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.
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 row of
T contains the vertex IDs
that define a triangle or tetrahedron. The vertex IDs are the row
numbers of the input points. The ID of a triangle or tetrahedron in the
triangulation is the corresponding row number in
Points, specified as a matrix whose columns are the
z-coordinates of the triangulation
points. The row numbers of
P are the vertex IDs in
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
ConnectivityList— Triangulation connectivity list
Triangulation connectivity list, represented as a matrix with the following characteristics:
Each element in
TR.ConnectivityList is a vertex
Each row represents a triangle or tetrahedron in the triangulation.
Each row number of
TR.ConnectivityList is a
triangle or tetrahedron ID.
|Convert coordinates from barycentric to Cartesian|
|Convert coordinates from Cartesian to barycentric|
|Circumcenter of triangle or tetrahedron|
|Triangles or tetrahedra attached to specified edge|
|Triangulation unit normal vectors|
|Handle sharp edges of triangulation|
|Free boundary facets|
|Incenter of triangulation elements|
|Test if two vertices are connected by an edge|
|Triangle or tetrahedron neighbors|
|Triangle or tetrahedron enclosing point|
|Size of triangulation connectivity list|
|Triangles or tetrahedra attached to 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 = 3×2 1.0000 6.5000 2.5000 5.0000 2.5000 8.0000