An algorithm is presented for the triangulation of arbitrary non-convex polyhedral regions starting with a prescribed boundary triangulation matching existing mesh entities in the remainder of the domain. The algorithm is designed to circumvent the termination problems of volume meshing algorithms which manifest themselves in the inability to successfully create tetrahedra within small subdomains to be referred to herein as cavities. To address this need, a robust Delaunay algorithm with an e cient and termination guaranteed face recovery method is the most appropriate approach. The algorithm begins with Delaunay vertex insertion followed by a face recovery method that conserves the boundary of the cavity by utilizing local mesh modiÿcation operations such as edge split, collapse and swap and a new set of tools which we call complex splits. The local mesh modiÿcations are performed in such a manner that each original surface triangulation is represented either as was, or as a concatenation of triangles. When done in this manner, it is always possible to split the matching mesh entities, ensuring that a compatible mesh is created. The algorithm is robust and has been tested against complex manifold and non-manifold cavities resulting in a valid mesh of the entire domain.
Volume boundary layer mesh generation on non-smooth geometries with multiple normals is considered in this work. A new highlight is given to corner and ridge boundary layer mesh generation through the generalized Voronoi diagram in general, and the spherical Voronoi diagram in particular. This provides the keystone to allow for the first time boundary layer mesh generation at arbitrary corner configurations. The work proposed in [18] is revisited and compared with the new approach. A detailed description of the new algorithm is provided. The spherical Voronoi diagram delivers geometrically the optimal normals as well as topologically the optimal connectivities, as far as normality is concerned. Numerical examples illustrate the accuracy and robustness of the method. This approach seems to handle arbitrary geometry boundary layer mesh generation, in theory as well as in practice.This example represents a cube inside another cube and is illustrated in Figure 5. Some archetypal convex corners are displayed. The difficulty here relies in accurately meshing the mixed convex concave corners. Because of the planar faces, it is easier to appreciate the exact position of the extruded surface. The intersection between the convex ridges and the planar faces are exact, thanks to the location of the Voronoi bisectors for the direction, and the geodesic distance for the computation of the offset modulus. The spherical Voronoi diagram for each of these mixed corners corresponds to the one presented before in Figure 3. The relevant part consists of the spherical parabolic bisectors between the reflex vertex and the bottom face. As mentioned in Section 4, because of the particular surface discretization, this bisector has been split in various parts. Algorithm 3 gathers all these bisectors to create only one group. The group is then meshed along its bisector given the angle provided for discretizing the multiple normals. This group is a vertex/edge bisector. Then, Algorithm 4 sew these edges with the multiple normals from the ridge on one side, and to the triangle faces associated with the bisectors on the other side. The final mesh has 23 Kpoints and 125 Kelems. The boundary layer has 10 layers and reaches up to layer 5 before producing inverted elements. Sharov exampleThis example is extracted from [12] and is displayed in Figure 6. Four ridges abut on the complex corner, two concave and two convex. There is no single normal that ensures visibility for the complex corner of this geometry. Therefore, multiple normals are mandatory for this example. The Voronoi diagram is quite complex for this example, and presents two reflex vertices arising from the two convex ridges. It displays the geometry vertex/edge bisectors and the vertex/vertex bisectors. For this example, Algorithm 3 identifies three different groups, one for the vertex/vertex bisector and two BOUNDARY LAYER MESH GENERATION ON ARBITRARY GEOMETRIES 167 Figure 5. A cube inside a cube.for the edge/vertex bisectors associated with the two different reflex vertices. The zo...
Markov chains have frequently been applied to match the probable routes with a set of GPS trip data that a pilot vehicle is emitting over a specific graph road network. This class of mapmatching (MM) algorithms presently demonstrates and involve statistical and ad-hoc measures to drive the Markov chain transitional probabilities in picking the best route combinations constrained over the graph road network. In this study, we have devised an adaptive scheme to modify the Markov Chain (MC) kernel window as we move along the GPS samples to reduce the mistakes that can happen by the use of narrower MC widths. The measure for temporarily increasing the MC window width is chosen to be the ratio between the geodesic distance of current route to the actual geodesic distance between each pair of GPS samples. This adaptive use of MC has shown to have hardened the results significantly with tolerable computational cost increase. The details of the overall algorithm are depicted by the example routes extracted from various vehicle trips and the results are shown to validate the usefulness of the algorithm in practice.
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