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Quasitriangulation
A quasi-triangulation is a subdivision of a geometric object into simplices, where vertices are not points but arbitrary sloped line segments. This division is not a triangulation in the geometric sense. It is a topological triangulation, however. A quasi-triangulation may have some of the characteristics of a Delaunay triangulation In mathematics and computational geometry, a Delaunay triangulation (also known as a Delone triangulation) for a given set P of discrete points in a general position is a triangulation DT(P) such that no point in P is inside the circumcircle o .... References {{reflist Triangulation (geometry) ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Delaunay Triangulation
In mathematics and computational geometry, a Delaunay triangulation (also known as a Delone triangulation) for a given set P of discrete points in a general position is a triangulation DT(P) such that no point in P is inside the circumcircle of any triangle in DT(P). Delaunay triangulations maximize the minimum of all the angles of the triangles in the triangulation; they tend to avoid sliver triangles. The triangulation is named after Boris Delaunay for his work on this topic from 1934. For a set of points on the same line there is no Delaunay triangulation (the notion of triangulation is degenerate for this case). For four or more points on the same circle (e.g., the vertices of a rectangle) the Delaunay triangulation is not unique: each of the two possible triangulations that split the quadrangle into two triangles satisfies the "Delaunay condition", i.e., the requirement that the circumcircles of all triangles have empty interiors. By considering circumscribed spheres, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quasitriangulation
A quasi-triangulation is a subdivision of a geometric object into simplices, where vertices are not points but arbitrary sloped line segments. This division is not a triangulation in the geometric sense. It is a topological triangulation, however. A quasi-triangulation may have some of the characteristics of a Delaunay triangulation In mathematics and computational geometry, a Delaunay triangulation (also known as a Delone triangulation) for a given set P of discrete points in a general position is a triangulation DT(P) such that no point in P is inside the circumcircle o .... References {{reflist Triangulation (geometry) ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Triangulation (geometry)
In geometry, a triangulation is a subdivision of a planar object into triangles, and by extension the subdivision of a higher-dimension geometric object into simplices. Triangulations of a three-dimensional volume would involve subdividing it into tetrahedra packed together. In most instances, the triangles of a triangulation are required to meet edge-to-edge and vertex-to-vertex. Types Different types of triangulations may be defined, depending both on what geometric object is to be subdivided and on how the subdivision is determined. * A triangulation T of \mathbb^d is a subdivision of \mathbb^d into d-dimensional simplices such that any two simplices in T intersect in a common face (a simplex of any lower dimension) or not at all, and any bounded set in \mathbb^d intersects only finitely many simplices in T. That is, it is a locally finite simplicial complex that covers the entire space. * A point-set triangulation, i.e., a triangulation of a discrete set of points \mathcal\su ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Triangulation (topology)
In mathematics, triangulation describes the replacement of topological spaces by piecewise linear spaces, i.e. the choice of a homeomorphism in a suitable simplicial complex. Spaces being homeomorphic to a simplicial complex are called triangulable. Triangulation has various uses in different branches of mathematics, for instance in algebraic topology, in complex analysis or in modeling. Motivation On the one hand, it is sometimes useful to forget about superfluous information of topological spaces: The replacement of the original spaces with simplicial complexes may help to recognize crucial properties and to gain a better understanding of the considered object. On the other hand, simplicial complexes are objects of combinatorial character and therefore one can assign them quantities rising from their combinatorial pattern, for instance, the Euler characteristic. Triangulation allows now to assign such quantities to topological spaces. Investigations concerning the exist ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
