Three-dimensional alpha shapes

Frequently, data in scientific computing is in its abstract form a finite point set in space, and it is sometimes useful or required to compute what one might call the ``shape'' of the set. For that purpose, this paper introduces the formal notion of the family of $\alpha$-shapes of a finite point set in \Real^3. Each shape is a well-defined polytope, derived from the Delaunay triangulation of the point set, with a parameter \alpha \in \Real controlling the desired level of detail. An algorithm is presented that constructs the entire family of shapes for a given set of size $n$ in time $O(n^2)$, worst case. A robust implementation of the algorithm is discussed and several applications in the area of scientific computing are mentioned.Comment: 32 page

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Coordinated Science Laboratory was formerly known as Control Systems LaboratoryNational Science Foundation / ECS-84-10902 and CCR-87-14565Amoco Foundatio

Simulation of Simplicity: A Technique to Cope with Degenerate Cases in Geometric Algorithms

This paper describes a general-purpose programming technique, called the Simulation of Simplicity, which can be used to cope with degenerate input data for geometric algorithms. It relieves the programmer from the task to provide a consistent treatment for every single special case that can occur. The programs that use the technique tend to be considerably smaller and more robust than those that do not use it. We believe that this technique will become a standard tool in writing geometric software

Fast Randomized Point Location without Preprocessing in Two- and Three-dimensional Delaunay Triangulations

This paper studies the point location problem in Delaunay triangulations without preprocessing and additional storage. The proposed procedure finds the query point simply by "walking through" the triangulation, after selecting a "good starting point" by random sampling. The analysis generalizes and extends a recent result for d = 2 dimensions by proving this procedure to take expected time close to O(n 1=(d+1) ) for point location in Delaunay triangulations of n random points in d = 3 dimensions. Empirical results in both two and three dimensions show that this procedure is efficient in practice

Human beta-defensin-2 and -3 enhance pro-inflammatory cytokine expression induced by TLR ligands via ATP-release in a P2X7R dependent manner

Our previous results indicate that HBD2 and HBD3 are chemotactic for a broad spectrum of leukocytes in a CCR6- and CCR2-dependent manner. In this study we report that pre-stimulation of primary human macrophages or THP-1 cells with HBD2 or HBD3 results in a synergistic, enhanced expression of pro-inflammatory cytokines and chemokines induced by TLR ligand re-stimulation. Experiments using specific inhibitors of the ATP-gated channel receptor P2X7 or its functional ligand ATP, suggest that the enhanced expression of pro-inflammatory cytokines and chemokines seems to be mediated by P2X7R. Furthermore, our data provide evidence that beta-defensins do not directly interact with P2X7R but rather induce the release of intracellular ATP. Interference with ATP release abrogated the synergistic effect mediated by HBD2 and HBD3 pre-stimulation in THP-1 cells. However, extracellular ATP alone seems not to be sufficient to elicit the enhanced synergistic effect on cytokine and chemokine expression observed by pre-stimulation of primary human macrophages or THP-1 cells with HBD2 or HBD3. Collectively, our findings provide new insights into the molecular mechanisms how HBD2 and HBD3 interact with cells of myeloid origin and demonstrate their immuno-modulating functions during innate immune responses. (C) 2016 Elsevier GmbH. All rights reserved

Fast Randomized Point Location without Preprocessing in Two- and Three-Dimensional Delaunay Triangulations

This paper studies the point location problem in Delaunay triangulations without preprocessing and additional storage. The proposed procedure finds the query point simply by "walking through" the triangulation, after selecting a "good starting point" by random sampling. The analysis generalizes and extends a recent result for d = 2 dimensions by proving this procedure to take expected time close to O(n^(1/(d+1))) for point location in Delaunay triangulations of n random points in d = 3 dimensions. Empirical results in both two and three dimensions show that this procedure is efficient in practice