Delaunay triangulation

About: Delaunay triangulation is a research topic. Over the lifetime, 5816 publications have been published within this topic receiving 126615 citations. The topic is also known as: Delone triangulation.

Flying Voxel Method with Delaunay Triangulation Criterion for Façade/Feature Detection for Computation

Abstract: A new algorithm is introduced to directly reconstruct geometric models of building facades from terrestrial laser scanning data without using either manual intervention or a third-party, computer-aided design (CAD) package. The algorithm detects building boundaries and features and converts the point cloud data into a solid model appropriate for computational modeling. The algorithm combines a voxel-based technique with a Delaunay triangulation–based criterion. In the first phase, the algorithm detects boundary points of the facade and its features from the raw data. Subsequently, the algorithm determines whether holes are actual openings or data deficits caused by occlusions and then fills unrealistic openings. The algorithm’s second phase creates a solid model using voxels in an octree representation. The algorithm was applied to the facades of three masonry buildings, successfully detected all openings, and correctly reconstructed the facade boundaries. Geometric validation of the models agains...

Anisotropic Mesh Generation with Particles.

Abstract: : Many important real world problems require meshing, that is the approximation of a given geometry by a set of simpler elements such as triangles or quadrilaterals in two dimensions, and tetrahedra or hexahedra in three dimensions. Applications include finite element analysis and computer graphics. This work focuses on the former. A physically based model of interacting 'particles' is introduced to uniformly spread points over a 2-dimensional polygonal domain. The set of points is triangulated to form a triangle mesh. Delaunay triangulation is used because it guarantees a low computational cost and reasonably well shaped elements. Several particle interaction (repulsion and attraction) models are investigated ranging from Gaussian energy potentials to Laplacian smoothing. Particle population control mechanisms are introduced to make the size of the mesh elements converge to the desired size. In most applications spatial mesh adaptivity is desirable. Triangles should not only adapt in size but also in shape, to better fit the function to approximate. Computational fluid dynamics simulations typically require triangles stretched in the direction of the flow. A metric tensor is introduced to quantify the stretching. The triangulation procedure is changed to generate 'Delaunay' meshes in the Riemannian space defined by the metric. This new approach to mesh generation appears quite promising.

FH-OAOS: A Fast Four-Step Heuristic for Obstacle-Avoiding Octilinear Steiner Tree Construction

Abstract: With the sharp increase of very large-scale integrated (VLSI) circuit density, we are faced with many knotty issues. Particularly in the routing phase of VLSI physical design, the interconnection effects directly relate to the final performance of circuits. However, the optimization capability of traditional rectilinear architecture is limited; thus, both academia and industry have been devoted to nonrectilinear architecture in recent years, especially octilinear architecture, which is the most promising because it can greatly improve the performance of modern chips. In this article, we design FH-OAOS, an obstacle-avoiding algorithm in octilinear architecture, by constructing an obstacle-avoiding the octilinear Steiner minimal tree (OAOSMT). Our approach first constructs an obstacle-free Euclidean minimal spanning tree (OFEMST) on the given pins based on Delaunay triangulation (DT). Then, two lookup tables about OFEMST’s edge are generated, which can be seen as the information center of FH-OAOS and can provide information support for algorithm operation. Next, an efficient obstacle-avoiding strategy is proposed to convert the OFEMST into an obstacle-avoiding octilinear Steiner tree (OAOST). Finally, the generated OAOST is refined to construct the final OAOSMT by applying three effective strategies. Experimental results on various benchmarks show that FH-OAOS achieves 66.39 times speedup on average, while the average wirelength of the final OAOSMT is only 0.36p larger than the best existing solution.

Forward modeling of gravity data using finite-volume and finite-element methods on unstructured grids

Abstract: Minimum-structure inversion is one of the most effective tools for the inversion of gravity data. However, the standard Gauss-Newton algorithms that are commonly used for the minimization procedure and that employ forward solvers based on analytic formulas require large memory storage for the formation and inversion of the involved matrices. An alternative to the analytical solvers are numerical ones that result in sparse matrices. This sparsity suits gradient-based minimization methods that avoid the explicit formation of the inversion matrices and that solve the system of equations using memory-efficient iterative techniques. We have developed several numerical schemes for the forward modeling of gravity data using the finite-element and finite-volume methods on unstructured grids. In the finite-volume method, a Delaunay tetrahedral grid and its dual Voronoi grid are used to find the primary solution (i.e., gravitational potential) at the centers and vertices of the tetrahedra, respectively (cel...