delaunay 四面体网格生成程序


delaunay 四面体网格生成程序,c++语言版。用于有限元的四面体网格的生成生成,网格,有限元,四面体网格,网格生成,适用于,应用于,有限元网格,四面体,面体网格。

这里为组成的四面体的体积,类似于三角形也可以用笛卡尔坐标的一个行列式表示出来。 3维重心坐标和2维一样,可以确定一点是否位于四面体内部,也能对四面体网格上函数插值。因为利用重心坐标可以极大地简化3维插值,四面体网格经常用于有限元分析。尤其是Delaunay三角剖分,由于其独特性,关于点集的很多种几何图都和Delaunay三角剖分相关,如Voronoi图,EMST树,Gabriel图等。

Delaunay tetrahedral mesh generation program

Delaunay tetrahedral mesh generation program.

In mathematics and computational geometry, a Delaunay triangulation for a set P of points in a plane 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 angle of all the angles of the triangles in the triangulation; they tend to avoid skinny 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, the notion of Delaunay triangulation extends to three and higher dimensions. Generalizations are possible to metrics other than Euclidean. However in these cases a Delaunay triangulation is not guaranteed to exist or be unique.

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