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Let be a metric space with distance function .Let be a set of indices and let () be a tuple (indexed collection) of nonempty subsets (the sites) in the space .The Voronoi cell, or Voronoi region, , associated with the site is the set of all points in whose distance to is not greater than their distance to the other sites , where is any index different from .
A common type of lattice graph (known under different names, such as grid graph or square grid graph) is the graph whose vertices correspond to the points in the plane with integer coordinates, x-coordinates being in the range 1, ..., n, y-coordinates being in the range 1, ..., m, and two vertices being connected by an edge whenever the corresponding points are at distance 1.
Centroidal Voronoi tessellations are useful in data compression, optimal quadrature, optimal quantization, clustering, and optimal mesh generation. [3]A weighted centroidal Voronoi diagrams is a CVT in which each centroid is weighted according to a certain function.
Mesh is a measurement of particle size often used in determining the particle-size distribution of a granular material. For example, a sample from a truckload of peanuts may be placed atop a mesh with 5 mm openings. When the mesh is shaken, small broken pieces and dust pass through the mesh while whole peanuts are retained on the mesh.
Line-Surface Distance - Compute distance from a line to the mesh; Line-Surface Intersection - Compute intersection of line and the mesh; Cross Section - Compute the curves created by a cross-section of a plane through a mesh; Centroid - Compute the centroid, geometric center, of the mesh; Center-of-Mass - Compute the center of mass, balance ...
Typically, the domain to be meshed is specified as a coarse simplicial complex; for the mesh to be numerically stable, it must be refined, for instance by using Ruppert's algorithm. The increasing popularity of finite element method and boundary element method techniques increases the incentive to improve automatic meshing algorithms. However ...
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A metric space defined over a set of points in terms of distances in a graph defined over the set is called a graph metric. The vertex set (of an undirected graph) and the distance function form a metric space, if and only if the graph is connected. The eccentricity ϵ(v) of a vertex v is the greatest distance between v and any other vertex; in ...