Delaunay triangulation is an effective way to build a triangulation of a cloud of points, i.e., a partitioning of the points into simplices (triangles in 2D, tetrahedra in 3D, and so on), such that ...no two simplices overlap and every point in the set is a vertex of at least one simplex. Such a triangulation has been shown to have several interesting properties in terms of the structure of the simplices it constructs (e.g., maximising the minimum angle of the triangles in the bi-dimensional case) and has several critical applications in the contexts of computer graphics, computational geometry, mobile robotics or indoor localisation, to name a few application domains. This review paper revolves around three main pillars: (I) algorithms, (II) implementations over central processing units (CPUs), graphics processing units (GPUs), and field programmable gate arrays (FPGAs), and (III) applications. Specifically, the paper provides a comprehensive review of the main state-of-the-art algorithmic approaches to compute the Delaunay Triangulation. Subsequently, it delivers a critical review of implementations of Delaunay triangulation over CPUs, GPUs, and FPGAs. Finally, the paper covers a broad and multi-disciplinary range of possible applications of this technique.
A triangulation is called z-knotted if it has a single zigzag (up to reversing). A z-orientation on a triangulation is a minimal collection of zigzags which double covers the set of edges. An edge is ...of type I if zigzags from the z-orientation pass through it in different directions, otherwise this edge is of type II. If all zigzags from the z-orientation contain precisely two edges of type I after any edge of type II, then the z-oriented triangulation is said to be z-homogeneous. We describe an algorithm transferring each z-homogeneous triangulation to other z-homogeneous triangulation which is also z-knotted.
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We present the first 3D triangulation of Transient Luminous Events (TLEs) over Africa. The 6 TLEs were simultaneously observed in the middle atmosphere from Sutherland and Carnarvon in South Africa, ...separated by 192 km, during the 2019 sprites campaign. These two distinctive locations have low radio interference and are free from light pollution. The lightning times, locations, peak current, and polarities, which initiated the observed TLEs, were obtained from the South African Lightning Detection Network and Earth Networks Total Lightning Networks. We investigate the TLEs' altitude and horizontal displacement from their parent lightning strokes. TLEs appear approximately 12.5 to 49.3 km away from their parent lightning strokes. We found that TLE altitudes range from 29 to 92.6 km. The lightning electric field and peak current may be related to the displacement of TLEs and the TLEs' horizontal spread.
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The author emphasised the importance of cognitive methods and business management methods, as well as the necessity to adopt an open-minded approach that requires combining multiple approaches in the ...research process. In order to make the research more credible, the author suggested using triangulation of research methods, allowing to expand the scope of the studied phenomenon. The application of combined research methods also permits achieving higher quality of conducted research, as well as limiting measurement errors that may occur when just one method is used. The author pointed out that for each research process an appropriate research methodology should be selected depending on the type of research problem. It might be necessary to refine the approach, tool or method in order to strengthen the research process. The author designed a concept of a modern formula for organisational changes in an enterprise in the form of a model and verified the model against the example of selected enterprises. He made an attempt to develop a research method to be used in the implementation of basic research processes in management sciences and in the implementation of organisational changes in an enterprise. The developed research method, called "LIDER" (covering three stages), has been used by the author to identify areas of activity and to assess the readiness of change leaders to carry out organisational changes in an enterprise. The nature of the research will determine the decision as to the precise research design, creation of a research model and selection of specific research methods.
Cycles in 5-connected triangulations Alahmadi, A.; Aldred, R.E.L.; Thomassen, C.
Journal of combinatorial theory. Series B,
January 2020, 2020-01-00, Volume:
140
Journal Article
Peer reviewed
Open access
We show that in 5-connected planar and projective planar triangulations on n vertices, the number of Hamiltonian cycles grows exponentially with n. The result is best possible in the sense that ...4-connected triangulations on n vertices on any fixed surface may have only polynomially many cycles. Also, there is an infinite class of 5-connected graphs (not on a fixed surface) which have only polynomially many cycles. The result also extends to 5-connected triangulations of the torus if a long standing conjecture of Nash-Williams holds. For any fixed surface, we show that every 5-connected triangulation of large face-width on that surface contains exponentially many cycles.
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NLZOH, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UILJ, UL, UM, UPCLJ, UPUK, ZAGLJ, ZRSKP
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