Publications

Despite high practical demand, algorithmic hexahedral meshing with guarantees on robustness and quality remains unsolved. A promising direction follows the idea of integer-grid maps, which pull back the Cartesian hexahedral grid formed by integer isoplanes from a parametric domain to a surface-conforming hexahedral mesh of the input object. Since directly optimizing for a high-quality integer-grid map is mathematically challenging, the construction is usually split into two steps: (1) generation of a surface-aligned octahedral field and (2) generation of an integer-grid map that best aligns to the octahedral field. The main robustness issue stems from the fact that smooth octahedral fields frequently exhibit singularity graphs that are not appropriate for hexahedral meshing and induce heavily degenerate integer-grid maps. The first contribution of this work is an enumeration of all local configurations that exist in hex meshes with bounded edge valence, and a generalization of the Hopf-Poincaré formula to octahedral fields, leading to necessary local and global conditions for the hex-meshability of an octahedral field in terms of its singularity graph. The second contribution is a novel algorithm to generate octahedral fields with prescribed hex-meshable singularity graphs, which requires the solution of a large non-linear mixed-integer algebraic system. This algorithm is an important step toward robust automatic hexahedral meshing since it enables the generation of a hex-meshable octahedral field.

Feature curves on 3D shapes provide important hints about significant parts of the geometry and reveal their underlying structure. However, when we process real world data, automatically detected feature curves are affected by measurement uncertainty, missing data, and sampling resolution, leading to noisy, fragmented, and incomplete feature curve networks. These artifacts make further processing unreliable. In this paper we analyze the global co-occurrence information in noisy feature curve networks to fill in missing data and suppress weakly supported feature curves. For this we propose an unsupervised approach to find meaningful structure within the incomplete data by detecting multiple occurrences of feature curve configurations (co-occurrence analysis). We cluster and merge these into feature curve templates, which we leverage to identify strongly supported feature curve segments as well as to complete missing data in the feature curve network. In the presence of significant noise, previous approaches had to resort to user input, while our method performs fully automatic feature curve co-completion. Finding feature reoccurrences however, is challenging since naive feature curve comparison fails in this setting due to fragmentation and partial overlaps of curve segments. To tackle this problem we propose a robust method for partial curve matching. This provides us with the means to apply symmetry detection methods to identify co-occurring configurations. Finally, Bayesian model selection enables us to detect and group re-occurrences that describe the data well and with low redundancy.

Abstract Hexahedral meshes generated from polycube mapping often exhibit a low number of singularities but also poor-quality elements located near the surface. It is thus necessary to improve the overall mesh quality, in terms of the minimum scaled Jacobian (MSJ) or average SJ (ASJ). Improving the quality may be obtained via global padding (or pillowing), which pushes the singularities inside by adding an extra layer of hexahedra on the entire domain boundary. Such a global padding operation suffers from a large increase of complexity, with unnecessary hexahedra added. In addition, the quality of elements near the boundary may decrease. We propose a novel optimization method which inserts sheets of hexahedra so as to perform selective padding, where it is most needed for improving the mesh quality. A sheet can pad part of the domain boundary, traverse the domain and form singularities. Our global formulation, based on solving a binary problem, enables us to control the balance between quality improvement, increase of complexity and number of singularities. We show in a series of experiments that our approach increases the MSJ value and preserves (or even improves) the ASJ, while adding fewer hexahedra than global padding.

Functional maps have gained popularity as a versatile framework for representing intrinsic correspondence between 3D shapes using algebraic machinery. A key ingredient for this framework is the ability to find pairs of corresponding functions (typically, feature descriptors) across the shapes. This is a challenging problem on its own, and when the shapes are strongly non-isometric, nearly impossible to solve automatically. In this paper, we use feature curve correspondences to provide flexible abstractions of semantically similar parts of non-isometric shapes. We design a user interface implementing an interactive process for constructing shape correspondence, allowing the user to update the functional map at interactive rates by introducing feature curve correspondences. We add feature curve preservation constraints to the functional map framework and propose an efficient numerical method to optimize the map with immediate feedback. Experimental results show that our approach establishes correspondences between geometrically diverse shapes with just a few clicks.

