SIGGRAPH 2018

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.

Computer Graphics Forum (Proc. EUROGRAPHICS 2018)

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.

IEEE Transactions on Visualization and Computer Graphics

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.