منابع مشابه
Stabbing Delaunay Tetrahedralizations
A Delaunay tetrahedralization of n vertices is exhibited for which a straight line can pass through the interiors of Θ(n) tetrahedra. This solves an open problem of Nina Amenta, who asked whether a line can stab more than O(n) tetrahedra. The construction generalizes to higher dimensions: in d dimensions, a line can stab the interiors of Θ(ndd/2e) Delaunay d-simplices. The relationship between ...
متن کاملDelaunay Tetrahedralizations: Honor Degenerated Cases
The definition of a Delaunay tetrahedralization (DT) of a set S of points is well known: a DT is a tetrahedralization of S in which every simplex (tetrahedron, triangle, or edge) is Delaunay. A simplex is Delaunay if all of its vertices can be connected by a circumsphere that encloses no other vertex. An important remark made in virtually all papers on this topic is that “although any number of...
متن کاملOn Refinement of Constrained Delaunay Tetrahedralizations
This paper discusses the problem of refining constrained Delaunay tetrahedralizations (CDTs) into good quality meshes suitable for adaptive numerical simulations. A practical algorithm which extends the basic Delaunay refinement scheme is proposed. It generates an isotropic mesh corresponding to a sizing function which can be either user-specified or automatically derived from the geometric dat...
متن کاملKinetic and dynamic Delaunay tetrahedralizations in three dimensions
We describe the implementation of algorithms to construct and maintain threedimensional dynamic Delaunay triangulations with kinetic vertices using a threesimplex data structure. The code is capable of constructing the geometric dual, the Voronoi or Dirichlet tessellation. Initially, a given list of points is triangulated. Time evolution of the triangulation is not only governed by kinetic vert...
متن کاملDynamic Delaunay tetrahedralizations and Voronoi tessellations in three dimensions
We describe the implementation of an incremental insertion algorithm to construct and maintain three-dimensional Delaunay triangulations with dynamic vertices using a three-simplex data structure. The code is capable of constructing the geometric dual, the Voronoi or Dirichlet tesselation. A given list of generators is triangulated and volumes as well as contact surfaces of the Dirichlet region...
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ژورنال
عنوان ژورنال: Discrete & Computational Geometry
سال: 2004
ISSN: 0179-5376,1432-0444
DOI: 10.1007/s00454-004-1095-5