One machine, one minute, three billion tetrahedra

This paper presents a new scalable parallelization scheme to generate the 3D Delaunay triangulation of a given set of points. Our first contribution is an efficient serial implementation of the incremental Delaunay insertion algorithm. A simple dedicated data structure, an efficient sorting of the points and the optimization of the insertion algorithm have permitted to accelerate reference implementations by a factor three. Our second contribution is a multi-threaded version of the Delaunay kernel that is able to concurrently insert vertices. Moore curve coordinates are used to partition the point set, avoiding heavy synchronization overheads. Conflicts are managed by modifying the partitions with a simple rescaling of the space-filling curve. The performances of our implementation have been measured on three different processors, an Intel core-i7, an Intel Xeon Phi and an AMD EPYC, on which we have been able to compute 3 billion tetrahedra in 53 seconds. This corresponds to a generation rate of over 55 million tetrahedra per second. We finally show how this very efficient parallel Delaunay triangulation can be integrated in a Delaunay refinement mesh generator which takes as input the triangulated surface boundary of the volume to mesh

There are 174 Subdivisions of the Hexahedron into Tetrahedra

This article answers an important theoretical question: How many different subdivisions of the hexahedron into tetrahedra are there? It is well known that the cube has five subdivisions into 6 tetrahedra and one subdivision into 5 tetrahedra. However, all hexahedra are not cubes and moving the vertex positions increases the number of subdivisions. Recent hexahedral dominant meshing methods try to take these configurations into account for combining tetrahedra into hexahedra, but fail to enumerate them all: they use only a set of 10 subdivisions among the 174 we found in this article. The enumeration of these 174 subdivisions of the hexahedron into tetrahedra is our combinatorial result. Each of the 174 subdivisions has between 5 and 15 tetrahedra and is actually a class of 2 to 48 equivalent instances which are identical up to vertex relabeling. We further show that exactly 171 of these subdivisions have a geometrical realization, i.e. there exist coordinates of the eight hexahedron vertices in a three-dimensional space such that the geometrical tetrahedral mesh is valid. We exhibit the tetrahedral meshes for these configurations and show in particular subdivisions of hexahedra with 15 tetrahedra that have a strictly positive Jacobian

Finding Hexahedrizations for Small Quadrangulations of the Sphere

This paper tackles the challenging problem of constrained hexahedral meshing. An algorithm is introduced to build combinatorial hexahedral meshes whose boundary facets exactly match a given quadrangulation of the topological sphere. This algorithm is the first practical solution to the problem. It is able to compute small hexahedral meshes of quadrangulations for which the previously known best solutions could only be built by hand or contained thousands of hexahedra. These challenging quadrangulations include the boundaries of transition templates that are critical for the success of general hexahedral meshing algorithms. The algorithm proposed in this paper is dedicated to building combinatorial hexahedral meshes of small quadrangulations and ignores the geometrical problem. The key idea of the method is to exploit the equivalence between quad flips in the boundary and the insertion of hexahedra glued to this boundary. The tree of all sequences of flipping operations is explored, searching for a path that transforms the input quadrangulation Q into a new quadrangulation for which a hexahedral mesh is known. When a small hexahedral mesh exists, a sequence transforming Q into the boundary of a cube is found; otherwise, a set of pre-computed hexahedral meshes is used. A novel approach to deal with the large number of problem symmetries is proposed. Combined with an efficient backtracking search, it allows small shellable hexahedral meshes to be found for all even quadrangulations with up to 20 quadrangles. All 54,943 such quadrangulations were meshed using no more than 72 hexahedra. This algorithm is also used to find a construction to fill arbitrary domains, thereby proving that any ball-shaped domain bounded by n quadrangles can be meshed with no more than 78 n hexahedra. This very significantly lowers the previous upper bound of 5396 n.Comment: Accepted for SIGGRAPH 201

Identifying combinations of tetrahedra into hexahedra: a vertex based strategy

Indirect hex-dominant meshing methods rely on the detection of adjacent tetrahedra an algorithm that performs this identification and builds the set of all possible combinations of tetrahedral elements of an input mesh T into hexahedra, prisms, or pyramids. All identified cells are valid for engineering analysis. First, all combinations of eight/six/five vertices whose connectivity in T matches the connectivity of a hexahedron/prism/pyramid are computed. The subset of tetrahedra of T triangulating each potential cell is then determined. Quality checks allow to early discard poor quality cells and to dramatically improve the efficiency of the method. Each potential hexahedron/prism/pyramid is computed only once. Around 3 millions potential hexahedra are computed in 10 seconds on a laptop. We finally demonstrate that the set of potential hexes built by our algorithm is significantly larger than those built using predefined patterns of subdivision of a hexahedron in tetrahedral elements.Comment: Preprint submitted to CAD (26th IMR special issue

Exploring first and second-order spatio-temporal structures of lightning strike impacts in the French Alps using subsampling

We model cloud-to-ground lightning strike impacts in the French Alps over the period 2011-2021 (approximately 1.4 million of events) using spatio-temporal point processes. We investigate first and higher-order structure for this point pattern and address the questions of homogeneity of the intensity function, first-order separability and dependence between events. The tuning of nonparametric methods and the different tests we consider in this study make the computational cost very expensive. We therefore suggest different subsampling strategies to achieve these tasks

