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Triangulation in 2D or 3D
Use triangulation to create an inmemory representation of any 2D or 3D triangulation data that is in matrix format, such as the matrix output from the delaunay function or other software tools. When your data is represented using triangulation, you can perform topological and geometric queries, which you can use to develop geometric algorithms. For example, you can find the triangles or tetrahedra attached to a vertex, those that share an edge, their circumcenters, and other features.
TR = triangulation(T,P) creates a 2D or 3D triangulation representation using the triangulation connectivity list, T, and the points in matrix P.
TR = triangulation(T,x,y) creates a 2D triangulation representation with the point coordinates specified as column vectors, x and y.
TR = triangulation(T,x,y,z) creates a 3D triangulation representation with the point coordinates specified as column vectors, x, y, and z.
T 
Triangulation connectivity list, specified as an mbyn matrix, where m is the number of triangles or tetrahedra, and n is the number of vertices per triangle or tetrahedron. Each element in T is a Vertex ID. Each row of T contains the vertex IDs that define a triangle or tetrahedron. 
P 
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. 
Points 
Points in the triangulation, represented as a matrix containing the following information:

ConnectivityList 
Triangulation connectivity list, represented as a matrix. This matrix contains the following information:

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 
A row number of the matrix, TR.Points. Use this ID to refer a specific vertex in the triangulation.
A row number of the matrix, TR.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.