Delaunay() function MATLAB Purpose

Question

I want to generate triangle meshes in MATLAB with the delaunay function in 2-D. So I declare the X- and Y- values and set tri=delaunay(X,Y). Then I use triplot to plot it. However, what does tri give me? Does it give each of my triangle a special designation number? After reading through some of the MATLAB tutorials I still DON'T understand it.

Answer 1

The delaunay function returns tri as an Mx3 matrix of triangle connectivity, where each of the M triangles is represented as an integer triplet that indexes into the X,Y vertex position arrays.

It's probably easier with a simple example:

%% a simple square box
X = [0.0; 1.0; 1.0; 0.0];
Y = [0.0; 0.0; 1.0; 1.0];

%% an example output from delaunay()
tri = [1,2,3  %% 1st triangle connects vertices 1,2,3
       1,3,4  %% 2nd triangle connects vertices 1,3,4
      ];

The triangles are just numbered linearly - tri(1,:) is the first triangle, tri(n,:) is the nth triangle etc. If you wanted to re-order the list of traingles you could permute the array, but the indexing would always have to be linear - if there are M triangles the indexing must encompass 1:M.

Hope this helps.