Delaunay triangulation

The surface triangulation is carried out, after descriptor generation, using the program detri (26) which provides a robust 3D Delaunay triangulation coupled to a randomized incremental flip algorithm (Fig. 3). 

Rebay, S. (1993) Efficient unstructured mesh generation by means of Delaunay triangulation and Bowyer-Watson algorithm, J. Comp. Phys. 106 (1), 125... 

To define a local subset of Pareto-optimal solutions dose to y the Delaunay triangulation is calculated for the set Z = ZHf u y. The Delaunay triangidation subdivides the convex hull of a set of points into disjunct simplices. Each simplex consists of d + points whereby d denotes the dimension of the data set. A specific property of the Delaunay triangulation is that for each simplex the circumhypersphere constituted by its points is empty which implies that the Delaunay triangulation is unique. Let D denote the set of Delaunay simplices where each simplex Ak is a set of d+1 points, i.e.di,= ... 

Delaunay triangulation maximizes the minimum angle of all simplices. Alternatively, the procedure could be briefly described as finding all adjacent points off in the Delaunay graph. 

To illustrate the determination of, Figure j.l7 shows a Delaunay triangulation for an artificial data set drawn from a bivariate uniform distribution. 

Figure 4.17 Example of Delaunay triangulation-based sub-sample generation...

Liebscher, S., Kirschstein, T., and Becker, G. RDELA—a Delaunay-triangulation-based, location and covariance estimator with high breakdown point. Statistics and Computing,... 

There are several different strategies for discretizing the geometry into fundamental elements. For bioelectric field problems, two approaches to mesh generation have become standard the divide and conquer (or subsequent subdivision) strategy and the so-called Delaunay triangulation strategy. 

A. Bowyer. Computing Dirichlet tesselations. Comp. /., 24 162-166, 1981. One of the first papers on the Delaunay triangulation in 3-space. 

Surface (3D) Reconstruction Surface reconstruction from point clouds is fundamental in many applications. Using the raw point clouds or volumetric data acquired from an unknown surface, an approximation of the surface can be constructed and used to compare it with CAD models or for smface-based automated programming. Reconstruction methods can be classified into two types the computational geometry approach focuses on the piecewise-linear interpolation of unorganised points and defines the surface as a carefiilly chosen sub-set of the Delaunay triangulation in a Cartesian coordinate system, and the computer graphics... 

Delaunay triangulation of source data point set is created. 

Figure 5. The Delaunay triangulation of a boreholes point set and 2 shapes of this set (shades of a gray color).

Piecewise linear interpolation based on Delaunay triangulation is used to get the surface over the selected shape. A buffer zone is used for 1-dimensional simplexes. 

As the parameter a varies from —oo to 0 and on to oo, the corresponding alpha complex goes from the empty set to the dual complex of the ball collection, and on to the Delaunay triangulation associated to the set of the centers... 

In this work, 2D finite element models of normal vessel and atherosclerotic vessels with 50% and 90% plaque deposition were developed using Comsol 3.5a. Boundary conditions were applied to the developed models and a distributed load was applied on the inner wall of the vessel. Further, the developed models were meshed using Delaunay triangulation method. The developed vessels were subjected to a transient analysis and the parameters such as total displacement, Von Mises stress and strain energy density were analyzed for normal and atherosclerotic vessels. 

An algorithm of Voronoi tessellation [16] and Delaunay triangulation [17] was used as basis for precise determination of all adjacent particle neighbors. 

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