Publications

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Over the past decade, polyhedral meshing has been gaining popularity as a better alternative to tetrahedral meshing in certain applications. Within the class of polyhedral elements, Voronoi cells are particularly attractive thanks to their special geometric structure. What has been missing so far is a Voronoi mesher that is sufficiently robust to run automatically on complex models. In this video, we illustrate the main ideas behind the VoroCrust algorithm, highlighting both the theoretical guarantees and the practical challenges imposed by realistic inputs.

Abstract not provided.

Over the past decade, polyhedral meshing has been gaining popularity as a better alternative to tetrahedral meshing in certain applications. Within the class of polyhedral elements, Voronoi cells are particularly attractive thanks to their special geometric structure. What has been missing so far is a Voronoi mesher that is sufficiently robust to run automatically on complex models. In this video, we illustrate the main ideas behind the VoroCrust algorithm, highlighting both the theoretical guarantees and the practical challenges imposed by realistic inputs.

We study the problem of decomposing a volume bounded by a smooth surface into a collection of Voronoi cells. Unlike the dual problem of conforming Delaunay meshing, a principled solution to this problem for generic smooth surfaces remained elusive. VoroCrust leverages ideas from α-shapes and the power crust algorithm to produce unweighted Voronoi cells conforming to the surface, yielding the first provably-correct algorithm for this problem. Given an ϵ-sample on the bounding surface, with a weak σ-sparsity condition, we work with the balls of radius δ times the local feature size centered at each sample. The corners of this union of balls are the Voronoi sites, on both sides of the surface. The facets common to cells on opposite sides reconstruct the surface. For appropriate values of ϵ, σ and δ, we prove that the surface reconstruction is isotopic to the bounding surface. With the surface protected, the enclosed volume can be further decomposed into an isotopic volume mesh of fat Voronoi cells by generating a bounded number of sites in its interior. Compared to state-of-the-art methods based on clipping, VoroCrust cells are full Voronoi cells, with convexity and fatness guarantees. Compared to the power crust algorithm, VoroCrust cells are not filtered, are unweighted, and offer greater flexibility in meshing the enclosed volume by either structured grids or random samples.

The quality of automatic signal detections from sensor networks depends on individual detector trigger levels (TLs) from each sensor. The largely manual process of identifying effective TLs is painstaking and does not guarantee optimal configuration settings, yet achieving superior automatic detection of signals and ultimately, events, is closely related to these parameters. We present a Dynamic Detector Tuning (DDT) system that automatically adjusts effective TL settings for signal detectors to the current state of the environment by leveraging cooperation within a local neighborhood of network sensors. After a stabilization period, the DDT algorithm can adapt in near-real time to changing conditions and automatically tune a signal detector to identify (detect) signals from only events of interest. Our current work focuses on reducing false signal detections early in the seismic signal processing pipeline, which leads to fewer false events and has a significant impact on reducing analyst time and effort. This system provides an important new method to automatically tune detector TLs for a network of sensors and is applicable to both existing sensor performance boosting and new sensor deployment. With ground truth on detections from a local neighborhood of seismic sensors within a network monitoring the Mount Erebus volcano in Antarctica, we show that DDT reduces the number of false detections by 18% and the number of missed detections by 11% when compared with optimal fixed TLs for all sensors.