides not only a qualitative analy- sis but also produces quantitative results. We describe techniques for explicitly computing parametrizations of the implicitly defined manifold and of the relevant jump and hit sets. This allows us to compute the dynamical evolution of the system including the aforementioned jump phenomena. As main tools we use homotopy ap- proaches in conjunction with tools from differential ge- ometry such as geodesic polar coordinates. We discuss how to numerically realize and how to apply them to several examples from mechanics, electrical engineering and biology. |

Benjamin Berger, Alexander Vais and Franz-Erich Wolter Subimage Sensitive Eigenvalue Spectra for Image Comparison 2013 Beschreibungstext anzeigen This paper was presented within the NASAGEM Workshop of CGI 2013, see Table of Contents CGI. This publication is a contribution to basic research in image comparison using eigenvalue spectra as features. The differential-geometric approach of eigenvalue spectrum based descriptors is naturally applicable to shape data, but so far little work has been done to transfer it to the setting of image data painted on a rectangle or general curved surface. We present a new semi-global feature descriptor that also contains information about geometry of shapes visible in the image. This may not only improve the performance of the resulting distance measures, but may even enable us to approach the partial matching problem using eigenvalue spectra, which were previously only considered as global feature descriptors. We introduce some concepts that are useful in designing and understanding the behavior of similar fingerprinting algorithms for images (and surfaces) and discuss some preliminary results. |

Hannes Thielhelm, Alexander Vais, Franz-Erich Wolter Geodesic Bifurcation on Smooth Surfaces 2013 Beschreibungstext anzeigen This paper was presented within the NASAGEM Workshop of CGI 2013, see Table of Contents CGI. Within Riemannian geometry the geodesic exponential map is an essential tool for various distance related investigations and computations. Several natural questions can be formulated in terms of its preimages, usually leading to quite challenging non- linear problems. In this context we recently proposed an approach for computing multiple geodesics connecting two arbitrary points on two-dimensional surfaces in situations where an ambiguity of these connecting geodesics is indicated by the presence of so-called focal curves. The essence of the approach consists in exploiting the structure of the associated focal curve and using a suitable curve for a homotopy algorithm to collect the geodesic connections. In this follow-up discussion we extend those constructions to overcome a significant limitation inherent in the previous method, i.e. the necessity to construct homotopy curves artificially. We show that considering homotopy curves meeting a focal curve tangentially leads to a singularity that we investigate thoroughly. Solving this so–called geodesic bifurcation analytically and dealing with it numerically provides not only theoretical insights, but also allows geodesics to be used as homotopy curves. This yields a stable computational tool in the context of computing distances. This is applicable in common situations where there is a curvature induced non-injectivity of the exponential map. In particular we illustrate how applying geodesic bifurcation solves the distance problem on compact manifolds with a single closed focal curve. Furthermore the presented investigations provide natural initial values for computing cut loci and medial curves using the medial differential equation. |