Changes in the starch-protein interface depending on common wheat grain hardness revealed using atomic force microscopy

The Atomic Force Microscope tip was used to progressively abrade the surface of non-cutted starch granules embedded in the endosperm protein matrix in grain sections from wheat near-isogenic lines differing in the puroindoline b gene and thus hardness. In the hard near-isogenic wheat lines, starch granules exhibited two distinct profiles corresponding either to abrasion in the surrounding protein layer or the starch granule. An additional profile, only identified in soft lines, revealed a marked stop in the abrasion at the protein-starch transition similar to a lipid interface playing a lubricant role. It was related to the presence of both wild-type puroindolines, already suggested to act at the starch-protein interface through their association with polar lipids.This study revealed, for the first time, in situ differences in the nano-mechanical properties at the starch-protein interface in the endosperm of wheat grains depending on the puroindoline allelic status

Étude de la récidive post-traitement chez des agresseurs sexuels judiciarisés

The aim of the current study was to assess the role of a treatment program (uncompleted; completed ; extended) on the posttreat-ment recidivism of sexual aggressors. Data on five types of recidivism (sexual ; violent ; property offense ; against a person ; total) were gathered for 102 pedophiles and 70 rapists. The recidivism rates for pedophiles who completed the treatment program was lower than for those of the pedophiles who did not complete the treatment. As to the rapists, the recidivism rates were lower for those who underwent an extended treatment program than for the other two groups. These data show that a treatment program reduces the recidivism rate in sexual aggressors. The optimal duration of treatment, however, varies according to the type of offender

Wavefunction tomography of topological dimer chains with long-range couplings

The ability to tailor with a high accuracy the inter-site connectivity in a lattice is a crucial tool for realizing novel topological phases of matter. Here, we report the experimental realization of photonic dimer chains with long-range hopping terms of arbitrary strength and phase, providing a rich generalization of the celebrated Su-Schrieffer-Heeger model. Our experiment is based on a synthetic dimension scheme involving the frequency modes of an optical fiber loop platform. This setup provides direct access to both the band dispersion and the geometry of the Bloch wavefunctions throughout the entire Brillouin zone allowing us to extract the winding number for any possible configuration. Finally, we highlight a topological phase transition solely driven by a time-reversal-breaking synthetic gauge field associated with the phase of the long-range hopping, providing a route for engineering topological bands in photonic lattices belonging to the AIII symmetry class

Compositional and functional trajectories of herbaceous communities after deer density control in clear-cut boreal forests

Overabundant populations of large herbivores have strong persistent effects on forest composition, structure, and function. However, the mechanism through which plant communities recover their original composition and function after herbivore management remains poorly understood. We assessed the temporal trajectories of the herbaceous communities in Abies balsamea (L.) Mill. and Picea glauca (Moench) Voss stands on Anticosti Island (Quebec, Canada) over 8 years following clear-cutting and deer management. The impact of deer exclusion or reduction to 7.5 and 15 deer·km–2 was compared with benchmark in situ deer densities (27 and 56 deer·km–2). Effects of deer management treatments on plant species and functional trait assemblages over time were assessed using principal response curves. Although complete deer exclusion seemed necessary to modify species composition from that occurring under intense browsing, a reduced density of 7.5 deer·km–2 was sufficient to induce significant changes in functional trait assemblages of regenerating stands. For instance, reduced deer densities favored plants with brightly colored flowers and compound inflorescences pollinated by animals and producing large seeds and fleshy fruits dispersed by animals. We conclude that the boreal forest's herbaceous communities are resilient to chronic browsing when deer population reduction and forest clearcutting are applied in synergy.Les populations surabondantes de grands herbivores ont des effets majeurs et persistants sur la composition, la structure et le fonctionnement de la forêt. Toutefois, le mécanisme par lequel les communautés végétales retrouvent leur composition et leur fonctionnement originels en réponse au contrôle des herbivores demeure mal compris. Nous avons évalué les trajectoires temporelles des communautés herbacées dans des peuplements d'Abies balsamea (L.) Mill. et de Picea glauca (Moench) Voss à l'île d'Anticosti (Québec, Canada) pendant 8 années après avoir effectué une coupe à blanc et contrôlé les populations de cerfs. L'impact de l'exclusion du cerf ou d'une réduction de la densité à 7,5 ou 15 cerfs·km–2 a été comparé à des densités témoins in situ (27 et 56 cerfs·km–2). Les effets des traitements de gestion du cerf sur les espèces végétales et les assemblages de traits fonctionnels ont été évalués en fonction du temps au moyen de la méthode des courbes de réponses principales. Bien que l'exclusion complète du cerf ait semblé nécessaire pour modifier la composition spécifique par rapport à celle observée en conditions de broutage intense, une densité réduite à 7,5 cerfs·km–2 était suffisante pour induire des changements significatifs dans les assemblages de traits fonctionnels des peuplements en régénération. À titre d'exemple, des densités réduites de cerfs ont favorisé les plantes à fleurs de couleur vive et les plantes à fleurs composées pollinisées par les animaux et produisant de grosses graines et des fruits charnus dispersés par les animaux. Nous concluons que les communautés herbacées de la forêt boréale sont résilientes au broutage chronique quand une réduction des populations de cerfs et une coupe forestière à blanc sont appliquées en synergie