Triangulation in 2-D or 3-D
triangulation to create an in-memory
representation of any 2-D or 3-D 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
To create a
triangulation object, use the
triangulation function with input arguments that define the
triangulation's points and connectivity.
TR = triangulation(T,P)
TR = triangulation(T,x,y)
TR = triangulation(T,x,y,z)
T— Triangulation connectivity list
Triangulation connectivity list, specified as an
n 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
contains the vertex IDs that define a triangle or tetrahedron.
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-coordinates of triangulation points, specified as a column vector.
y-coordinates of triangulation points, specified as a column vector.
z-coordinates of triangulation points, specified as a column vector.
Points— Triangulation points
Triangulation points, represented as a matrix with the following characteristics:
Each row in
TR.Points contains the coordinates
of a vertex.
Each row number of
TR.Points is a vertex ID.
ConnectivityList— Triangulation connectivity list
|Convert point coordinates from barycentric to Cartesian|
|Convert point coordinates from Cartesian to barycentric|
|Circumcenter of triangle or tetrahedron|
|Triangles or tetrahedra attached to specified edge|
|Triangulation face normal|
|Triangulation sharp edges|
|Query free boundary facets|
|Incenter of triangle or tetrahedron|
|Test if two vertices are connected by edge|
|Vertex closest to specified location|
|Neighbors to specified triangle or tetrahedron|
|Triangle or tetrahedron containing specified point|
|Size of triangulation connectivity list|
|Triangles or tetrahedra attached to specified vertex|
|Triangulation vertex normal|
Define and plot the points in a 2-D triangulation.
P = [ 2.5 8.0 6.5 8.0 2.5 5.0 6.5 5.0 1.0 6.5 8.0 6.5];
Define the triangulation connectivity list.
T = [5 3 1; 3 2 1; 3 4 2; 4 6 2];
Create and plot the triangulation representation.
TR = triangulation(T,P)
TR = triangulation with properties: Points: [6x2 double] ConnectivityList: [4x3 double]
Examine the coordinates of the vertices of the first triangle.
ans = 1.0000 6.5000 2.5000 5.0000 2.5000 8.0000
A triangle or tetrahedron ID is a row number of the matrix
this ID to refer a specific vertex in the triangulation.
A vertex ID is a row number of the matrix
TR.ConnectivityList. Use this ID
to refer a specific triangle or tetrahedron.