delaunaytriangulation function: How to associate triangles with edges?

Hi, I'm trying to perform finite volume method (CFD) calculations based on Matlab's built in "delaunaytriangulation" function. The function lists each triangle as a set of vertices or points. Similarly, the function lists each edge/face a set of vertices or points.

But I need each triangle information as a set of faces/edges to be able to loop over all edges for flux.

I get from dt.ConnectivityList command:

dt.ConnectivityList output

Point id_1 Point id_2 Point id_3 (Triangle no 1)

Point id_4 Point id_5 Point id_6 (Triangle no 2)

.... (And so on)

dt.Edge output

Point id_1 Point id_2 (Edge no 1)

POint id_3 Point id_4 (Edge no 2)

... (And so on)

What I need

Edge id_1 Edge id_2 Edge id_3 (Triangle no 1)

Edge id_4 Edge id_5 Edge id_6 (Triangle no 2)

.... (And so on)

Thank you very much.

Answer 1

[KSSV]

DelaunayTriangulation supports lot of functions....check this documentation for the functions it supports. I think edges should work for you.

https://in.mathworks.com/help/matlab/ref/delaunaytriangulation.html

[KSSV]

Burak Pehlivan commented: Hi, edges command gives the vertex (id) sets of edges. I want the edge (id) sets of triangles.

Answer 2

[Precise Simulation]

With the gridedge function included with the Matlab FEA Toolbox you can reconstruct and recover the grid edge numbering like this:

   p = rand(10,2);
   t = delaunay(p);

   [e,ev] = gridedge(t',2);
   help gridedge, e'

where e contains the edge numbering for each cell, and ev the vertices for each edge. Alternativley, the following code snippet should work with a different edge numbering:

   p = rand(10,2);
   t = delaunay(p);
                       
   e = []; e2c = [];
   for i=1:3
     e = [e; t(:,[i mod(i,3)+1])];
     e2c = [e2c; [i*ones(size(t,1),1) [1:size(t,1)]']];
   end
   [~,~,ei] = unique(sort(e,2),'rows');
   e = zeros(3,size(t,1));
   e(e2c(:,1)+3*(e2c(:,2)-1)) = ei;
   e'

Similarly, the gridface function can be used to reconstruct grid cell faces from 3D triangulations.

[Burak Pehlivan]

Hi, Can you explain the code snippet a bit? Does it return a set of point ids, or a set of edge ids?

[Burak Pehlivan]

I need the set of edge ids.

[Precise Simulation]

e contains the edge ids like you were asking (3 edges per triangle x n_triangles), ev contains the points ids for each edge (2 points per edge x n_edges).

[Burak Pehlivan]

Hi, As far as I understand, since delaunay returns the set of point ids, e also contains the set of point ids.

[Precise Simulation]

The last lines reindexes e to give edge numbers. Try it on a small grid to see.