# Unstructured mesh generation

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==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 | + | 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== |

## Revision as of 17:06, 23 October 2006

<< 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.

## Quadtree/Octree Methods

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