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Domain-Modeling Techniques
Published in Alexandru Telea, Data Visualization, 2014
Another surface reconstruction method for unoriented point sets is provided by alpha shapes [Edelsbrunner et al. 83]. The intuition behind alpha shapes can be best described by Edelsbrunner’s carving analogy: Assume that the 2D or 3D space containing our point set P is filled up with ice cream, and we have a spherical spoon of radius α, we first carve out all ice cream we can without removing, or touching, any point. The resulting shape will have a boundary composed of spherical pieces (in 3D) or circle arcs (in 2D). The alpha shape corresponding to P is obtained by straightening out these curved parts into line segments (in 2D), respectively triangles (in 3D).
Modeling of capillary fluid flow in concrete using a DEM-CFD approach
Published in Günther Meschke, Bernhard Pichler, Jan G. Rots, Computational Modelling of Concrete and Concrete Structures, 2022
M. Krzaczek, M. Nitka, J. Tejchman
This algorithm is repeated for each VP in VPN using an explicit formulation. The discretization algorithm is based on the alpha-shape theory and the Delaunay triangulation. The grid remeshing is automatically performed when the topological properties of the grid geometry change (Krzaczek et al. 2020). The computational results (e.g. pressures) are accurately transformed from the old grid to the new one by assuming that the mass is a topological invariant. The coupling scheme of DEM with CFD is described in detail in (Krzaczek et al. 2020).
Evaluating spatial accessibility to healthcare services from the lens of emergency hospital visits based on floating car data
Published in International Journal of Digital Earth, 2022
Wei Jiao, Wei Huang, Hongchao Fan
In order to solve these problems, the alpha-shape algorithm have been developed to extract the data boundary from a set of unordered points (Figure 8(a)) (Asaeedi, Didehvar, and Mohades 2013). The algorithm has a simple structure and only needs one parameter, namely the radius α of a circle. The principle of obtaining a reasonable contour of the point set is briefly described as follows. For point set S, in order to obtain its reasonable contour, the algorithm adaptively selects a parameter α to represent the radius of a circle. Next, any two points in S are traversed to distinguish whether they are in boundary or not. If the selected two points can form a circle with radius α and the circle contains no other points, the two points are considered to be a part of contour. Obtain points on all edges of S in turn, until they form a closed loop, then the algorithm ends. This method can effectively avoid the space expansion problem of the data boundary (Mu and Liu 2011; Jiao, Fan, and Wang 2020).
Surface detection and modeling of an arbitrary point cloud from 3D sketching
Published in Computer-Aided Design and Applications, 2018
Ariel Schwartz, Ronit Schneor, Gila Molcho, Miri Weiss Cohen
The concept of alpha shapes developed by Edelsbrunner and Mucke [5] formalizes the intuitive notion of “shape” for spatial point sets. The alpha shape is a mathematically well-defined generalization of the convex hull and is a subgraph of the Delaunay triangulation [4,9]. It is defined intuitively as: α-shapes are a generalization of the convex hull of a point set. Let S be a finite set in and α a real number with . For α= x, the α-shape is identical to the convex hull of S. However, as α decreases, the α-shape shrinks to cavities.