Publikationen nach Jahren

While the animation and rendering techniques used in the domain of textile simulation have dramatically evolved during the last two decades, the ability to manipulate and modify virtual textiles intuitively using dedicated ergonomic devices has been definitely neglected. The project HAPTEX combines research in the field of textile simulation and haptic interfaces. HAPTEX aims to provide a virtual reality system allowing for multipoint haptic interaction with a piece of virtual fabric simulated in real-time. The fundamental research undertaken by the project ranges from the physics-based simulation of textiles to the design and development of novel tactile and force-feedback rendering strategies and interfaces.

This paper proposes to use the Laplace-Beltrami spectrum (LBS) as a global shape descriptor for medical shape analysis. The approach allows for shape comparisons using minimal shape preprocessing. In particular, no registration, mapping, or remeshing is necessary. The discriminatory power of the method is tested on a population of female caudate shapes of normal control subjects and of subjects with schizotypal personality disorder.

While moving a fingertip over a fine surface we experience a sensation that gives us an idea of its properties. A satisfactory simulation of this feeling is still an unsolved problem. In this paper we describe a rendering strategy based on vibrations which play an important role in the tactile exploration of fine surfaces. To produce appropriate excitation patterns we use an array of vibrating contactor pins. Similar to the colour model in computer graphics we simulate arbitrary vibrations as a superposition of only two sinewaves. Each sinewave is intended for the excitation of a specific population of mechanoreceptors. We carried out first tests of our rendering strategy on Brownian surfaces of different fractal dimension.

In the area of image retrieval from data bases and for copyright protection of large image collections there is a growing demand for unique but easily computable fingerprints for images. These fingerprints can be used to quickly identify every image within a larger set of possibly similar images. This paper introduces a novel method to automatically obtain such fingerprints from an image. It is based on a re-interpretation of an image as a Riemannian manifold. This representation is feasible for gray value images and color images. We discuss the use of the spectrum of eigenvalues of different variants of the Laplace operator as a fingerprint and show the usability of this approach in several use cases. Contrary to existing works in this area we do not only use the discrete Laplacian, but also with a particular emphasis the underlying continuous operator. This allows better results in comparing the resulting spectra and deeper insights in the problems arising. We show how the well known discrete Laplacian is related to the continuous Laplace-Beltrami operator. Furthermore we introduce the new concept of solid height functions to overcome some potential limitations of the method.

The sixth International Conference on Cyberworlds (Cyber- worlds 2007) took place in the beautiful town of Hannover, Germany, in October 2007. The HAPTEX Workshop 2007 was co-hosted with the conference.

A geometric model of an object – in most cases being a subset of the three dimensional space – can be used to better understand the object’s structure or behavior. Therefore data such as the geometry, the topology and other application specific data have to be represented by the model. With the help of a computer it is possible to manipulate, process or display these data. We will discuss different approaches for representing such an object: Volume based representations describe the object in a direct way, whereas boundary representations describe the object indirectly by specifying its boundary. A variety of different surface patches can be used to model the object’s boundary. For many applications it is sufficient to know only the boundary of an object. For special objects explicit or implicit mathematical representations can easily be given. An explicit representation is a map from a known parameter space for in- stance the unit cube to 3D-space. Implicit representations are equations or relations such as the set of zeros of a functional with three unknowns. These can be very efficient in special cases.

The proceedings of The CYBERWORLDS 2007, held October 24-27 in Hannover, Germany. In addition to the 35 papers selected for the October 2007 conference on cyberworlds, this volume also publishes 10 papers from a workshop on modeling virtual reality systems incorporating haptic and tactile feedback and 13 papers from a second workshop on advanced mathematical methods for geometric modeling and shape analysis. The cyberworld papers explore data management, artificial intelligence, cyber ethics, virtual humans, distributed virtual environments, human interaction, and visualization. Other topics include subjective fabric evaluation, anisotropic bending stiffness on particles grids, fast inverse forging simulation via medial axis transform, encoding animated meshes in local coordinates, and parametric reconstruction of bent tube surfaces.

Real-time cloth simulation involves many computational challenges to be solved, particularly in the context of haptic applications, where high frame rates are necessary for obtaining a satisfying experience. In this paper, we present an interactive cloth simulation system that offers a compromise between a realistic physics-based simulation of fabrics and a haptic application meeting high requirements in terms of computation speed. Our system allows the user to interact with the fabric using two fingers. The required performance of the system is achieved by introducing an intermediate layer responsible for the simulation of the small section of the surface being in contact with the fingers. We compare several contact models to obtain the best compromise in the context of haptic applications.

