Triangulation in 2-D or 3-D
Use 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 other features.
Triangulation connectivity list, specified as an m-by-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 T 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 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|
|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.
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: [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