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Use the delaunayTriangulation class to create a 2D or 3D triangulation from a set of points. When your points are in 2D, you can specify edge constraints .
You can perform a variety of topological and geometric queries on a delaunayTriangulation, including any triangulation query. For example, locate a facet that contains a specific point, find the vertices of the convex hull, or compute the Voronoi Diagram.
DT = delaunayTriangulation(P) creates a Delaunay triangulation from the points in P. Matrix P has 2 or 3 columns, depending on whether your points are in 2D or 3D space.
DT = delaunayTriangulation(P,C) specifies the edge constraints in matrix C. In this case, P specifies points in 2D. Each row of C defines the start and end vertex IDs of a constrained edge.
DT = delaunayTriangulation(x,y) creates a 2D Delaunay triangulation from the point coordinates in the column vectors, x and y.
DT = delaunayTriangulation(x,y,C) specifies the edge constraints in matrix C.
DT = delaunayTriangulation(x,y,z) creates a 3D Delaunay triangulation from the point coordinates in the column vectors, x, y, and z.
DT = delaunayTriangulation() creates an empty Delaunay triangulation.
P 
Input points, specified as a matrix whose columns are the x, y, (and possibly z) coordinates of the triangulation points. The row numbers of P are the vertex IDs in the triangulation. 
x 
xcoordinates vector, specified as a column vector containing the xcoordinates of the triangulation points. 
y 
ycoordinates vector, specified as a column vector containing the ycoordinates of the triangulation points. 
z 
zcoordinates vector, specified as a column vector containing the zcoordinates of the triangulation points. 
C 
Vertex IDs of constrained edges, specified as a 2column matrix. Each row of C corresponds to a constrained edge and contains two IDs:
You can specify edge constraints for 2D triangulations only. 
ConnectivityList 
Triangulation connectivity list, represented as a matrix. This matrix contains the following information:

convexHull  Convex hull 
isInterior  Test if triangle is in interior of 2D constrained Delaunay triangulation 
nearestNeighbor  Vertex closest to specified location 
pointLocation  Triangle or tetrahedron containing specified location 
voronoiDiagram  Voronoi diagram 
barycentricToCartesian  Converts point coordinates from barycentric to Cartesian 
cartesianToBarycentric  Converts point coordinates from Cartesian to barycentric 
circumcenter  Circumcenter of triangle or tetrahedron 
edgeAttachments  Triangles or tetrahedra attached to specified edge 
edges  Triangulation edges 
faceNormal  Triangulation face normal 
featureEdges  Triangulation sharp edges 
freeBoundary  Triangulation facets referenced by only one triangle or tetrahedron 
incenter  Incenter of triangle or tetrahedron 
isConnected  Test if two vertices are connected by edge 
neighbors  Neighbors to specified triangle or tetrahedron 
size  Size of triangulation connectivity list 
vertexAttachments  Triangles or tetrahedra attached to specified vertex 
vertexNormal  Triangulation vertex normal 
In a 2D Delaunay triangulation, the circumcircle associated with each triangle does not contain any points in its interior. Similarly, a 3D Delaunay triangulation does not have any points in the interior of the circumsphere associated with each tetrahedron. This definition extends to ND, although delaunayTriangulation supports only 2D and 3D.
A row number of the matrix, DT.Points. Use this ID to refer a specific vertex in the triangulation.
A row number of the matrix, DT.ConnectivityList. Use this ID to refer a specific triangle or tetrahedron.
Value. To learn how value classes affect copy operations, see Copying Objects in the MATLAB^{®} documentation.