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# delaunay

Delaunay triangulation

 Note:   Qhull-specific options are no longer supported. Remove the OPTIONS argument from all instances in your code that pass it to delaunay.

## Syntax

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

## Definitions

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.

## Description

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.

## Visualization

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

 Displays the triangles defined in the m-by-3 matrix TRI. 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 triplot, except in 3-D space. tetramesh Plots a triangulation composed of tetrahedra.

## Examples

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### Plot Delaunay Triangulation

Plot the Delaunay triangulation of a large dataset.

```load seamount
tri = delaunay(x,y);
trisurf(tri,x,y,z);
```