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TRI = delaunay(x,y)
Given a set of data points, the Delaunay triangulation is a set of lines connecting each point to its natural neighbors. The Delaunay triangulation is related to the Voronoi diagram — the circle circumscribed about a Delaunay triangle has its center at the vertex of a Voronoi polygon.

TRI = delaunay(x,y) for the data points defined by vectors x and y, returns a set of triangles such that no data points are contained in any triangle's circumscribed circle. Each row of the m-by-3 matrix TRI defines one such triangle and contains indices into x and y. If the original data points are collinear or x is empty, the triangles cannot be computed and delaunay returns an empty matrix.
TRI = delaunay(x,y,options) specifies a cell array of strings options that were previously used by Qhull. Qhull-specific options are no longer required and are currently ignored. Support for these options will be removed in a future release.
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 DelaunayTri instead.
delaunay uses CGAL, see http://www.cgal.org.
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. |
Plot the Delaunay triangulation of a large dataset:
load seamount tri = delaunay(x,y); trisurf(tri,x,y,z);

DelaunayTri, TriScatteredInterp, plot, triplot, trimesh, trisurf
![]() | DelaunayTri | delaunay3 | ![]() |

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