## Documentation Center |

Delaunay triangulation

`TRI = delaunay(X,Y)TRI = delaunay(X,Y,Z)TRI = delaunay(X)`

`delaunay` creates a Delaunay triangulation
of a set of points in 2-D or 3-D space. A 2-D Delaunay triangulation
ensures that the circumcircle associated with each triangle contains
no other point in its interior. This definition extends naturally
to higher dimensions.

`TRI = delaunay(X,Y)` creates
a 2-D Delaunay triangulation of the points (`X`,`Y`),
where `X` and `Y` are column-vectors. `TRI` is
a matrix representing the set of triangles that make up the triangulation.
The matrix is of size `mtri`-by-3, where `mtri` is
the number of triangles. Each row of `TRI` specifies
a triangle defined by indices with respect to the points.

`TRI = delaunay(X,Y,Z)` creates
a 3-D Delaunay triangulation of the points (`X`,`Y`,`Z`),
where `X`, `Y`, and `Z` are
column-vectors. `TRI` is a matrix representing the
set of tetrahedra that make up the triangulation. The matrix is of
size `mtri`-by-4, where `mtri` is
the number of tetrahedra. Each row of `TRI` specifies
a tetrahedron defined by indices with respect to the points.

`TRI = delaunay(X)` creates
a 2-D or 3-D Delaunay triangulation from the point coordinates `X`.
This variant supports the definition of points in matrix format. `X` is
of size `mpts`-by-`ndim`, where `mpts` is
the number of points and `ndim` is the dimension
of the space where the points reside, 2 ≦ `ndim` ≦
3. The output triangulation is equivalent to that of the dedicated
functions supporting the 2-input or 3-input calling syntax.

`delaunay` produces an isolated triangulation,
useful for applications like plotting surfaces via the `trisurf` function.
If you wish to query the triangulation; for example, to perform nearest
neighbor, point location, or topology queries, use `delaunayTriangulation` instead.

Use one of these functions to plot the output of `delaunay`:

Displays the triangles defined in the | |

Displays each triangle defined in the m-by-3 matrix TRI as a surface in 3-D space. To see a 2-D surface, you can supply a vector of some constant value for the third dimension. For example trisurf(TRI,x,y,zeros(size(x))) | |

Displays each triangle defined in the m-by-3 matrix TRI as a mesh in 3-D space. To see a 2-D surface, you can supply a vector of some constant value for the third dimension. For example, trimesh(TRI,x,y,zeros(size(x))) produces
almost the same result as | |

tetramesh | Plots a triangulation composed of tetrahedra. |

`delaunayTriangulation` | `plot` | `scatteredInterpolant` | `trimesh` | `triplot` | `trisurf`

Was this topic helpful?