# Unstructured mesh generation

(Difference between revisions)
 Revision as of 22:42, 18 October 2006 (view source)Jasond (Talk | contribs) (Meshing reorganization)← Older edit Latest revision as of 22:32, 15 May 2007 (view source)Jasond (Talk | contribs) (One intermediate revision not shown) Line 1: Line 1: + {{Meshing table of contents}} [[Structured mesh generation|<< Structured Mesh Generation]] | '''Unstructured Mesh Generation''' | [[ Mesh adaptation|Mesh Adaptation>>]] [[Structured mesh generation|<< Structured Mesh Generation]] | '''Unstructured Mesh Generation''' | [[ Mesh adaptation|Mesh Adaptation>>]] Line 4: Line 5: ==Delaunay Methods== ==Delaunay Methods== - Many of the commonly used unstructured mesh generation techniques are based upon the properties of the [http://en.wikipedia.org/wiki/Delaunay_triangulation Delaunay triangulation] and its dual, the [http://en.wikipedia.org/wiki/Voronoi_diagram  Voronoi diagram].  Given a set of points in a plane, a Delaunay triangulation of these points is the set of triangles such that no point is inside the circumcircle of a triangle.  The triangulation is unique if no three points are on the same line and no four points are on the same circle.  A similar definition holds for higher dimension, with tetrahedra replacing triangles in 3D. + Many of the commonly used unstructured mesh generation techniques are based upon the properties of the [http://en.wikipedia.org/wiki/Delaunay_triangulation Delaunay triangulation] and its dual, the [http://en.wikipedia.org/wiki/Voronoi_diagram  Voronoi diagram].  Given a set of points in a plane, a Delaunay triangulation of these points is the set of triangles such that no point is inside the circumcircle of a triangle.  The triangulation is unique if no three points are on the same line and no four points are on the same circle.  A similar definition holds for higher dimensions, with tetrahedra replacing triangles in 3D. ==Quadtree/Octree Methods== ==Quadtree/Octree Methods==

## Latest revision as of 22:32, 15 May 2007

 Introduction Mesh classification Structured mesh generation Unstructured mesh generation Special topics

<< Structured Mesh Generation | Unstructured Mesh Generation | Mesh Adaptation>>

It is difficult make general statements about unstructured mesh generation algorithms because the most prominent methods are very different in nature. The most popular family of algorithms are those based upon Delaunay triangulation, but other methods, such as quadtree/octree approaches are also used.

## Delaunay Methods

Many of the commonly used unstructured mesh generation techniques are based upon the properties of the Delaunay triangulation and its dual, the Voronoi diagram. Given a set of points in a plane, a Delaunay triangulation of these points is the set of triangles such that no point is inside the circumcircle of a triangle. The triangulation is unique if no three points are on the same line and no four points are on the same circle. A similar definition holds for higher dimensions, with tetrahedra replacing triangles in 3D.