The EU funded RTD project "HAPTEX" addresses the challenge of developing a Virtual Reality (VR) system for the realistic and accurate rendering of the physical interactions of humans with textiles, through the real-time generation of artificial visual and haptic stimuli. This challenge concerns the development of both the SW and the HW components of the VR system, as well as it implies a substantial advancement in the understanding of the mechanisms underlying the human haptic perception of fine physical properties like those of textiles. This paper reports some important details relating to the technical implementation of the developed HW and SW components with special emphasis on the issues related to their integration into a single VR system. Furthermore some preliminary results relating to the functional tests carried out on the integrated system are also reported.

In this work we present an approach to generate a tactile representation from an image that may be a photograph or a scan of cloth. A large class of fabrics can be generated by repetition of a parallelogram primitive. That means there are two non-collinear directions where the pattern is periodically repeated. The method we present is based on analysing the repetitive structure of the sample, that is to find the two principle directions of repetition, and building a model from that analysis. We compare our method to a technique developed by Gang Huang.

The main contribution of this work is the generalization of the Medial Axis Transform (MAT) and the Medial Axis Inverse Transform MAIT) to complete Riemannian manifolds. It is known that almost every solid can be reconstructed from its medial axis and the corresponding radius function. In the past this reconstruction scheme has only been implemented in Euclidean spaces. We use the concept of Fermi coordinates that represent a natural generalization of conventional coordinates. However, this concept only works out properly if some substantial conditions for the radius function are established. Several approaches for the computation of the medial axis have been implemented so far but almost all of them lack good numerical results. Usually numerical errors occur because the approaches operate on a discretised model of the corresponding objects. In this work we will assume that both the 3D Riemannian space and the modelled object can be represented by smooth mappings and coordinate charts respectively. Therefore, we can introduce the so called medial equations that will allow us to compute medial surface patches using the implicit function theorem. Finally we will give examples for the MAT and the MAIT and show to what extent the inverse transform is applicable in the context of Computer Aided Geometric Design. The Geodesic Medial Modeller is one of those applications.

The Voronoi diagram has been investigated intensively throughout the last decades. This has been done not only in the context of Euclidean geometry but also in curved spaces. Most methods typically make use of some fast marching cube algorithms. In this work we will focus on the computation of Voronoi diagrams including Voronoi objects that are contained in a Riemannian manifold with a differentiable structure. Our approach relies on the precise computation of shortest joins of any two given points on the manifold. For these computations we did not apply shooting or related methods. Instead, we used a new perturbation method that operates on a family of deformed manifolds. To reduce time and space complexity we suggest to use a randomised incremental construction scheme (RICS). In this work, we also present several examples of Voronoi diagrams computed with our method.

This paper proposes to use the volumetric Laplace spectrum as a global shape descriptor for medical shape analysis. The approach allows for shape comparisons using minimal shape preprocessing. In particular, no registration, mapping, or remeshing is necessary. All computations can be performed directly on the voxel representations of the shapes. The discriminatory power of the method is tested on a population of female caudate shapes (brain structure) of normal control subjects and of subjects with schizotypal personality disorder. The behavior and properties of the volumetric Laplace spectrum are discussed extensively for both the Dirichlet and Neumann boundary condition showing advantages of the Neumann spectra. Both, the computations of spectra on 3D voxel data for shape matching as well as the use of the Neumann spectrum for shape analysis are completely new.

Modern multimedia applications generate vast amounts of image data. With the availability of cheap photo hardware and affordable rendering software even more such data is being collected. In order to manage huge collections of image data one needs short representations of the data sets, or to be more precise invariant features being appropriate to identify a specific voxel data set using just a few numbers. This paper describes a variation of a method introduced by Reuter, Wolter and Peinecke based on the computation of the spectrum of the Laplace operator for the image for generating an invariant feature vector - a fingerprint. Opposed to previous techniques interpreting the image as a height function we make use of the representation of the image as a density function. We discuss the use of the spectrum of eigenvalues of the Laplace mass density operator as a fingerprint and show the usability of this approach in several cases. Instead of using the discrete Laplace-Kirchhoff operator the approach presented in this paper is based on the continuous Laplace operator allowing better results in comparing the resulting spectra and deeper insights into the problems arising when comparing two spectra generated using discrete Laplacians.

Hot metal forging and precision-forging of machine parts are important production techniques. Forging processes generally consist of several steps and have to be designed from top down. Beginning with the final product, the design engineer derives the intermediate steps of the process in inverse order, using simulations to evaluate and validate them. The simulations are generally based on the finite element method, a widely employed technique in engineering. Two problems exist with this method: 1. The run-time of the simulations is often very long, depending on the spatial and temporal resolution of the simulated process. 2. The simulation progresses from one intermediate step to the next, while the engineer has to lay out the steps in inverse order. We propose a technique which adresses these problems, by following an approach relying on the geometry of the form and elementary plasticity theory. This method allows for a coarse approximation of the material flow that can be inverted.