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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.
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 ...
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.
In this work a statistical method based on the distance distribution is used to deal with outliers, occlusion, appearance, and disappearance, which enables subset-subset matching. There exist many ICP variants, [ 6 ] from which point-to-point and point-to-plane are the most popular.
MeshLab an open source mesh processing tool that is able to accurately simplify 3D polygonal meshes. Polygon Cruncher a commercial software from Mootools that reduces the number of polygons of objects without changing their appearance. Simplygon a commercial mesh processing package for remeshing general input meshes into real-time renderable ...
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On triangular mesh surfaces, the problem of computing this mapping is called mesh parameterization. The parameter domain is the surface that the mesh is mapped onto. Parameterization was mainly used for mapping textures to surfaces. Recently, it has become a powerful tool for many applications in mesh processing.