996 research outputs found
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
Conforming restricted Delaunay mesh generation for piecewise smooth complexes
A Frontal-Delaunay refinement algorithm for mesh generation in piecewise
smooth domains is described. Built using a restricted Delaunay framework, this
new algorithm combines a number of novel features, including: (i) an
unweighted, conforming restricted Delaunay representation for domains specified
as a (non-manifold) collection of piecewise smooth surface patches and curve
segments, (ii) a protection strategy for domains containing curve segments that
subtend sharply acute angles, and (iii) a new class of off-centre refinement
rules designed to achieve high-quality point-placement along embedded curve
features. Experimental comparisons show that the new Frontal-Delaunay algorithm
outperforms a classical (statically weighted) restricted Delaunay-refinement
technique for a number of three-dimensional benchmark problems.Comment: To appear at the 25th International Meshing Roundtabl
TetGen, towards a quality tetrahedral mesh generator
TetGen is a C++ program for generating quality tetrahedral meshes aimed to support numerical methods and scientific computing. It is also a research project for studying the underlying mathematical problems and evaluating algorithms. This paper presents the essential meshing components developed in TetGen for robust and efficient software implementation. And it highlights the state-of-the-art algorithms and technologies currently implemented and developed in TetGen for automatic quality tetrahedral mesh generation
Locally optimal Delaunay-refinement and optimisation-based mesh generation
The field of mesh generation concerns the development of efficient algorithmic techniques to construct high-quality tessellations of complex geometrical objects. In this thesis, I investigate the problem of unstructured simplicial mesh generation for problems in two- and three-dimensional spaces, in which meshes consist of collections of triangular and tetrahedral elements. I focus on the development of efficient algorithms and computer programs to produce high-quality meshes for planar, surface and volumetric objects of arbitrary complexity. I develop and implement a number of new algorithms for mesh construction based on the Frontal-Delaunay paradigm - a hybridisation of conventional Delaunay-refinement and advancing-front techniques. I show that the proposed algorithms are a significant improvement on existing approaches, typically outperforming the Delaunay-refinement technique in terms of both element shape- and size-quality, while offering significantly improved theoretical robustness compared to advancing-front techniques. I verify experimentally that the proposed methods achieve the same element shape- and size-guarantees that are typically associated with conventional Delaunay-refinement techniques. In addition to mesh construction, methods for mesh improvement are also investigated. I develop and implement a family of techniques designed to improve the element shape quality of existing simplicial meshes, using a combination of optimisation-based vertex smoothing, local topological transformation and vertex insertion techniques. These operations are interleaved according to a new priority-based schedule, and I show that the resulting algorithms are competitive with existing state-of-the-art approaches in terms of mesh quality, while offering significant improvements in computational efficiency. Optimised C++ implementations for the proposed mesh generation and mesh optimisation algorithms are provided in the JIGSAW and JITTERBUG software libraries
Interior boundary-aligned unstructured grid generation and cell-centered versus vertex-centered CVD-MPFA performance
Grid generation for reservoir simulation must honor classical key constraints and ensure boundary alignment such that control-volume boundaries are aligned with geological features including layers, shale barriers, fractures, faults, pinch-outs, and multilateral wells. Novel unstructured grid generation methods are proposed that automate control-volume and/or control point boundary alignment and yield perpendicular-bisector (PEBI) meshes both with respect to primal and dual (essentially PEBI) cells. In order to honor geological features in the primal configuration, we introduce the idea of protection circles that contain segments of key geological boundaries, while in order to generate a dual-cell feature aligned grid, we construct halos around key geological features. The grids generated are employed to study comparative performance of cell-centred versus cell-vertex flux-continuous control-volume distributed multi-point flux approximation (CVD-MPFA) finite-volume formulations using equivalent degrees of freedom and thus ensure application of the most efficient methods. The CVD-MPFA formulation (c.f. Edwards et al.) in cell-centred and cell-vertex modes is somewhat analogous and requires switching control-volume from primal to dual or vice versa, together with appropriate data structures and boundary conditions, however dual-cells are generated after primal grid generation. The relative benefits of both types of approximation, i.e., cell-centred versus vertex-centred, are contrasted in terms of flow resolution and degrees of freedom required
Unstructured Grid Generation Techniques and Software
The Workshop on Unstructured Grid Generation Techniques and Software was conducted for NASA to assess its unstructured grid activities, improve the coordination among NASA centers, and promote technology transfer to industry. The proceedings represent contributions from Ames, Langley, and Lewis Research Centers, and the Johnson and Marshall Space Flight Centers. This report is a compilation of the presentations made at the workshop
Multi-View Stereo with Single-View Semantic Mesh Refinement
While 3D reconstruction is a well-established and widely explored research
topic, semantic 3D reconstruction has only recently witnessed an increasing
share of attention from the Computer Vision community. Semantic annotations
allow in fact to enforce strong class-dependent priors, as planarity for ground
and walls, which can be exploited to refine the reconstruction often resulting
in non-trivial performance improvements. State-of-the art methods propose
volumetric approaches to fuse RGB image data with semantic labels; even if
successful, they do not scale well and fail to output high resolution meshes.
In this paper we propose a novel method to refine both the geometry and the
semantic labeling of a given mesh. We refine the mesh geometry by applying a
variational method that optimizes a composite energy made of a state-of-the-art
pairwise photo-metric term and a single-view term that models the semantic
consistency between the labels of the 3D mesh and those of the segmented
images. We also update the semantic labeling through a novel Markov Random
Field (MRF) formulation that, together with the classical data and smoothness
terms, takes into account class-specific priors estimated directly from the
annotated mesh. This is in contrast to state-of-the-art methods that are
typically based on handcrafted or learned priors. We are the first, jointly
with the very recent and seminal work of [M. Blaha et al arXiv:1706.08336,
2017], to propose the use of semantics inside a mesh refinement framework.
Differently from [M. Blaha et al arXiv:1706.08336, 2017], which adopts a more
classical pairwise comparison to estimate the flow of the mesh, we apply a
single-view comparison between the semantically annotated image and the current
3D mesh labels; this improves the robustness in case of noisy segmentations.Comment: {\pounds}D Reconstruction Meets Semantic, ICCV worksho
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