# DelaunayTri

(Not recommended) Delaunay triangulation in 2-D and 3-D

`DelaunayTri`

is not recommended. Use `delaunayTriangulation`

instead.

## Description

`DelaunayTri`

creates a Delaunay triangulation object from a
set of points. You can incrementally modify the triangulation by adding or removing points. In
2-D triangulations you can impose edge constraints. You can perform topological and geometric
queries, and compute the Voronoi diagram and convex hull.

## Creation

### Syntax

### Description

creates an empty Delaunay
triangulation.`DT`

= DelaunayTri

,
`DT`

= DelaunayTri(`X`

)

and
`DT`

= DelaunayTri(`x`

,`y`

)

create a Delaunay triangulation from a set of points. The points can be specified as an
`DT`

= DelaunayTri(`x`

,`y`

,`z`

)`mpts`

-by-`ndim`

matrix `X`

, where
`mpts`

is the number of points and `ndim`

is the
dimension of the space where the points reside (`ndim`

is 2 or 3).
Alternatively, the points can be specified as column vectors `(x,y)`

or
`(x,y,z)`

for 2-D and 3-D input.

creates a constrained Delaunay triangulation. This feature is only supported for 2-D
triangulations.`DT`

= DelaunayTri(___,`C`

)

### Input Arguments

## Properties

## Object Functions

In addition to the below object functions, `DelaunayTri`

objects support indexing into the triangulation using parentheses `()`

. The
syntax is the same as for arrays.

`baryToCart` | (Not recommended) Convert point coordinates from barycentric to Cartesian |

`cartToBary` | (Not recommended) Convert point coordinates from Cartesian to barycentric |

`circumcenters` | (Not recommended) Circumcenters of specified simplices |

`convexHull` | (Not recommended) Convex hull of Delaunay triangulation |

`edgeAttachments` | (Not recommended) Triangles or tetrahedra attached to specified edge |

`edges` | (Not recommended) Triangulation edges |

`faceNormals` | (Not recommended) Unit normals to specified triangles |

`featureEdges` | (Not recommended) Sharp edges of surface triangulation |

`freeBoundary` | (Not recommended) Free boundary facets |

`incenters` | (Not recommended) Incenters of specified simplices |

`inOutStatus` | (Not recommended) Status of triangles in 2-D constrained Delaunay triangulation |

`isEdge` | (Not recommended) Test if vertices are joined by edge |

`nearestNeighbor` | (Not recommended) Vertex closest to specified point |

`neighbors` | (Not recommended) Triangle or tetrahedron neighbors |

`pointLocation` | (Not recommended) Triangle or tetrahedron enclosing point |

`size` | (Not recommended) Size of triangulation matrix |

`vertexAttachments` | (Not recommended) Triangles or tetrahedra attached to vertex |

`voronoiDiagram` | (Not recommended) Voronoi diagram of Delaunay triangulation |

## Examples

## More About

## Tips

`DelaunayTri`

can produce incorrect or inconsistent results when boundary constraints intersect or overlap. To avoid this behavior, use constraints that form one or multiple closed boundaries that do not intersect or overlap.

## Version History

**Introduced in R2009a**

## See Also

`triangulation`

| `delaunayTriangulation`

| `scatteredInterpolant`