Output of delaunay function

My question is two part:

tri=delaunay(M(:,1),M(:,2));

trisurf(tri,M(:,1),M(:,2),M(:,3))

Q.1 How do I interpret the matrix tri?( i want to know how the numbering of the vertices are done.)

Q.2 How do I delete certain triangles after the applying the function delaunay? ( I am not concerned about losing the property of delaunay triangulation. )

Thank You

P.S: I am new to MATLAB and excuse me if the questions I asked are silly.

Answer 1

[Kenneth Eaton]

As per the function documentation, the matrix tri returned from DELAUNAY will be an N-by-3 matrix where N is the number of triangles created. Therefore, each row of tri represents one triangle. The three values for each row represent indices into the set of x and y vertices, which are M(:,1) and M(:,2), respectively, in your example.

For example, consider the case where the first row of tri is [1 2 4]. This defines a triangle whose 3 vertices are at coordinates ( M(1,1), M(1,2)), ( M(2,1), M(2,2)), and ( M(4,1), M(4,2)).

If you want to remove a triangle from tri, all you have to do is remove the given row. For example, if you want to remove the second triangle, you could do this:

tri(2,:) = [];

[David Jenkins]

I'm having a similar problem.

Your explanation seems logical however when I enter the example given on the MATLAB help page:

[x,y]=meshgrid(1:15,1:15);

tri = delaunay(x,y);

z = peaks(15);

trimesh(tri,x,y,z)

My values of tri however don't seem to correspond to indices of x and y. x and y are 15x15 arrays however the first few lines of tri are:

[40 25 24; 18 4 3; 9 24 25]

How can I be getting values >15 if they are supposed to reference indices of a 15x15 array

[Kenneth Eaton]

@David: What happens is that the 15-by-15 arrays in x and y are reshaped into 225-by-1 column vectors within DELAUNAY, so the indices in tri represent linear indices into the original matrices.