In virtual environments, the space that can be explored by real walking is limited by the size of the tracked area. To enable unimpeded walking through large virtual spaces in small real-world surroundings, redirection techniques are used. These unnoticeably manipulate the user’s virtual walking trajectory. It is important to know how strongly such techniques can be applied without the user noticing the manipulation—or getting cybersick. Previously, this was estimated by measuring a detection threshold (DT) in highly-controlled psychophysical studies, which experimentally isolate the effect but do not aim for perceived immersion in the context of VR applications. While these studies suggest that only relatively low degrees of manipulation are tolerable, we claim that, besides establishing detection thresholds, it is important to know when the user’s immersion breaks. We hypothesize that the degree of unnoticed manipulation is significantly different from the detection threshold when the user is immersed in a task. We conducted three studies: a) to devise an experimental paradigm to measure the threshold of limited immersion (TLI), b) to measure the TLI for slowly decreasing and increasing rotation gains, and c) to establish a baseline of cybersickness for our experimental setup. For rotation gains greater than 1.0, we found that immersion breaks quite late after the gain is detectable. However, for gains lesser than 1.0, some users reported a break of immersion even before established detection thresholds were reached. Apparently, the developed metric measures an additional quality of user experience. This article contributes to the development of effective spatial compression methods by utilizing the break of immersion as a benchmark for redirection techniques.

Fluid artwork refers to works of art based on the aesthetics of fluid motion, such as smoke photography, ink injection into water, and paper marbling. Inspired by such types of art, we created Fluid Sketching as a novel medium for creating 3D fluid artwork in immersive virtual environments. It allows artists to draw 3D fluid-like sketches and manipulate them via six degrees of freedom input devices. Different sets of brush strokes are available, varying different characteristics of the fluid. Because of fluid's nature, the diffusion of the drawn fluid sketch is animated, and artists have control over altering the fluid properties and stopping the diffusion process whenever they are satisfied with the current result. Furthermore, they can shape the drawn sketch by directly interacting with it, either with their hand or by blowing into the fluid. We rely on particle advection via curl-noise as a fast procedural method for animating the fluid flow.

The question of representation of 3D geometry is of vital importance when it comes to leveraging the recent advances in the field of machine learning for geometry processing tasks. For common unstructured surface meshes state-of-the-art methods rely on patch-based or mapping-based techniques that introduce resampling operations in order to encode neighborhood information in a structured and regular manner. We investigate whether such resampling can be avoided, and propose a simple and direct encoding approach. It does not only increase processing efficiency due to its simplicity - its direct nature also avoids any loss in data fidelity. To evaluate the proposed method, we perform a number of experiments in the challenging domain of intrinsic, non-rigid shape correspondence estimation. In comparisons to current methods we observe that our approach is able to achieve highly competitive results.

Cybersickness poses a crucial threat to applications in the domain of Virtual Reality. Yet, its predictors are insufficiently explored when redirection techniques are applied. Those techniques let users explore large virtual spaces by natural walking in a smaller tracked space. This is achieved by unnoticeably manipulating the user’s virtual walking trajectory. Unfortunately, this also makes the application more prone to cause Cybersickness. We conducted a user study with a semi-structured interview to get quantitative and qualitative insights into this domain. Results show that Cybersickness arises, but also eases ten minutes after the exposure. Quantitative results indicate that a tolerance towards Cybersickness might be related to self-efficacy constructs and therefore learnable or trainable, while qualitative results indicate that users’ endurance of Cybersickness is dependent on symptom factors such as intensity and duration, as well as factors of usage context and motivation. The role of Cybersickness in Virtual Reality environments is discussed in terms of the applicability of redirected walking techniques.

Real walking is the most natural and intuitive way to navigate the world around us. In Virtual Reality, the limited tracking area of commercially available systems typically does not match the size of the virtual environment we wish to explore. Spatial compression methods enable the user to walk further in the virtual environment than the real tracking bounds permit. This demo gives a glimpse into our ongoing research on spatial compression in VR. Visitors can walk through a realistic model of the Aachen Cathedral within a room-sized tracking area.

In fused deposition modeling (FDM) an object is usually constructed layer-by-layer. Using FDM 3D printers it is however also possible to extrude filament directly in 3D space. Using this technique, a wireframe version of an object can be created by directly printing the wireframe edges into 3D space. This way the print time can be reduced and significant material saving can be achieved. This paper presents a technique for wireframe mesh generation with application in 3D printing. The proposed technique transforms triangle meshes into polygonal meshes, from which the edges can be printed to create the wiremesh. Furthermore, the method is able to generate near-constant density of lines, even in regions parallel to the build platform.

In this paper, we consider the problem of joint antenna selection and analog beamformer design in a downlink single-group multicast network. Our objective is to reduce the hardware requirement by minimizing the number of required phase shifters at the transmitter while fulfilling given quality of constraints. We formulate the problem as an L0 minimization problem and devise a novel branch-and-cut based algorithm to solve the formulated mixed-integer nonlinear program optimally. We also propose a suboptimal heuristic algorithm to solve the above problem with a low computational complexity. Furthermore, the performance of the suboptimal method is evaluated against the developed optimal method, which serves as a benchmark.