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
or other software tools. When your data is represented using
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.
Triangulation connectivity list, specified as an
Points, specified as a matrix whose columns are the
x-coordinates vector, specified as a column vector containing the x-coordinates of the triangulation points.
y-coordinates vector, specified as a column vector containing the y-coordinates of the triangulation points.
z-coordinates vector, specified as a column vector containing the z-coordinates of the triangulation points.
Points in the triangulation, represented as a matrix containing the following information:
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|
|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|
|nearestNeighbor||Vertex closest to specified location|
|neighbors||Neighbors to specified triangle or tetrahedron|
|pointLocation||Triangle or tetrahedron containing specified point|
|size||Size of triangulation connectivity list|
|vertexAttachments||Triangles or tetrahedra attached to specified vertex|
|vertexNormal||Triangulation vertex normal|
Value. To learn how value classes affect copy operations, see Copying Objects in the MATLAB® documentation.
Define the points in the 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 triangles. This is the triangulation connectivity list.
T = [5 3 1; 3 2 1; 3 4 2; 4 6 2];
Create the triangulation representation.
TR = triangulation(T,P)
TR = triangulation with properties: Points: [6×2 double] ConnectivityList: [4×3 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 row number of the matrix,
this ID to refer a specific vertex in the triangulation.
A row number of the matrix,
Use this ID to refer a specific triangle or tetrahedron.